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A tuning fork vibrates with frequency 256 Hz and gives one best 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 = 340 m s−1) [JEE-Main On line-2018]

1. 190 cm
2. 180 cm
3. 220 cm
4. 200 cm

Correct answer: 200 cm

Solution

The length of the pipe can be calculated using the formula for the fundamental frequency of an open pipe, which is given by f = v / (2L). Rearranging this gives L = v / (2f). Substituting the speed of sound (340 m/s) and the frequency (256 Hz) results in a length of 200 cm, confirming that option D is correct.

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