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A sound source capable of producing soun...

A sound source capable of producing sound of variable frequencies is located at a distance of 1 m from a reflecting wall as shown in the figure. A detector D is lying at a point shown in the figure. The various distances are also indicated. If the speed of sound in air is `340" "ms^(-1)`, find the frequencies of sound within the audible range, which will have maximum intensity at detector?

Text Solution

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The sound waves reach point D. One reaches D directly from S and the other after reflection from the wall.

The reflected wave appears to come from the virtual image S' of the source (remember that sound waves from the ordinary laws of reflection and refraction). this image S' is distant 1 m from the wall just like the source. the two path lengths, now are
`SD=sqrt(20^(2)+10^(2))=22.36m`
and `S'D=sqrt(22^(2)+10^(2))=24.17m`
`therefore` The path length difference between the two waves is given by
`Deltax=24.17-22.36=1.81m`
When the path difference of 1.81m equals `nlamda`, a maxima is formed at D.
`implies1.81=nlamda` where `n=0,1,2,` . . . .
For frequencies, we have
`1.81=(n(340))/(v)`
or `v=n((340)/(1.82))`
or `v=188Hz, 376Hz, 564Hz`, . . .. . ,n(188)Hz.
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