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Two sound sources S(1) and S(2) emit pur...

Two sound sources `S_(1)` and `S_(2)` emit pure sinussoidal waves in phase . If the speed of sound is `350 m//s` , then
(a) for what frequencies does constructive interference occur at point `P` ?
(b) for what frequencies does destructive interference occur at point `P` ?

Text Solution

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The correct Answer is:
A, B, C
path difference, `Deltax = sqrt((2)^(2) + (4)^(2)) - sqrt((1)^(2) + (4)^(2)`
=`4.47- 4.12 = 0.35m`
(a) constructive interference occurs when the path difference is an interger multiple of wavelength.
or `Deltax = nlambda = (n nu)/(f)` or `f=(n nu)/(Deltax)` where, `n = 1,2, 3,..`
`:. f = (350)/(0.35),(2xx350)/(0.35), (3xx 350)/(0.35)` ,..
`f= 1000 H_(Z), 2000H_(Z), 3000 H_(Z)` ,.. etc.
(b) Destructive interference ooccurs when the difference is a half - integer multiple of wavelengths
or `Deltax= (2n + 1) (lambda)/(2)` `n= 0,1,2`,..
or `Deltax= (2n + 1) (nu)/(2f)` :. `f=((2n +1)nu)/(2 Deltax)`
`= (350)/(2xx0.35), (3xx350)/(2xx0.35), (5xx350)/(2xx 0.35)` ,..
`= 500H_(Z), 1500H _(Z), 2500 H_(Z)` ,..
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