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? ... $cm$ (Speed of sound of air is $340\, ms^{-1}$)
JEE MAIN 2018, Medium
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According to question, tuning fork gives $1\, beat/second$ with $(N)\, 3^{rd}$ normal mode. Therefore, organ pipe will have frequency $\left( {256 \pm 1} \right)\,Hz$. In open organ pipe, frequency
$\mathrm{n}=\frac{\mathrm{NV}}{2 \ell}$
or, $255=\frac{3 \times 340}{2 \times \ell} \Rightarrow \ell=2 \mathrm{m}=200 \mathrm{cm}$
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