Wave-notes Wavelength The distance to where the wave repeats, (crest to crest or trough to trough). l meters (m) Amplitude The height of a wave measured from the center of the undisturbed material to the highest or lowest point of the wave (crest or trough). A meters (m) Crest The high point of a wave. Trough The low point of a wave Frequency The number of to and fro vibrations in a given time. For waves: The number of waves that pass in a given interval of time. f 1/s or Hertz (Hz) Period The time for a particular motion to repeat. For waves: The time for one complete wave to pass. T Wave speed The distance a wave travels divided by the time the wave travels. v Frequency and period are reciprocals of each other. f = 1/T or T = 1/f Period: The time for one complete wave to pass. symbol: T units: seconds (s) Frequency: The number of waves produced per unit of time. symbol: f units: 1/seconds or (Hz), (1/s) Frequency and period are reciprocals of each other. f = 1/T and T = 1/f Same equation just rearranged.

Wavelength: The distance from crest to crest. symbol: l units: meters (m) Wave speed: How fast a wave travels. The distance the wave travels divided by the time the wave travels. symbol: v units: meters/second (m/s) v = f*l Check the difference between wave speed and frequency! Types of Waves There are two types of waves that we will consider in this course, transverse and longitudinal. Transverse waves have the material that makes up the wave move at right angles to the direction of travel of the wave. Examples would be a guitar string or phone cord vibrating, or the crowd wave in a stadium (people stand then sit back down). Notice in the diagram below how the particle move up and down as the wave moves to the right. Longitudinal waves are those which move the particles that make up the wave parallel to the direction of travel of the wave. Examples would be sound waves and water waves under the surface. In the diagram below, you can see how the particles move right and left as the wave moves to the right (particles move parallel to wave travel direction): Click here to see the differences between these two waves - along with examples of standing waves for each type.

Water waves are a bit complicated, but generally the waves at the surface are thought of as transverse and the waves deeper down are longitudinal. They actaully are a combination of the two as particles move in ellipses. The deeper you go, the more longitudinal they become. Check out the diagram below: The Doppler Effect The Doppler Effect was first described by Christian Doppler (1803 - 1853) of Austria. The motion of a source of a wave or the motion of the receiver of the wave can affect the frequency of the wave. The best definition is as follows. The Doppler Effect is the apparent change in frequency of a wave due to the relative motion of the source or the receiver of the wave. All types of waves, sound, light, water, can exhibit the Doppler Effect. Example: A motorcycle moving toward you, the pitch is increased compared to when it is moving away from you. Why? The speed of a wave in a material is constant. As you can see in this example, a source of waves which is stationary emits circular wavefronts in all directions. An observer to the right and left would observe the same wavelength and frequency.

If the source moves to the right, you see the following: As the source or receiver moves toward each other the waves in front appear to squish together. A shorter wavelength means a higher frequency (bigger number). The product of wavelength and the wave frequency must equal the wave speed at all times. As the source or receiver move away from each other the opposite happens. The wavelength is longer which means the frequency must be lower (smaller number) in order for the wave speed to remain the same. In the picture above, you can see an observer to the right would observe a shorter wavelength, higher frequency. An observer to the left of this source would observe a longer wavelength, lower frequency. Applications of the Doppler Effect 1. Police use the Doppler Effect with radar waves to measure the speeds of cars. The radar compares the difference in the frequencies of the wave leaving the gun and the wave after reflecting off the speeding car. Yes, they can catch you coming or going. The radars do not work as well when shot at an angle to the car. They work best head on or going directly away. 2. Doppler Shift of Visible Light A light source moving away from us would have a lower frequency (Red shift).

A light source (such a galaxy) moving toward us would have a higher frequency (Blue shift). Astronomers have observed that all galaxies are moving away from the earth and have a slight red shift in the light coming to us. (Cool!) 3. Bow waves, shock waves and sonic booms If you have ever been in a boat, you have experienced the Doppler Effect with water. When you are traveling at a very slow speed in water the waves in front of the boat bunch together. As the boat moves faster the front begins to ride up on the constructive interference of the crests as they pile up on each other. When the speed of the boat equals the speed of the waves, there will be a very large amplitude wave built up in front of the boat called a WAVE BARRIER. see the diagram below: When the boat travels faster than the waves can move, a wake is created behind the boat. This is called a BOW WAVE. The wake is a line of constructive interference making a large amplitude wave in the shape of a V behind the boat. Check it out below: Planes do the same thing in air when they fly faster than the speed of sound.

The 3-dimensional cone shaped wake behind the plane has a special name. It is called a SHOCK WAVE. The shock wave is produced in the same manner as a wake. The air molecules squish together such that a region of high pressure is produced. Instead of two dimensions as with the boat the plane has a three dimensional wake (shock wave). When this compressed air passes by your ear it causes your eardrum to move violently inward. This violent motion is registered as a BOOM by your brain. Hence, the name sonic boom. There are actually two shock waves around planes, one at the leading edge and one at the trailing edge of the plane. Here is an F4 Phantom 30 feet off the runway going slightly faster than the speed of sound. Notice the two shock waves (one up front behind cockpit and one off the wings) in the cone shape. These "clouds" are formed as the compressed air, which is just ahead of the cloud, returns to lower pressure condensing the water vapor onto particles in the air. This is why clouds form behind the wings of normal commercial jets as well. They are called con-trails (for condensation trails).

