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 heard by the running person shall be close to :

• A. 753 Hz
• B. 500 Hz
• C. 333 Hz
• D. 666 Hz

Answer 1

Answer: (D)

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 $
= $335.56 \times 2 = 671.12$