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)

666 Hz

Frequency of the sound produced by flute,
$f=2\left(\frac{v}{2\ell }\right)=\frac{2\times 330}{2\times 0.5}=660Hz$
Velocity of observer, $v_0=10\times \frac{5}{18}=\frac{25}{9}m/s$
$\therefore$ frequency detected by observer, $f^{\prime }=\left[\frac{v+v_0}{v}\right]f$
$\therefore f^{\prime }=\left[\frac{\frac{25}{9}+330}{330}\right]660$
$=335.56\times 2\approx 666$
$\therefore$ closest answer is (4)