If you have ever seen someone crack a whip you have experienced a shock wave in air. The tip of the whip is actually traveling faster that the speed of sound (about 700 mph). Neat. See the Doppler Effect in Action! To see this Doppler Effect in action, click here. It will open an applet in a separate window. You'll do an activity where you can change the speed of the moving object from slower than the wave speed to faster (so you can see the plane going faster than the speed of sound, etc.). You can also change the speed of the wave. This only demonstrates a moving wave source. This is a great visual of the Doppler Effect - check it out! Interference of Waves 1. The bending of waves through an opening is known as __diffraction_. 2. The two types of waves are _longitudinal_ and _transverse_. 3. How do the particles in a particular medium move when a longitudinal wave passes through the medium? the particles in the medium vibrate parallel to the direction of motion of the wave. 4. How do the particles in a particular medium move when a transverse wave passes through the medium?

the particles in the medium vibrate perpendicular to the direction of motion of the wave. 5. Sound is an example of a _longitudinal_ wave. 6. Although they are not true examples of this type of wave, the waves on the surface of water approximate _transverse_ waves. 7. The distance between two successive wave crests (or troughs) is called the _wavelength_ of the wave. 8. The height of a wave crest (or depth of trough) above the original undisturbed surface is called the _amplitude_ of the wave. 9. The number of waves that pass by a fixed point each second is defined as the _frequency_ of the wave and has units of _hertz_. 10. The symbol for wavelength is __l__ and __f_ for frequency. 11. The time between two successive wave crests is called the _period_ of the wave. 12. When two or more waves meet at the same point, they add or subtract to form a new wave. This is known as the _principle of superposition_. (more than one word) 13. When two wave crests meet, they form a larger wave.

This is an example of _constructive_ interference. 14. When a wave crest meets a wave trough, the resulting wave is a smaller wave. This is an example of __destructive__ interference. 15. The following picture shows two wave pulses on a string traveling toward each other at a constant speed. a. In the space below draw the resulting disturbance of the string when the two waves are on top of each other. a straight line should be drawn b. In the space below draw the resulting disturbance of the string after the two waves have passed each other. 16. Please label the following parts of the wave below. Wavelength, Crest, Trough, Amplitude 1. _wavelength_ 2. _amplitude_ 3. _crest_ 4. _trough_ 17. What is the diffraction of waves? The bending of waves as they move through an opening or around an obstacle. The amount of diffraction is greatest when the opening or obstacle is much smaller that the wavelength. 18. Parallel water wave fronts are coming in towards two narrow openings (there is a wall between them on the other side so the waves can't interfere on the backside).

In the diagram below, draw in the diffracted waves behind (to the right of) each opening to demonstrate the difference between the diffraction of the waves due to each opening. 19. Draw in the reflected wave fronts for the circular waves that are heading away from the focus of the reflector and towards the curved reflective surface below. Learner Goal 2 Please answer all questions in the space provided. Make sure that you show your work and include formulas and units. Please use the proper set up too. v=l·f v=l/T T=1/f 1. A water wave has a frequency of 2 Hz. and a wavelength of 0.5 meters. What is the wave speed of the water (in m/s)? Given: f = 2 Hz l = 0.5 m Want: v Eqn: v = l·f Solve: v = (2 Hz)(0.5m) = 1.0 m/s 2. A light wave is traveling at 300,000,000 meters/second. If the wavelength of the light wave is 0.0000005 meters, what is the frequency of the light wave (in Hz)?

Given: v = 3.0 x 10^8m/s l = 5.0 x 10^-7m Want: f Solve: f = (3.0 x 10^8m/s)/(5.0 x 10^-7m) f = 6.0 x 10^14 Hz 3. What is the period of the light wave in #2 above (in seconds)? Given: f = 1.5 x 10^14 Hz Eqn: T = 1/f Solve: T = 1/6.0 x 10^14 Hz T = 1.67 x 10^-15s 4. A middle C note (a sound wave) has a frequency of 256 Hz. If the speed of sound is 340 meters/sec., what is the wavelength of the middle C sound wave (in meters)? Given: v = 340 m/s f = 256 Hz Want: l Solve: l = (340 m/s)/(256 Hz) l= 1.33 m 5.

One of the FM radio stations listened to in our area is 94.5 FM. This means that the frequency of the radio waves is 94.5 million Hz or megahertz (MHz). If the radio waves travel at 300,000,000 meters/second, what is the wavelength of the radio wave (in meters)? Given: v = 3.0 x 10^8m/s f = 9.45 x 10^7Hz Want: l Solve: l= (3.0 x 10^8m/s)/(9.45 x 10^7Hz) l = 3.17 m Learner Goal 3 1. Draw pictures of bow waves for a boat traveling on water below the wave speed, at the wave speed and faster than the wave speed of the water. Pictures for this section can be found in your text book on pages 384-385. 2. Whips , if cracked properly , are able to make small sonic booms near the end that is moving. Explain how this is possible. The tip of the whip is traveling at a speed greater than the speed of sound.

when this happens small shock waves are produced at the tip of the whip. 3. The radar gun that police use to catch people speeding is based on the Doppler effect. In the space below explain how a radar gun works. If you need to draw a picture do so, make sure you write an explanation of what you drew. The radar gun works by sending out a radio wave of a set frequency. This wave bounces off the object being detected and changes frequency. The radar gun detects the frequency change and compares the outgoing frequency with the incoming frequency. The speed of the object is calculated based on the difference in frequencies. 4. Does the Doppler effect occur for only some types of waves or all types of waves? Explain. The Doppler effect is the apparent change in frequency of a wave due to the relative motion of the source of the wave or the receiver of the wave. All waves show this effect. 5. Why is it that a subsonic aircraft, no matter how loud it may be, cannot produce a sonic boom? A subsonic aircraft cannot produce a sonic boom because of the fact that it needs to be traveling faster than the speed of sound in air in order for the shock wave to be developed.

