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# Suppose length of a pipe is $42.10cm$long and speed of sound in air is $350m/s$ (at room temperature). Then what is the frequency of the fifth overtone of an air column vibrating in a pipe closed at one end? ( given inner dia. of pipe is $3.5cm$)

Last updated date: 23rd Jul 2024
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Hint: In order to answer this first we know about the fundamental frequency .In a vibrating object the lowest resonant frequency is known as fundamental frequency.

Complete step-by-step solution:
From this problem we get,
$v\Rightarrow 350m/s$,
$l\Rightarrow 42.10\times {{10}^{-2}}m$
$d\Rightarrow 3.5cm\Rightarrow 3.5\times {{10}^{-2}}m$
Here fundamental frequency at one end is given by ,
$n=\dfrac{V}{4L}$
$\Rightarrow$$n=\dfrac{350}{4\times 42.10\times {{10}^{-2}}}$
$\Rightarrow n=202.78Hz$
Again the $Pth$ overtone , $\Rightarrow np=(2p+1)n$
Now , the frequency of $Pth$ overtone is , $\Rightarrow {{n}_{5}}=(2\times 5+1)202.78$
$\Rightarrow {{n}_{5}}=2230.59Hz$
Therefore , the frequency of $Pth$ overtone of a vibrating air column is $2230.59Hz$.

Note: Reverberation is the inclination of a framework to vibrate with expanding amplitudes at certain frequencies of excitation. The resonator may have a crucial recurrence and quite a few sounds.