Question

A train standing at a certain distance from a railway platform is blowing a whistle of frequency 500 Hz. If the speed of sound is $340m{s}^{-1}$, the frequency and wavelength of the sound of the whistle heard by a man running towards the engine with a speed of $10m{s}^{-1}$ respectively are

• A. 500 Hz, 0.7 m
• B. 500 Hz, 0.68 m
• C. 486 Hz, 0.7 m
• D. 515 Hz, 0.68 m

Answer 1

The correct option is D 515 Hz, 0.68 m

Since the source of sound is stationary, the wavelength remains unchanged by the motion of the observer.
Therefore, $\lambda =\frac{v}{f}=\frac{340}{500}=0.68m$
The frequency of sound heard by the observer, $f^{\prime }=\frac{Speedofsoundrelativetotheobserver}{Wavelength}$
$=\frac{340+10}{0.68}=514.7\simeq 515Hz$
Hence, the correct choice is (d).