Solving Billy and Speakers: 16m, 0.8m, 3000 Hz

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AI Thread Summary
To determine how far Bill must walk to reach the m=1 maximum of sound interference, the wavelength of the sound needs to be calculated first, which is found to be approximately 0.1143 meters. The key is to identify the point along the wall where the distance from each speaker differs by half a wavelength. This involves applying the geometry of the setup, considering the speakers' positions and the distance to the wall. The solution requires understanding the relationship between the interference pattern and the geometry of the speakers' arrangement. Ultimately, solving this problem hinges on accurately applying these principles to find the correct walking distance for Bill.
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Homework Statement



Two lound speakers are each located 16m from a wall and are 0.8m apart. They play a 3000 Hz sound, both speakers are in phase. Bill is located at the wall at the m=0 maximum of sound interference. If he walks along the wall, how far does he have to walk to hear m=1 maximum? (The speed of sound is 343 m/s.)


Homework Equations



2pi * (x2-x1) / lambda = 2mpi
vsound = lambda*f


The Attempt at a Solution



343 m/s = lambda*3000Hz
lambda= .1143 meters

Beyond that, I do not know how to solve it.
Thank you.
 
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Sounds like you have a little geometry problem. Don't you just need to find the point away from the mid-line whose distance from each speaker is different by half a wavelength?
 

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