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Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to 5000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320 m s-1.

Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to 5000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320 m s-1.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Sol. The path difference of the two sound waves is given by ∆L = 6.4 – 6.0 = 0.4 m The wavelength of either wave = λ = V/p = 320/p (m/s) For destructive interference ∆L = (2n +1)λ/2 where n is an integers. Or 0.4 m = 2n + ½ * 320/p ⇒ p = n = 320/0.4 = 800 2n+1/2 Hz = (2n + 1) 400 Hz Thus the frequency within the specified range which cause destructive interference are 1200 Hz, 2000 Hz, 2800 Hz, 3600 Hz and 44400 Hz.

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