Two stereo speakers are placed 3 m apart. They are playing the same sound, which

Question

Two stereo speakers are placed 3 m apart. They are playing the same sound, which has a frequency of 450 Hz. A person stands at a point that is 8 m in front of the speakers and halfway between them (they are the same distance from each of the speakers). One speaker is moved, increasing the separation between the two speakers. What minimum distance would this speaker need to be moved in order to produce a relative minimum in the intensity of the sound heard by the person standing in front?

Answer is 1.43 m.
Please explain how you got this.

Explanation / Answer

w, is w = 343/450 = .762m So the distance is the hypotenuse, and you want to increase it by .762/2 = .381m. Use trig to find out how far the speaker moved to the side (the other side of the triangle stayed the same as neither person nor the speaker moved backward or forward). Hypotenuse was (8^2 + 1.5^2)^(1/2) = 8.139m, now add the half wave length to make it 8.520. This makes the side along which the speaker moved (8.520^2 - 8^2)^(1/2) = 2.93m, which would indicate it moved 1.43m to the side (2.93 - 1.5 = 1.43)

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