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 (in Hz) heard by the running person shall be

Answer 1

Answer: 666

Frequency of the sound produced by open flute
$f=2\left(\frac{v}{2\ell }\right)=\frac{2\times 330}{2\times 0.5}=660Hz$
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,
$f^{\prime }=\left[\frac{v+v_0}{v}\right]f=\left[\frac{\frac{25}{9}+330}{330}\right]660$
$=\frac{2995}{9\times 330}\times 660$ or, $f^{\prime }=665.55\simeq 666Hz$