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Question

Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of the speakers as shown in figure. find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 ms.


A

200 (2n+1)

where n = 0,1,2,......49

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B

200 (2n+1)

where n = 0,1,2,......49

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C

320 (2n+1)

where n = 0,1,2,......49

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D

320 (2n+1)

where n = 0,1,2,......49

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Solution

The correct option is B

200 (2n+1)

where n = 0,1,2,......49


As shown in the figure the path difference x = (3.2)2 + (2.4)23.2

Again ,the wavelength of the either sound waves =220f

We know,destructive interference will occur

If x = (2n+1)λ2

(3.2)2 + (2.4)2 (3.2) = (2n+1)2 220f

solving we get

f = (2n+1)4002 = 200(2n+1)

where n = 0,1,2,......49


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