The Anatomy of a Wave The Physics Classroom » Physics Tutorial » Waves » The Anatomy of a Wave Waves - Lesson 2 - Properties of a Wave The Anatomy of a Wave The Anatomy of a Wave The Wave Equation A transverse wave is a wave in which the particles of the medium are displaced in a direction perpendicular to the direction of energy transport. A transverse wave can be created in a rope if the rope is stretched out horizontally and the end is vibrated back-and-forth in a vertical direction. If a snapshot of such a transverse wave could be taken so as to freeze the shape of the rope in time, then it would look like the following diagram. The dashed line drawn through the center of the diagram represents the equilibrium or rest position of the string. This is the position that the string would assume if there were no disturbance moving through it. Once a disturbance is introduced into the string, the particles of the string begin to vibrate upwards and downwards. At any given moment in time, a particle on the medium could be above or below the rest position. Points A, E and H on the diagram represent the crests of this wave.

The crest of a wave is the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position. Points C and J on the diagram represent the troughs of this wave. The trough of a wave is the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position. The wave shown above can be described by a variety of properties. One such property is amplitude. The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position. In the diagram above, the amplitude could be measured as the distance of a line segment that is perpendicular to the rest position and extends vertically upward from the rest position to point A. The wavelength is another property of a wave that is portrayed in the diagram above. The wavelength of a wave is simply the length of one complete wave cycle. If you were to trace your finger across the wave in the diagram above, you would notice that your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic and regular fashion over both time and space.

And the length of one such spatial repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave. In the diagram above, the wavelength is the horizontal distance from A to E, or the horizontal distance from B to F, or the horizontal distance from D to G, or the horizontal distance from E to H. Any one of these distance measurements would suffice in determining the wavelength of this wave. A longitudinal wave is a wave in which the particles of the medium are displaced in a direction parallel to the direction of energy transport. A longitudinal wave can be created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated back-and-forth in a horizontal direction. If a snapshot of such a longitudinal wave could be taken so as to freeze the shape of the slinky in time, then it would look like the following diagram. Because the coils of the slinky are vibrating longitudinally, there are regions where they become pressed together and other regions where they are spread apart.

A region where the coils are pressed together in a small amount of space is known as a compression. A compression is a point on a medium through which a longitudinal wave is traveling that has the maximum density. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling that has the minimum density. Points A, C and E on the diagram above represent compressions and points B, D, and F represent rarefactions. While a transverse wave has an alternating pattern of crests and troughs, a longitudinal wave has an alternating pattern of compressions and rarefactions. As discussed above, the wavelength of a wave is the length of one complete cycle of a wave. For a transverse wave, the wavelength is determined by measuring from crest to crest. A longitudinal wave does not have crest; so how can its wavelength be determined? The wavelength can always be determined by measuring the distance between any two corresponding points on adjacent waves. In the case of a longitudinal wave, a wavelength measurement is made by measuring the distance from a compression to the next compression or from a rarefaction to the next rarefaction.

On the diagram above, the distance from point A to point C or from point B to point D would be representative of the wavelength. Sound Waves and Physics of Music Review with Answers #2 [ #10 | #11 | #12 | #13 | #14 | #15 | #16 | #17 | #18 | #19 | #20 | #21 | #22 | #23 | #24 | #25 | #26 | #27 | #28 | #29 | #30 | #31 | #32 | #33 | #34 | #35 | #36 | #37 | #38 | #39 | #40 | #41 | #42 | #43 | #44 | #45 | #46 | #47 | #48 | #49 | #50 | #51 | #52 ] 24. A certain note is produced when a person blows air into an organ pipe. The manner in which one blows on a organ pipe (or any pipe) will effect the characteristics of the sound which is produced.

If the person blows slightly harder, the most probable change will be that the sound wave will increase in ____. a. amplitude 46. The diagrams below represent four different standing wave patterns in air columns of the same length. Which of the columns is/are vibrating at its/their fundamental frequency? Include all that apply. Answer: CD The fundamental frequency is the lowest possible frequency for that instrument, and thus the longest possible wavelength. For open tubes, there would be anti-nodes on each end and a node in the middle. For closed end tubes, there would be a node on the closed end, an anti-node on the open end, and nothing in the middle. Diagram C is the third harmonic for a closed end tube and diagram D is the second harmonic for an open-end tube.

Useful Web Links [ #10 | #11 | #12 | #13 | #14 | #15 | #16 | #17 | #18 | #19 | #20 | #21 | #22 | #23 | #24 | #25 | #26 | #27 | #28 | #29 | #30 | #31 | #32 | #33 | #34 | #35 | #36 | #37 | #38 | #39 | #40 | #41 | #42 | #43 | #44 | #45 | #46 | #47 | #48 | #49 | #50 | #51 | #52 ] 47. The diagrams above ( Question #46 ) represent four different standing wave patterns in air columns of equal length. Which of the columns will produce the note having the highest pitch? a. A Waves Glossary | SECOORA Waves Glossary Wave concepts and terminology for students and teachers.

By Margaret Olsen, SouthEast COSEE Education Specialist You can download the glossary as a Microsoft Word document or an Adobe PDF Wave The repeating and periodic disturbance that travels through a medium (e.g. water) from one location to another location. Wave characteristics The highest part of a wave. The lowest part of a wave. The vertical distance between the highest (crest) and lowest (trough) parts of a wave. Wavelength The distance from a certain point on one wave to the same point on the next wave (e.g. distance between two consecutive wave crests or between two consecutive wave troughs). Wave amplitude One half the distance from the crest to the trough. Wave amplitude is a more technical term for wave height and is used in engineering technology. Wave frequency The number of waves passing a fixed point in a specified period of time. Frequency has units of waves per second or cycles per second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle per second. The time it takes for two successive crests (one wavelength) to pass a specified point. Wave speed The distance the wave travels divided by the time it takes to travel that distance.

