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JEE Main 2018 (15 Apr, Shift 1) · Beats

Beats question from JEE Main 2018 (15 Apr, Shift 1)

Q60JEE Main 2018 · 15 APR · SHIFT 1Medium

Beats

A tuning fork vibrates with frequency $256\text{ Hz}$ 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 $340\text{ ms}^{-1}$ )

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Answer: (d)

Third normal mode of an open pipe: $f = \frac{3v}{2L}$ .
1 beat/s with 256 Hz, so $f = 255$ Hz or $257$ Hz.
With $f = 255$ Hz: $L = \frac{3 \times 340}{2 \times 255} = 2$ m $= 200$ cm (257 Hz gives 198.4 cm, not an option).
So the answer is (d) $200$ cm.

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