A tuning fork vibrates with frequency 256, Hz | vedclass

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(D) The tuning fork has a frequency $f = 256\, Hz$. It produces $1\, beat/s$ with the third normal mode of an open pipe. Therefore,the frequency of th

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$200$

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(D) The tuning fork has a frequency $f = 256\, Hz$. It produces $1\, beat/s$ with the third normal mode of an open pipe. Therefore,the frequency of the third normal mode $f_3$ is $256 \pm 1\, Hz$,which is $255\, Hz$ or $257\, Hz$.For an open pipe,the frequency of the $N^{th}$ normal mode is given by $f_N = \frac{N v}{2L}$,where $N=3$,$v = 340\, m/s$,and $L$ is the length of the pipe.Case $1$: $255 = \frac{3 	imes 340}{2L} \Rightarrow L = \frac{1020}{510} = 2\, m = 200\, cm$.Case $2$: $257 = \frac{3 	imes 340}{2L} \Rightarrow L = \frac{1020}{514} \approx 1.98\, m = 198\, cm$.Given the options,$200\, cm$ is the correct value.

$A$ tuning fork vibrates with frequency $256\, Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe in $cm$? (Speed of sound in air is $340\, m/s$)

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