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The length of a pipe open at both ends i...

The length of a pipe open at both ends is 48 cm and its fundamental frequency is 320 Hz. If the speed of sound be `320 ms^( -1)` then determine the diameter of the pipe. If one end of the pipe be closed, then what will be the fundamental frequency?

Text Solution

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`f_(0)=(v)/(2[L+2e])=(v)/(2[L+2xx0.6r])[as=e0.6r]`
So subsituting the given data,
`320=(320xx100)/(2[48+1.2r]) or r=(10)/(6) cm`
So `D=2r=xx(10//6)=3.33 cm`
Now when one end is closed,
`f_(c)=(v)/(4(L+0.6r))=(340xx100)/(4[48+0.6xx(10//6)])=163.3 Hz`
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