Wave speed is determined by dividing the wavelength by the wave period. In symbols c = λBB; / T, where c is the wave speed, λ (lambda) is the wavelength, and T is the period. Wave Steepness The ratio of height to wavelength. When wave steepness exceeds 1:7, breakers form. If a wave has a height of one foot and a length from crest to crest of 8 feet, then the ratio is 1:8 and this wave is not going to break. But if the height is 1 foot and the length decreases to 5 feet, then the ratio is 1:5 and this wave has now become so steep that the crest topples and the wave breaks. Types of Ocean Waves Capillary waves Very small waves with wavelengths less than 1.7 cm or 0.68 inches. They are the first waves to form when the wind blows over the surface of the water and are created by the friction of wind and the surface tension of the water. These tiny little waves increase the surface area of the sea surface and if the wind continues to blow, the size of the wave will increase in size and become a wind wave. Small waves causing the ocean surface to be rough.

Ripples The ruffling of the water’s surface due to pressure variations of the wind on the water. This creates stress on the water and results in tiny short wavelength waves called ripples. Ripples are often called capillary waves. The motion of a ripple is governed by surface tension. Standing Wave Waves that move back and forth (oscillate) in a vertical position. They do not move forward but appear as crests and troughs in a fixed position. Standing waves are created when a wave strikes an obstruction head-on and then are reflected backwards in the direction they came from. Swell The smooth undulation (rising and falling of waves) of the ocean surface that forms as waves move away from the storm center where they are created. As waves move out and away from the storm center, they sort themselves out into groups of similar speeds and wavelengths. This produces the smooth undulating ocean surface called a swell. Swells may travel thousands of kilometers from the storm center until they strike shore. Other terms Beaufort Scale A scale of wind velocity used for estimating the force or speed of winds. It is a numbered scale from 0 to 12 to describe wave size and sea conditions.

The Beaufort Scale was developed by Rear Admiral Sir Francis Beaufort. 0 on the Beaufort scale represents the calmest of seas (the water is so smooth that it looks like glass). A 12 on the Beaufort scale represents hurricane force waves. Breakers When a wave approaches shore, it touches bottom and the front of the wave slows down and the back overtakes the front. This forces the water into a peak that curves forward. This peak will eventually fall forward in a tumbling rush of foam and water called a breaker. Waves break on or near shore or over reefs or offshore sandbars. There are three types of breaking waves: plunging breakers, spilling breakers and collapsing breakers. Breakers may be one or a combination of these types. Basic Waves Theory - Pass My Exams: Easy exam revision notes for GSCE Physics Home > GCSE Physics > Basic Waves Theory What are waves? Waves transfer energy from one point to another without transferring matter. They consist of disturbances which transfer the energy in the direction the wave travels without transferring matter.

There are two types of waves: Transverse waves Longitudinal waves Transverse Waves Transverse waves are wave in which the vibrations of the particles or medium in which the wave travels are at right angles to the direction in which the wave travels. Water waves are an example of transverse waves. These can be observed in a ripple tank. The animation below shows transverse waves created in a ripple tank. From the above animation it can be seen that the rubber duck only moves up and down whilst the energy of the wave moves along the tank. Thus the water only move up and down or in other words at right angles to the direction of travel of the wave. The energy however is passed along the water from one wave to the other. The diagram above gives a side view of transverse water wave. Transverse waves consist of high parts or peaks called crests and low parts called troughs. The distance between two successive crests or two successive troughs is the wavelength for a transverse wave. The height of the crest from the undisturbed water position or the depth of the trough from the undisturbed water position is the amplitude of the wave.

Everything Maths and Science You are here: Home › Grade 12 Physical Science › Doppler effect › The Doppler effect with sound The Doppler effect with sound You, the person hearing the sounds, are called the observer or listener and the thing emitting the sound is called the source. As mentioned in the introduction, there are two situations which lead to the Doppler effect: When the source moves relative to a stationary observer. When the observer moves relative to a stationary source. In points 1 and 2 above there is relative motion between the source and the observer. Both the source and the observer can be moving at the same time but we won't deal with that case in this chapter. Definition 1: Doppler effect The Doppler effect is the change in the observed frequency of a wave when the source or the detector moves relative to the transmitting medium. The Doppler effect occurs when a source of waves and/or observer move relative to each other, resulting in the observer measuring a different frequency of the waves than the frequency that the source is emitting. The medium that the waves are travelling through, the transmitting medium, is also stationary in the cases we will study. The question that probably comes to mind is: "How does the Doppler effect come about?".

We can understand what is happening by thinking through the situation in detail. Case 1: Moving source, stationary observer Let us consider a source of sound waves with a constant frequency and amplitude. The sound waves can be represented as concentric circles where each circle represents a crest or peak as the wavefronts radiate away from the source. This is because the waves travel away from the source in all directions and the distance between consecutive crests or consecutive troughs in a wave is constant (the wavelength as we learnt in Grade 10). In this figure the crests are represented by by the black lines and the troughs by the orange lines. Figure 1: Stationary sound source as more wavefronts are emmitted. The sound source is the police car in the middle and is stationary. For the Doppler effect to take place (manifest), the source must be moving relative to the observer. Let's consider the following situation: The source (represented by the black dot) emits one wave (the black circles represent the crests of the sound wave) that moves away from the source at the same rate in all directions. The distance between the crests represents the wavelength (\(\lambda\)) of the sound.

