Cumulative sound level formula? - Page 1
Forum section: electronics / general

author: Synthtech
author_rank: Regular Contributor
timestamp: July 07, 2019, 12:40:15 am
content: For some reason one of those stupid questions popped into my head as I was out walking last evening. It went like this:I set up a pair of speakers side by side as close to each other as possible. I feed a 1kHZ sine wave through one of the two speakers and put a dB meter in front of them 1m away and set the volume level so that the meter reads 80dBA.If I then turn on the second speaker so that it is putting out exactly the same signal at the same level, in phase, what will I see on the meter? 88dB? What formula is used to calculate cumulative sound level from multiple identical sources?

author: NiHaoMike
author_rank: Super Contributor
timestamp: July 07, 2019, 12:51:05 am
content: If you manage to get perfect constructive interference, the power level would increase by 3dB.

author: vk6zgo
author_rank: Super Contributor
timestamp: July 07, 2019, 03:54:59 am
content: Sound presssure in dB uses a similar formula to the dB voltage formula, which is a bit confusingChange in Sound pressure in dB = 20 logP1/P2 where "P" stands for pressure, not power, so I would suggest 86dBa.When I went to work at a hearing aid place, it confused the hell out of me!There were moves afoot at the time to use power rather than sound pressure in measurements, but what happened, I don't know, as I lost touch.

author: Brumby
author_rank: Unknown
timestamp: July 07, 2019, 06:48:31 am
content: I don't have a lot of practical experience with this sort of thing, but the first things that come to mind include:For individual speaker measurements...1. Is the sound level meter on axis (horizontally and vertically) to each speaker?2. Is each speaker on axis to the sound level meter?3. Is the wiring to each speaker of exactly the same characteristics (resistance, inductance)?4. Are you using two separate power amplifiers to drive each speaker? (Slight power difference)5. Are your conditions sufficiently anechoic. If not, room reflections could cause issues.6. Are the two speakers truly identical?7. Are the electrical connections to each speaker the same (ie. good, solid and identical)?The only way to make a proper comparison is to set up an experimental arrangement for one speaker and take your measurements, then remove it and place the other speaker in exactly the same position with exactly the same surroundings.For measurement of both speakers operating at the same time, you have all of the above - plus phase considerations.This could be a rabbit hole...

author: hamster_nz
author_rank: Super Contributor
timestamp: July 07, 2019, 07:20:50 am
content: Why not just test it with a pair of speakers and a cell phone sound level meter app?Two identical speakers driven with the same power should be +3 dB, which should be easily measured.You are doubling the accustic energy, (+3db) not the amplitude (+6db).

author: MyHeadHz
author_rank: Regular Contributor
timestamp: July 08, 2019, 02:22:06 pm
content: More information would be needed to answer your question. The theoretical peak will be up to 83dB (a doubling of SPL), and the lower limit would be 0dB (perfect cancelling of the sound waves). It will be neither of these, but it will be between the two values. This is quite a deep rabbit hole indeed. There are many factors involved, but those factors change depending on what you are trying to learn or accomplish.Many of the acoustical physics formulas have some assumptions built in (square cow stuff). They generally focus on one aspect or variable specifically, and you are just expected to know all the other factors involved in order to apply whatever formula in a meaningful manner. It is as if you must be aware of all the formulas and factors in all of acoustical physics at once before you can even use the most basic formulas. Because of all the factors, most formulas only start being applicable at some distance from the speaker.Common assumed factors:- The environment has infinite baffle. That means, once emanated, nothing alters the path of the sound by reflection, absorption, resonance, etc.- The medium (air, usually) is perfectly uniform in the environment, at an assumed temperature, moisture level (usually as a percentage of saturation), and content makeup (Nitrogen, oxygen, CO2, etc).- The 'speaker" and any speaker box is perfect with no resonances (electrically or mechanically). The energy input is 100% converted to SPL (measured in dB), the 'speaker' and components have no mass or size dimensions. All wave energy emitted magically comes from a single point in space.- The 'microphone' is also assumed similarly perfect, and won't affect the measured sound. Microphones are generally quite terrible, even good ones. Any values you get might make sense in a relative sense, but it wouldn't be reasonable to treat the values measured as more than interval data at the most.- Phase is relative. Electricity moves quite quickly through cables, but once it hits the diaphragm the wave is carried at the speed of sound in the experiment environment.(- I also recommend looking up Doppler effect calculations.)Obviously, these are all far from practical environments. Sound is quite complicated, but you can adjust testing parameters in order to correct enough to make measurements.- To take care of the errors of proximity and speaker imperfections, move the speakers farther apart. It won't be perfect, but it helps a lot.- I recommend using lower frequencies, around 20-40 Hz. It is much easier to simply walk around and hear the resonances/amplitude/standing waves/etc with your ears instead of painstakingly measuring and plotting out values on graphs before you can put together the observations. Although there is a lot to gain from higher frequencies as well.I recommend setting up two identical speakers apart by about 5-10 diaphragms apart, with the microphone 2-3x that distance. To make early calculations and observations easy, keep the microphone equidistant from both speakers- this takes out the phase parameters from your calculations. Then you need a function/tone generator (any computer will do), and a microphone. Once you get a good grasp on that, see how changing phase and frequencies changes the interference patterns as you move around. You can also take measurements, then change the room temperature by a few degrees. Try to predict how much a given peak in a standing wave will physically move.