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 :

Solution:

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

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