Question

A musician using an open flute of length $50\text{cm}$ produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of $10\text{km/h}$. If the wave speed is $330\text{m/s}$, the frequency heard by the running person shall be close to

• A. $\text{333 Hz}$
• B. $\text{753 Hz}$
• C. $\text{666 Hz}$
• D. $\text{500 Hz}$

Answer 1

The correct option is C $\text{666 Hz}$

According to Doppler's effect

When the observer is moving towards the source and source is stationary, $V_s=0$

Frequency detected by observer is
$f^{\prime }=\frac{(v+V_o)}{v}f.....\left(1\right)$

Frequency of the sound produced by open flute in second harmonic is
$f=2\left(\frac{v}{2l}\right)=\frac{2\times 330}{2\times 0.5}=660\text{Hz}$
Velocity of observer in $\text{m/s}$, $V_0=10\times \frac{5}{18}=\frac{25}{9}\text{m/s}$

Put all the values in equation $1$
$f^{\prime }=\left[\frac{\frac{25}{9}+330}{330}\right]660$
$f^{\prime }=\frac{2995}{9\times 330}\times 660\Rightarrow f^{\prime }=665.55\text{Hz}\approx 666\text{Hz}$