The closer together the crests, the higher the frequency (or pitch) of the sound according to \(f=\frac{v}{\lambda}\), where \(v\) (speed of sound) is constant. As this crest moves away, the source also moves and then emits more crests. Now the two circles are not concentric any more, but on the one side they are closer together and on the other side they are further apart. This is shown in the next diagram. If the source continues moving at the same speed in the same direction, then the distance between crests on the right of the source is constant. The distance between crests on the left is also constant. The distance between successive crests on the left is constant but larger than the distance between successive crests on the right. When a car approaches you, the sound waves that reach you have a shorter wavelength and a higher frequency. You hear a sound with a higher pitch. When the car moves away from you, the sound waves that reach you have a longer wavelength and lower frequency. You hear a sound with a lower pitch. Figure 2: Moving sound source as more wavefronts are emmitted.

Case 2: Moving observer, stationary source Just as we did before, let us consider a source (a police car) of sound waves with a constant frequency and amplitude. There are two observers, one on the left that will move away from the source and one on the right that will move towards the source. We have three diagrams: shows the overall situation with the siren starting at time \(t_1\); shows the situation at time \(t_2\) when the observers are moving; and shows the situation at \(t_3\) after the observers have been moving for a time interval, \(\Delta t=t_3-t_2\). The crests and troughs are numbered so you can see how they move further away and so that we can track which ones an observer has measured. The observers can hear the sound waves emitted by the police car and they start to move (we ignore the time it takes them to accelerate). The frequency of the wave that an observer measures is the number of complete waves cycles per unit time. By numbering the crests and troughs we can see which complete wave cycles have been measured by each of the observers in time, \(\Delta t\).

To find the frequency we divide the number of wave cycles by \(\Delta t\). In the time interval that passed, the observer moving towards the police car observed the crests and troughs numbered 1 through 5 (the portion of the wave is highlighted below). The observer moving away encountered a smaller portion of the wavefront, crest 3 and trough 4. The time interval for each of them is the same. To the observers this will mean that the frequency they measured is different. The motion of the observer will alter the frequency of the measured sound from a stationary source: An observer moving towards the source measures a higher frequency. An observer moving away from the source measures a lower frequency. It is important to note that we have only looked at the cases where the source and observer are moving directly towards or away from each other and these are the only cases we will consider. Note: We didn't actually need to analyse both cases. We could have used either explanation because of relative motion. The case of a stationary source with moving observer is the same as the case of the stationary observer and the moving source because the relative motion is the same. Do you agree? Discuss with your friends and try to convince yourselves that this is the case.

Being able to explain work to each other will help you understand it better. If you don't understand it, you won't be able to explain it convincingly. For a real conceptual test, discuss what you think will happen if the source and the observer are both moving, in the same direction and at the same speed. The formula that provides the relationship between the frequency emitted by the source and the frequency measured by the listener is: \[\boxed{{f}_{L}=\left(\frac{v\pm{v}_{L}}{v\pm{v}_{S}}\right){f}_{S}}\] where \({f}_{L}\) is the frequency perceived by the observer (listener), \({f}_{S}\) is the frequency of the source, \(v\) is the speed of the waves, \({v}_{L}\) the speed of the listener and \({v}_{S}\) the speed of the source. Note: The signs show whether or not the relative motion of the source and observer is towards each other or away from each other: Table 1 Lecture 14 (Waves, Wave Equation and Intensity) This is an introduction to Electricity, Strength of Materials and Waves.

Lecture 14 (Waves, Wave Equation and Intensity) In this lecture the following are introduced:  Wave motion as an energy transfer  Types of waves  The Intensity, Impedance and Pressure Amplitude of a Wave  Intensity Level and decibel scale  Hearing Loss  The Fletcher-Munson Curves and the Phon  Pitch Waves transfer energy Any vibrating body that is connected to its environment will transfer energy to its environment. The vibrations are then transferred though the environment from neighbour to neighbour. This energy transfer is called wave motion. Waves move energy through a medium without moving the whole medium. Leonardo di Vinci "waves made in a field of grain by the wind, ... we see the waves running across the field while the grain remains in place." Types of waves Longitudinal waves When waves transfer energy by pushing neighbours in the same direction that the energy moves, the waves are called longitudinal waves. In the simulation below (from Dr. Daniel A. Russell ) you can see energy move to the right while individual particles vibrate to the left and right about fixed points. The places when the particles cluster together are volumes of high pressure so these waves are also called pressure waves.

Sound waves are an example of pressure waves and they can move through gases, liquids and solids. For sound waves, the denser the medium the faster the speed. Speed through air (1atm, 200) =344 m.s-1 Speed through sea water = 1531 m.s-1 Speed through iron = 5130 m.s-1 Transverse waves When waves transfer energy by pulling neighbours sideways to the direction of travel, the waves are called transverse waves. In the simulation below (also from Dr. Daniel A. Russell ) you can see energy move to the right while individual particles vibrate up and down about fixed points. Electromagnetic waves (X-rays, light, radio, radar and TV waves) are examples of transverse waves formed by electric and magnetic fields vibrating together at right angles to the wave's motion. They don't need any medium so they can move through a vacuum, (good for us or we wouldn't see the Sun!). They all move at the same speed of 300,000 km.s-1 when they travel through vacuum. They slow down when they travel through a medium (this is an average speed between interactions).

