Question

# A musician using an open flute of length $50cm$ produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of $10km/h$. If the wave speed is $330m/s$, the frequency heard by the running person shall be close to

A

$666Hz$

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B

$753Hz$

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C

$500Hz$

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D

$333Hz$

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Solution

## The correct option is A $666Hz$Step 1. Given dataLength of open flute, $L=50cm=0.5m$Speed of person running, $s=10km/h$Speed of sound wave, ${v}_{s}=330m/s$Step 2. Frequency heard by running person isfrequency of second harmonics sound produced by open flute,${f}_{0}=2×\frac{{v}_{s}}{2L}=\frac{2×330}{2×0.5}\phantom{\rule{0ex}{0ex}}=660Hz$speed of observer, $s=10x\left(5/18\right)=\frac{25}{9}m/s$Frequency heard by running person is $f\text{'}=\frac{s+{v}_{s}}{s}{f}_{0}\phantom{\rule{0ex}{0ex}}=\frac{\frac{25}{9}+330}{330}×660\phantom{\rule{0ex}{0ex}}=665.5\approx 666Hz$Hence, option A is correct

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