Question

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 (in Hz) heard by the running person shall be

Answer 1

Frequency of the sound produced by open flute
$f =2 \left(\frac{v}{2 \ell}\right)=\frac{2\times330}{2\times0.5} = 660\,Hz$
Velocity of observer, $v_{0} = 10 \times \frac{5}{18} = \frac {25}{9} \, m/s$
As the source is moving towards the observer therefore, according to Doppler's effect
$\therefore $ Frequency detected by observer,
$f '=\left[\frac{v+v_{0}}{v}\right] f = \left[\frac{\frac{25}{9}+330}{330}\right]660$
$=\frac{2995}{9\times330}\times660$ or, $f' =665.55 \simeq 666\,Hz$