Physics home work - Sound waves?

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Joshua_32

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Suppose speakers A and B are placed 5.70 m apart and the speakers are vibrating in phase. They are playing identical 110 Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and an observer standing directly in front of speaker B so that a right angle is formed, such that he observes destructive interference?
 
Wavelength of the wave = 343/110 = 3.118 mLet the distance of the observer from B be 'b' and A be 'a' respectively.
then we have

a = sq rt[b^2 + 5.7^2] = b[1 + (1/2)*(5.7/b)^2] neglecting higher powers, or a = b + [0.5*(5.7^2)]/b or a-b = 16.245/b = 3.118/2 for least value of b. or b = 16.245 / (3.118/2) = 10.42
 
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