You are standing agasint the wall, as are two speakers. One is to your left and

Question

You are standing agasint the wall, as are two speakers. One is to your left and is 20.0m away from you, The other is also on your left and is 30.0m away from you. Then you walk 10.0 meter away from the wall in a straight line (so the closer speaker is now approximately 22.36068m=sqrt((20.0m)2+(10.0m)2) away) and the other is farther away. Your friend turns one on and it is 10dB by you. Then they turn it off and then turn the other one on and it is also 10 dB by you.Then, they turn both on. What is the smallest frequency (in Hz, three digits, like 12.3 or 1.23 or 0.123 or 0.0123) in the range 20Hz-20kHz that produces totally destructive interference?

Explanation / Answer

path difference = sqrt((30.0m)2+(10.0m)2) - sqrt((20.0m)2+(10.0m)2) = 9.2621 m

for shortest frequency, wavelength = 9.2621 x 2 = 18.5242 m

frequency = 340/18.5242 = 18.35 Hz < 20 Hz

so for next shortest frequency, wavelength = 9.2621 x 2/3 = 18.5242/3 m

frequency = 340 x 3/18.5242 = 55.06 Hz

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