Mechanically twisting or pulling a medium sideways is called shearing so waves formed this way are also called shear waves. Longitudinal and Transverse waves together Sometimes longitudinal and transverse waves occur together. Ocean waves are a combination of longitudinal and transverse waves because the surface of the water can be pulled sideways as well as pushed longitudinally. In the simulation below (also from Dr. Daniel A. Russell ) you can see energy move to the right while individual particles move clockwise in circles or ellipses. When ocean waves get to a shelving beach the speed of the waves changes relative to each other and circles go to ellipses and then the wave breaks. Seismic waves are formed when there is a sudden movement (or slip) between layers in the Earth's crust. This may happen anywhere between several km and several 100s km down from the surface. The wave motions that occur through the crust have Pressure ("P") components and Shear ("S") components. The P waves move at 5 - 14 km. s-1 The S waves move at 3 - 8 km.

s-1 When they reach the surface an Earthquake occurs, and the timing between the arrivals of the The S and P waves and their sizes at different places will enable the epicentre to be determined. (Note: seismic waves can also have "surface" waves. Again see Dr. Daniel A. Russell 's excellent pages for details.) Basic Wave Parameters The amplitude A, is half the height difference between a peak and a trough. The wavelength λ, is the distance between successive peaks (or troughs). The period T, is the time between successive peaks (or troughs). The wave speed c, is the speed at which peaks (or troughs) move. The frequency ν, (Greek letter "nu") measures the number of peaks (or troughs) that pass per second. Note that "c" (from the Latin word "celeritas" meaning swiftness) is used for wave speed, not "v". One reason is so that it is not confused with frequency. Example W1 Seismic Shear waves travel at 4000 m.s-1 and they have a period of 0.12s. Find the wavelength of these waves.

Answer W1 Representing Moving Shapes The station below has a frame of reference with axes labelled x and y. The engine and carriage below have a frame of reference at the end of the first carriage. It has axes labelled X and Y. The shape Y = F(X) is drawn on the side of the carriage in the (X,Y) frame of reference. The engine and carriage are moving at a constant speed c to the right (positive x axis). At time t = 0 s, the carriage and the station axes coincide. At time t s later: Vertical distance references do not change, i.e. Y = y at all times. The horizontal distance between the Y and y axes increases uniformly with time, i.e. d = ct. The distance X from the carriage origin to a point P on the side of the carriage will not change in time. The distance x from the station origin to the point P will increase with time, i.e. x = X + ct This means that the reference frames transform as: (x,y) ⇒ (X + ct, Y) and (X,Y) ⇒ (x - ct, y) In the carriage frame of reference: Y = F(X) defines a shape on the side of the carriage.

In the station frame of reference: y = f(x - ct) defines the same shape f(x) moving at a speed c to the right. Representing Transverse Sinusoidal Waves You can only have the sine of an angle. To represent a sine shape in space, the x distance has to be converted to get an angle. One complete cycle in space (one wavelength) is equivalent to one cycle in phase (2π radian). A fractional distance of a wavelength will equal the same fraction of 2π. φ is a phase angle, it relates a distance in space to a fraction of a wavelength. The relationship between phase angle and distance is given by: k is called the wave number: It is measured in radians per metre (rad.m-1). The wave speed is: Adding an initial phase α, (Greek letter "alpha") tells what is happening at time 0 s. Particle Motion in Transverse Sinusoidal Waves From Dr. Daniel A. Russell's transverse wave diagram above, while the wave moves at constant speed in the +x direction (to the right), the vibrating particles which make up the wave, move with simple harmonic motions in the y direction .

In concentrating on the particles, it is seen that neighbouring particles have slightly different x values which appear as slightly different initial phases in a Simple Harmonic Motion. At position x1, the equation y = A sin (kx1 - ωt + α) is effectively y = A sin (α1 - ωt), i.e. an SHM. The transverse displacements of particles are governed by: The transverse particle speeds are given by: Notice that displacement and particle speed are 90° out of phase (sines and cosines). When the particle is at its largest displacement, there is zero particle velocity. Maximum transverse particle velocity occurs as the particle crosses the axis. Example W2 A sinusoidal wave has a wavelength of 1.4m. Find the phase difference between a point 0.3m from the peak of a wave and another point 0.7m further along from the same peak. Answer W2 The equation of a transverse sinusoidal wave is given by: . (a) the amplitude of the wave, (b) the wavelength, (d) the wave speed, and (e) the displacement at position 0 m and time 0 s.

(f) the maximum transverse particle speed. Answer W3 Amplitude, A is 2 mm. The Intensity, Impedance and Pressure Amplitude of a Wave In general, an Intensity is a ratio. For example, pressure is the intensity of force as it is force/area. Also, density (symbol ρ) is the intensity of mass as it is mass/volume. The Intensity of waves (called Irradiance in Optics) is defined as the power delivered per unit area. The unit of Intensity will be W.m-2. The wave energy comes from the simple harmonic motion of its particles. The total energy will equal the maximum kinetic energy. Combining these two results: The Impedance of the medium (called the Specific Acoustic Impedance in Acoustics) is defined by the product of density and wave speed. In symbols: Impedance, z = ρc with a unit of Pa.s.m-1. The quantity Aω is the maximum transverse speed of the particles, so it has m.s-1. It can be seen that the intensity of a wave increases with its wavespeed c, amplitude A, and frequency ω.

Multiplying top and bottom by ρc: P0 is called the pressure amplitude, because when the unit for Impedance (Pa.s.m-1) is combined with Aω, a transverse speed term (m.s-1), it has the unit of Pressure (Pascal). It is useful when dealing with pressure waves . Example W4 A wave of frequency 1000 Hz travels in air of density 1.2 kg.m-3 at 340 m.s-1. If the wave has intensity 10 μW.m-2, find the displacement and pressure amplitudes. Answer W4 Intensity Level The intensity of a sound is given by power/area. It is an objective measurement and has the unit of W.m-2. Loudness is a subjective perception. For a long time it was thought that the ear responded logarithmically to sound intensity, i.e. that an increase of 100× in intensity (W.m-2) would be perceived as a loudness increase of 20×. The Intensity Level was defined to represent loudness.

