# Adding more than two coherent sound sources of different phases

• pitchtwit
In summary, if there are three coherent sources radiating omnidirectionally at the same frequency, then the equation for p^2 would be: p^2=p1^2+p2^2+p3^2+2*p1*p2*cos(B1-B2-B3), where p values are calculated from Lp = Lw - 10*log(4*pi*r^2).
pitchtwit
Does anyone know how to add more than two coherent sources that have different phases?

An example might be a sound source and a receiver with sound reaching the receiver directly and by two reflections via different paths - maybe off a hard floor and hard ceiling.

There's a good document on adding two coherent sources here - http://35.9.69.219/home/modules/pdf_modules/m205.pdf, but I can't find much on adding more than two.

Any help would be great,

Tom

My first suggestion would be to identify each path and determine its length in wavelengths.
This can be converted to phase differences and the waves (however many) add using the principle of superposition.
In optics a diffraction grating can be analysed in this way expanding from 2 sources to 3 sources to 4 sources and so on.
Not much specific help but I hope it triggers something for you.
The document you quoted is very good.

Consider the instantaneous amplitude of each signal at the receiver to be equal to its peak amplitude multiplied by the Sin of its angular frequency multiplied by the time of travel (with the speed of sound in that environment taken into account).

Thanks for that. I'm just wondering about something that's related. If a source radiates omnidirectionally at a certain height above a acoustically reflective surface, and there's a barrier in between the source and receiver, then on the source side there would be two signal paths - both of which end up at the top of the barrier - at the same point. These two paths can be considered as two separate coherent sound sources, but at the top of the barrier would they join together to form one sound path? Or is it best to consider all the sound paths as separate right until they meet the receiver - so not confusing anything too much?

I'm still having no success with this really.

Imagine if there were three coherent sources radiating omnidirectionally at the same frequency. Two of the sources had an acoustic power output of 1 W and were 1 wavelength away from the receiver. Then the third source had an acoustic power output of 6 W but was half a wavelength away.

Would I just use this equation?: -
p^2=p1^2+p2^2+p3^2+2*p1*p2*cos(B1-B2-B3),

where p values are calculated from Lp = Lw - 10*log(4*pi*r^2) and B values are the phase values of each source at the receiver and are calculated using k*r.

## 1. What is the principle behind adding more than two coherent sound sources of different phases?

The principle behind adding more than two coherent sound sources of different phases is known as constructive interference. This occurs when sound waves from different sources overlap and have the same phase, resulting in an increase in the overall amplitude of the sound.

## 2. Can the addition of multiple sound sources of different phases cancel each other out?

Yes, the addition of multiple sound sources of different phases can result in destructive interference. This happens when the sound waves from different sources are out of phase, resulting in a decrease in the overall amplitude of the sound.

## 3. How does the phase difference between sound sources affect the overall sound?

The phase difference between sound sources can greatly impact the resulting sound. When the phase difference is small, the sound waves will reinforce each other and create a louder sound. When the phase difference is large, the sound waves will cancel each other out and result in a softer sound.

## 4. Is it possible to add an infinite number of sound sources with different phases?

In theory, it is possible to add an infinite number of sound sources with different phases. However, in reality, this is not practical or necessary as a few well-placed sound sources can achieve the desired effect.

## 5. How is the overall amplitude and frequency affected when adding multiple sound sources?

The overall amplitude of the sound will increase with the addition of multiple sound sources, as long as they are in phase. The frequency of the sound will remain the same, as it is determined by the source producing the original sound waves.

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