Soundwave and interferance problem.

[hysics]

Here is the problem:

Two speakers separated by a distance of 3m emit sound waves of frequency 550Hz. The velocity of sound is 330m/s. Find the distances from the source at which the intensity of the sound will be a maximum.

What i have so far..

Since we are trying to look for the places where there is constrictive interference (maxima), we can use .. d sin x = lambda*n . Maxima will occur when the path difference is 0, 1 wavelength or an integral multiple of wavelengths (ie: lambda*n)

So we find the wavelength ..

lambda = V/f = 0.6 m

The first maxima should occur at 0m, then ..

3 sin x = 0.6

3 sin x = 0.6*2 , etc

I'm not seeing how to get the next distances after that (am I even in the right path?) :(. Any hints?

Thank you in advance.

 

[OlderDan]

Is that the full statement of the problem? You recognize that constructive intereference occurs when the path lengths are equal. Intensity drops off as you move away from the speakers. If you put that together, the maximum intensity is the point of constructive interference that is closest to the speakers, or perhaps very close to one of them. The problem may be looking for you to incorporate the intensity change with distance from each source.

 

[hysics]

Is that the full statement of the problem? You recognize that constructive intereference occurs when the path lengths are equal. Intensity drops off as you move away from the speakers. If you put that together, the maximum intensity is the point of constructive interference that is closest to the speakers, or perhaps very close to one of them. The problem may be looking for you to incorporate the intensity change with distance from each source.

Yes, unforunately, that is the full statement of the problem :(.

It also comes with a diagram similar to this:

S2
*
|
|
|
*______________________ 0
S1

As far as I understand, it is asking to find the position of points along the S1-0 line at which the intensity of the sound will be a maximum.

The problem comes with answers but I can't seem to understand how they get to them. hmmm..

 

[OlderDan]

What are the answers? That might help with interpretation of the problem?

 

[hysics]

Answer: 7.20m, 3.15m, 1.60m, 0.68m, 0m from S1

 

[OlderDan]

Answer: 7.20m, 3.15m, 1.60m, 0.68m, 0m from S1

OK, The problem is looking for the positions of the maxima along the line, as you thought. Each point is a place where the path length difference between S1 and S2 is a whole number multiple of one wavelength.

 

[hysics]

yes, even though I understand the general requirement, I'm still not seeing how to actually start solving it with what I know. :(

 

[OlderDan]

yes, even though I understand the general requirement, I'm still not seeing how to actually start solving it with what I know. :(

Can you write an equation for the distance from S2 to a point on the line, given the distance form S1 on the line (right triangle)? Can you find the wavelength of the sound? If you require S2 - S1 to be a multiple of the wavelength, then you will have two equations relating S1 and S2 that can be solved for both. The reason one answer is 0 is that the speakers are a whole number of a wavelengths apart.