Unit 4 - Waves

## 4-1 Oscillations

### **Definitions**

**Oscillation**: the movement of an object back and forth about a fixed average point

**Simple Harmonic Motion (SHM):** Oscillation where acceleration (caused by restoring force) is proportional to the displacement from a fixed point, and is always towards the fixed point.

**Equilibrium point**: the point about which an object oscillates.

**Amplitude**: max displacement from the equilibrium position

**Period (T)**: time taken for one complete cycle]

**Frequency (f)**: oscillations (cycles) per unit of time (Hz or s-1). Note that f = T-1

### **Graphs**

When shifting a displacement-time graph to the left by 0.25T, it becomes a velocity-time graph. If you shift a velocity-time graph to the left by 0.25T, it becomes the acceleration-time graph. This is called **phase difference**. No phase difference means they are **in phase**.

For an object undergoing SHM:

* Total energy (Kinetic and Potential) must remain constant
* At the equilibrium position, there is no potential energy. Thus, the kinetic energy is at a maximum
* At the maximum displacement, there is no kinetic energy, thus full potential energy.
* Graphically:

☀http://physicsnet.co.uk/wp-content/uploads/2010/05/shm-energy-graph.jpg

## 4-2 Travelling Waves

There are two types of waves:

**Transverse Waves:** Particles oscillate perpendicular to the transfer of energy

**Longitudinal Waves:** Particles oscillate parallel to the direction of transfer of energy

**Period (T):** In a displacement-time graph, the distance between crest to crest or trough to trough, defined as the time it takes to complete one full cycle

**Wavelength:** In a graph with x-axis being displacement, the distance for one full wave.

**Frequency**: is 1/T. Defined as how often the wave repeats

V = λ/T

V = Speed

λ = Wavelength

T = Period

### **Electromagnetic Waves (EM)**

* They are vibration of waves and have both electrical and magnetic properties
* All have speed of light (3 x 108)
* Different frequency has different properties.

https://www.google.ca/search?q=electromagnetic+spectrum&rlz=1C1JPGB\_enCA669CA685&biw=1440&bih=809&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwjf\_KD795PMAhVFl4MKHcE4AJ4QsAQIGg#imgrc=TluEcF4P1CNBBM%3A

## 4-3 Wave characteristics

**Intensity**: rate of energy transferred per unit area at right angles to wave velocity.

I = P/4𝝅r2

I = Intensity of wave

P = Power (Light power in terms of watt)

r = distance the wave traveled.

I ∝ A2

I = Intensity of wave

A= Amplitude of wave

### **Polarization**

I = I0cos2θ

where I0 is initial ray of light

θ = angle made between the two polarizing filters

## 4-4 Reflection and Refraction

Welcome back to grade 10 science!

nisin(i) = nrsin(r)

n = index of material.

i = incident angle

r= refracted angle

The **critical** angle is the incident angle for which the refracted angle is 90o and thus, not exiting the medium.

Angles above the critical angle will result in **total internal refraction**.

## 4-5 Interference and Standing Waves

Child Wave: Daddy, where did I come from?

Daddy Wave: Well, when two waves love each other very much... They bump into each other and that's how you were formed!

Child Wave: When I was forming, did it become more intense?

Daddy Wave: No. Intensity stayed the same, but the size (amplitude) of it increased. However, for your brother, the size of it decreased, and your mother wasn't satisfied that.

When two waves bump into each other, interference occurs.

**Constructive Interference** occurs when the amplitude of the two waves act in the same direction, thus adding the two amplitude.

**Destructive Interference** occurs when the amplitude of the two waves act in a different direction, thus subtracting the amplitude.

### **Standing Waves**

When two identical waves pass through each other, they produce something called a **standing wave**.

Standing waves have can have a **node**, which is a point in the resultant wave that doesn't move at all.

As the frequency increases, the wave vibrates more vigorously. We call the vibrating stages: harmonic.

Harmonics:

☀http://study.com/cimages/multimages/16/harmonics\_\_overtones\_waves.png

The next harmonic adds half a wavelength to its previous harmonic.

f = v/λ

f = frequency

v = speed of sound (will be given in question)

λ = wavelength

Patterns vary for ends that are open. The previous example has both ends closed. If there was one end open, then the first harmonic would be 1/4 of a wavelength. If it was both ends, then first harmonic would have half the wavelength like if both end were closed. However, it would start with the crest and trough instead of the node.

## 4-6 Diffraction

As a wave passes through a hole (aperture), they spread out. The smaller the aperture, the larger the spreading.

The larger the wavelength. the larger the diffraction.

If there were two apertures, then the waves can interfere with each other. This is described as Young's Double-Slit Experiment.

Two equations:

λ = yd/nL

λ = wavelength of the light

y = distance from the fringe of the interference pattern

d = distance between the two slits

n = which fringe

L = Length between projector and board

sinθ = 2λ/d

where θ is the angle made between n = 0 and n = n.