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In the shown figure ABCDE is a tube whic...

In the shown figure ABCDE is a tube which is open at A and D. A soruce of sound A is placed in front of A. if frequency of the source can be varried from 2000 Hz to 4000 Hz. Find frequencies at which a detector placed in front of D receives a maxima of intensity.
(Given speed of sound `=340m//s`)

Text Solution

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From the shown figure, the path difference the sounds going through two parts of the tube
`Deltax=ABCD-AED`
`=[(30+40+30)-(30+50)]cm`
`=20cm`
`=0.2m`
If frequency of the sound is f then wavelength of the sound
`lamda=(340)/(f)m`
How for maximum intensity at the place of detector `Deltax=nlamda`.
`Deltax=nlamda`
`0.2m=n(340)/(f)m`
or `f=(nxx3400)/(2)Hz`
or `f=nxx1700Hz`
Here n may be equal to 1,2,3,4
Now for n=1
f=1700Hz
for n=2
f=3400 Hz.
for n=3
f=5100Hz
and so on
as frequency of the source is varied between 2000 Hz to 4000 Hz the frequency at which a maxima is received by the detector is f=3400Hz
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