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2 loudspeakers are emitting sound waves ...

2 loudspeakers are emitting sound waves of wavelength lambda with an initial phase difference of `pi/2` at what minimum distance from O on line AB will one hear a maximum

A

`25lambda`

B

`(100lambda)/sqrt(15)`

C

`(25lambda)/3`

D

`50 lambda`

Text Solution

Verified by Experts

The correct Answer is:
C

`Deltaphi=2npi`
`Rightarrowpi/2+(2pi)/lambdad sin theta=2npi`
`(2pi)/lambdadsintheta=(2n-1/2)pi`
`sintheta=(2n-1/2)lambda/(2d)=1/2xxlambda/(2xx3lambda)=1/12`
`Rightarrowy/sqrt((100lambda))^(2)=1/12`
`144y^(2)=(100lambda)^(2)`
`yapprox(100lambda)/12 = (25lambda)/3`
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