Question

The apparent change in wavelength of sound waves is 2.5 cm when the source of sound is approaching stationary listener with a velocity 8 m/s. Apparent decrease in the frequency of source when observer recedes from the same source at rest with a velocity of 30 m/s is: (velocity of sound=340 m/s)

• A. 20 Hz
• B. 25 Hz
• C. 40 Hz
• D. 28 Hz

Answer 1

The correct option is D 28 Hz

Given: Change in wavelength, $\Delta \lambda =2.5cm=0.025m$

Velocity of source, $v_s=8m/s$

Velocity of sound, $v=340m/s$

We have apparent change in frequency when source is approaching the stationary observer.

$\Delta \lambda =\lambda .v_s/v$

$\lambda =\Delta \lambda .v/v_s=0.025\times 340/8=1.06m$

Now when observer recedes from the stationary source with velocity $v_o=30m/s$

Apparent frequency is given by: $\Delta f=f.v_o/v=\frac{v}{\lambda }.\frac{v_o}{v}$

$\Delta f=v_o/\lambda =30/1.06=28Hz$