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

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Solution:

Frequency of the sound produced by flute, $f = 2\left(\frac{v}{2 \ell}\right) = \frac{2 \times330}{2 \times0.5} = 660 Hz$ Velocity of observer, $v_{0} = 10 \times\frac{5}{18} = \frac{25}{9} m/s$ $\therefore$ frequency detected by observer, f' = $\left[\frac{v+v_{0}}{v}\right]f$ $\therefore f' = \left[\frac{\frac{25}{9 } +330}{330}\right] 660$ = 335.56 $\times$ 2 = 671.12 $\therefore$ closest answer is (4)

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