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Two audio speakers are kept some distana...

Two audio speakers are kept some distanace 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`.

Text Solution

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The correct Answer is:
A, B, C, D
The path difference of the two sound waves is given by
`/_\L=6.4-6.0=0.4m`
The wavelength of either wave
`lamda=V/p=320/p (m/s)`
For destructive inteference
`/_\L=(2n+1)lamda/2`
where n is an integers
`or 0.4m =2+1/2xx320/p`
`rarr p=n=320/0.4`
`=800 (2n+1)/2 Hz`
`=(2n+1)400Hz`
Thus the frequency within the specified range which cause detructive inteference are 1200 Hz, 2000 Hz, 2800Hz, 3600Hz and 4400 Hz.`
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