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 heard by the running person shall be close to

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

Answer 1

The correct option is A

$666Hz$

Step 1. Given data

Length of open flute, $L=50cm=0.5m$

Speed of person running, $s=10km/h$

Speed of sound wave, $v_s=330m/s$

Step 2. Frequency heard by running person is

frequency of second harmonics sound produced by open flute,

$$\begin{gathered} f_0=2\times \frac{v_s}{2L}=\frac{2\times 330}{2\times 0.5} \\ =660Hz \end{gathered}$$

speed of observer, $s=10x(5/18)=\frac{25}{9}m/s$

Frequency heard by running person is

$$\begin{gathered} f\text{'}=\frac{s+v_s}{s}{f}_0 \\ =\frac{{\displaystyle \frac{25}{9}}+330}{330}\times 660 \\ =665.5\approx 666Hz \end{gathered}$$

Hence, option A is correct