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A tuning fork vibrates with frequency $256 H z$ and gives one beat per second with the third normal mode of vibration of an open pipe. If we load the tuning fork with wax it will be in resonance at same third normal mode. What is the length of the pipe? (Speed of sound in air is $340 m s^{- 1}$ )

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$220 c m$

$200 c m$

$190 c m$

$180 c m$

answer is C.

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Detailed Solution

Organ pipe will have frequency either 255 or 257 Hz.
For frequency of tuning fork, 255 Hz
$255 = \frac{3 v}{2 l}, l = \frac{3 \times 340}{2 \times 255} m = 2 m \Rightarrow l = 200 c m$

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