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  4. 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 ? (Speed of sound in air is 340 ms-1)

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Q. 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 ? (Speed of sound in air is $340\, ms^{-1}$)

JEE MainJEE Main 2018Waves

Solution:

Given: Frequency of tuning fork $=256 Hz$.
It gives one beat per second with the third normal mode of vibration of an open pipe.
Therefore, frequency of open pipe $=(256+1) Hz$
Speed of sound in air is $340 m / s$.
Now we know, frequency of third normal mode of vibration of an open pipe is given as
$f=\frac{3 v_{\text {sound }}}{2 l}$
$\Rightarrow \frac{3 \times 340}{2 l}=255$
$\Rightarrow l=\frac{3 \times 340}{2 \times 255}=2\, m =200\, cm$