A tuning fork of frequency 340 , Hz is sounde | vedclass

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(D) The frequency of the tuning fork is $f = 340 \, Hz$ and the speed of sound is $v = 340 \, m/s$.The wavelength is $\lambda = \frac{v}{f} = \frac{34

Vedclass · Accepted Answer

$45$

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(D) The frequency of the tuning fork is $f = 340 \, Hz$ and the speed of sound is $v = 340 \, m/s$.The wavelength is $\lambda = \frac{v}{f} = \frac{340}{340} = 1 \, m = 100 \, cm$.For a pipe closed at one end,resonance occurs when the length of the air column $L$ satisfies $L = \frac{n \lambda}{4}$,where $n = 1, 3, 5, \ldots$.Substituting $\lambda = 100 \, cm$,we get $L = \frac{n 	imes 100}{4} = 25n \, cm$.Possible lengths of the air column are $L = 25 \, cm, 75 \, cm, 125 \, cm, \ldots$.Since the total length of the pipe is $120 \, cm$,the air column length $L$ must be $\le 120 \, cm$. Thus,the possible values for $L$ are $25 \, cm$ and $75 \, cm$.The height of the water column $h$ is given by $h = 120 - L$.To find the minimum height of the water column,we must choose the maximum possible length of the air column,which is $L = 75 \, cm$.Therefore,$h_{\min} = 120 \, cm - 75 \, cm = 45 \, cm$.

$A$ tuning fork of frequency $340 \, Hz$ is sounded above an organ pipe of length $120 \, cm$. Water is now slowly poured in it. The minimum height of water column required for resonance is .... $cm$ (speed of sound in air $= 340 \, m/s$)

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