It was accordingly based on a logarithmic scale and has the unit of Bel (after Alexander Graham Bell, not the Babylonian deity). The deciBel (β) is commonly used as the smallest difference in loudness that can be detected. The reference intensity I0 = 10-12 W.m-2 is the (alleged) quietest sound that can be heard. Only about 10% of people can hear this 0 dB sound and that only in the frequency range of 2kHz to 4kHz. About 50% of people can hear 20dB at 1kHz. (The frequency response will be looked at later.) Approximate Intensity Levels 160 Example W5 The average intensity level for each of two radios is set to 45dB. They are tuned to different radio stations. Find the average intensity level when they are both turned on. Answer W5 Here the Intensity doubles but the Intensity Level goes up by only 0.3 dB. Example W6 Sound radiates in a hemi-sphere from a rock band. If the sound level is 100 dB at 10 m, then find the sound level at 4 m.

Answer W6 First find the Intensity from the Intensity Level. Calculate the new Intensity. The key is that the radiated power is fixed and as it spreads out over greater areas the Intensity decreases in accordance with the following relationship. Calculate the new Intensity Level. Other Loudness measures There are other ways of representing the human response, some of these are: This puts the threshold of hearing at 4dB. and 1 Sone = 40dB at 1kHz. Degrees of Hearing Loss Hearing loss information . A person can have up to 25 dB hearing level and still have "normal" hearing. Those with a mild hearing loss (26-45 dB) may have difficulty hearing and understanding someone who is speaking from a distance or who has a soft voice. They will generally hear one-on-one conversations if they can see the speaker's face and are close to the speaker. Understanding conversations in noisy backgrounds may be difficult. Those with moderate hearing loss (46-65 dB) have difficulty understanding conversational levels of speech, even in quiet backgrounds. Trying to hear in noisy backgrounds is extremely difficult. Those with severe hearing loss (66-85 dB) have difficulty hearing in all situations.

Speech may be heard only if the speaker is talking loudly or at close range. Those with profound hearing loss (greater than 85 dB HL) may not hear even loud speech or environmental sounds. They may not use hearing as a primary method of communicating. The Fletcher-Munson Curves Fletcher and Munson were researchers who first accurately measured and published a set of curves showing the human's ear's frequency sensitivity versus loudness. The curves show the ear to be most sensitive to sounds in the 3 kHz to 4 kHz area, a range that corresponds to ear canal resonances. The lines give a unit called the phon. 100Hz at 71dB has the same apparent loudness as 60dB at 1kHz and hence it is 60 phons. The important range for speech is 300Hz - 3000Hz. Loud noise and age cause the high frequency response to decline. D.W. Robinson and R.S.

Dadson, re-did these lines in 1956 in an article titled: 'A re-determination of the equal-loudness relations for pure tones', British Journal of Applied Physics, 7, 1956, 166-181. These data are generally regarded as being more accurate than those of Fletcher and Munson. Both sources apply only to pure tones in otherwise silent free-field conditions, with a frontal plane wave etc. Pitch Frequency is measured objectively in Hertz. The subjective sensation of frequency is called the pitch of the note. The ear is not linear with frequency (Hertz). There is a "S" shaped curve between frequency and pitch. The ear is reasonably OK in the range 400Hz to 2.4kHz, but outside this range perception is pitch and frequency differ. For example, 300Hz is perceived as 500Hz, but 10kHz is perceived to be 3kHz. The subjective determination of frequency has a unit called the mel, and is thought to be due to the variable elastic properties of the basilar membrane in the ear. Summarising: Waves move energy through a medium without moving the whole medium.

In longitudinal waves the vibration is in the same orientation as the wave movement. In transverse waves the vibration is at right angles to the wave movement. Amplitude: A, is half the wave height. Wavelength: λ, is the distance between successive maxima (or minima). Frequency: ν, is the number of maxima (or minima) that pass per second and the reciprocal of the Period, T. Wavespeed: Regents Physics Wave Characteristics Regents Physics - Wave Characteristics Defining & Describing Waves A pulse is a single disturbance which carries energy through a medium or through space. Imagine you and your friend holding opposite ends of a slinky. If you quickly move your arm up and down, a single pulse will travel down the slinky toward your friend. If, instead, you generate several pulses at regular time intervals, you now have a wave carrying energy down the slinky. A wave, therefore is a repeated disturbance which carries energy. The mass of the slinky doesn't move from end of the slinky to the other, but the energy it carries does. When a pulse or wave reaches a hard boundary, it reflects off the boundary, and is inverted.

If a pulse or wave reaches a soft, or flexible, boundary, it still reflects off the boundary, but does not invert. Courtesy Penn State Schuylkill Waves at Boundaries Waves can be classified in several different waves. One type of wave, known as a mechanical wave, requires a medium (or material) through which to travel. Examples of mechanical waves include water waves, sound waves, slinky waves, and even seismic waves. Electromagnetic waves, on the other hand, do not require a medium in order to travel. Electromagnetic waves (or EM waves) are considered part of the Electromagnetic Spectrum. Examples of EM waves include light, radio waves, microwaves, and even X-rays. Further, waves can be classified based upon their direction of vibration. Waves in which the "particles" of the wave vibrate in the same direction as the wave direction are known as longitudinal, or compressional, waves. Examples of longitudinal waves include sound waves and seismic P waves. Waves in which the particles of the wave vibrate perpendicular to the wave's direction of motion are known as transverse waves.

Examples of transverse waves include seismic S waves, electromagnetic waves, and even stadium waves (the "human" waves you see at a baseball or football game!). Courtesy Penn State Schuylkill Transverse vs. Longitudinal It is important to note that in a transverse wave, the motion of the medium is perpendicular to the direction of the wave's velocity. This is illustrated clearly in the animation below. Wave Anatomy Waves have a number of characterisics which define their behavior. Looking at a transverse wave, we can identify specific locations on the wave. The highest points on the wave are known as crests. The lowest points on the wave are known as troughs. The amplitude of the wave, corresponding to the energy of the wave, is the distance from the baseline to a crest or the baseline to a trough. The length of the wave, or wavelength, noted with the Greek letter lambda ( ), is the distance between corresponding points on consecutive waves (i.e. crest to crest or trough to trough).

Points on the same wave with the same displacement from equilibrium moving in the same direction (such as a crest to a crest or a trough to a trough) are said to be in phase (phase difference is 0° or 360°). Points with opposite displacements from equilibrium (such as a crest to a trough) are said to be 180° out of phase. Question: The diagram represents a periodic wave. Which point on the wave is in phase with point P? Answer: Point C is in phase with point P, since point C represents a point with the same displacement from equilibrium moving in the same direction. Points that are in phase are located one or more whole wavelengths apart on a wave. Question: Two waves having the same frequency and amplitude are traveling in the same medium. Maximum constructive interference occurs at points where the phase difference between the two superposed waves is: Answer: 0°. In similar fashion, longitudinal, or compressional, waves also have amplitude and wavelength.

In the case of longitudinal waves, however, instead of crests and troughs, the longitudinal waves have areas of high density (compressions) and areas of low density (rarefactions), as shown in the representation of the particles of a sound wave. The wavelength, then, of a compressional wave is the distance between compressions, or the distance between rarefactions. Once again, the amplitude corresponds to the energy of the wave. Question: A longitudinal wave moves to the right through a uniform medium, as shown below. Points A, B, C, D, and E represent the positions of particles of the medium. What is the direction of the motion of the particles at position C as the wave moves to the right? Answer: The particles move to the left and right at position C, as the particles in a longitudinal wave vibrate parallel to the wave velocity: Question: Between which two points on the wave could you measure a complete wavelength? Answer: You could measure a complete wavelength between points A and C, since A and C represent the same point on successive waves. The Wave Equation The frequency (f) of a wave describes the number of waves that pass a given point in a time period of one second.

The higher the frequency, the more waves that pass. Frequency is measured in number of waves per second (1/s), also known as a Hertz (Hz). If 60 waves pass a given point in a second, the frequency of the wave would be 60 Hz. Closely related to frequency, the period (T) of a wave describes how long it takes for a single wave to pass a given point, and can be found as the reciprocal of the frequency. Period is a measurement of time, and therefore is measured in seconds. Both frequency and period were introduced earlier in our discussion of circular motion . Question: What is the period of a 60-hertz electromagnetic wave traveling at 3.0×108 meters per second? Answer: Because waves move through space, they must have a velocity. The velocity of a wave is a function of the type of wave, and the medium it travels through. Electromagnetic waves moving through a vacuum, for instance, travel at roughly 3*108 m/s. This value is so famous and common in physics it is given its own symbol, c. When an electromagnetic wave enters a different medium, such as glass, it slows down.

If the same wave were to then re-emerge from glass back into a vacuum, it would again travel at c, or 3*108 m/s. The speed of a wave can be easily related to its frequency and wavelength. Speed of a wave is determined by the wave type and the medium its traveling through. For a given wave speed, as frequency increases, wavelength must decrease, and vice versa. This can be shown mathematically using the wave equation: . Question: In a vacuum, all electromagnetic waves have the same: speed wavelength Answer: (1) speed. Question: The diagram below represents a periodic wave traveling through a uniform medium. If the frequency of the wave is 2.0 hertz, find the speed of the wave. Answer: The diagram shows a length of 6m for 1.5 wavelengths, therefore the wavelength ( ) must be 4m. Given both wavelength and frequency, we can use the wave equation to find the wave speed: Sound Waves Sound is a mechanical wave which we observe by detecting vibrations in the inner ear. Typically, we think of sound as traveling through air, therefore the particles vibrating are air molecules.

Sound can travel through other media as well, including water, wood, and even steel. The particles of a sound wave vibrate in a direction parallel with the direction of the sound wave's velocity, therefore sound is a longitudinal wave. The speed of sound in air at standard temperature and pressure (STP) is 331 m/s, a value which is supplied on the front of the Regents Physics Reference Table . Question: At an outdoor physics demonstration, a delay of 0.50 second was observed between the time sound waves left a loudspeaker and the time these sound waves reached a student through the air. If the air is at STP, how far was the student from the speaker? Answer: When we observe sound waves through hearing, we pick up the amplitude, or energy, of the wave as loudness. The frequency of the wave is perceived as pitch, with higher frequencies observed as a higher pitch. Typically, humans can hear a frequency range of 20Hz to 20,000 Hz, although young observers can often detect frequencies above 20,000 Hz, an ability which declines with age. Certain devices create strong sound waves at a single specific frequency.

If another object, having the same "natural frequency," is impacted by these sound waves, it may begin to vibrate at this frequency, producing more sound waves. The phenomenon where one object emitting a sound wave with a specific frequency causes another object with the same natural frequency to vibrate is known as resonance. A dramatic demonstration of resonance involves a singer breaking a glass by singing a high pitch note. The singer creates a sound wave with a frequency equal to the natural frequency of the glass, causing the glass to vibrate at its natural, or resonant, frequency so energetically that it shatters. Content on this page requires a newer version of Adobe Flash Player.

Question: For a constant sound wave, what is the distance between successive crests called?
Answer: Wavelength