Question

A railroad train is travelling at 30 m/s in still air. The frequency of the note emitted by the locomotive whistle is 500 Hz. The wavelength of the sound waves behind the locomotive is $748\times {10}^{-x}m$. Find x.

Answer 1

Apparent wavelength of sound , when source of sound is moving away from a stationary observer is given by ,

${\lambda }^{\prime }=\lambda \left(\frac{v+v_s}{v}\right)$ ,

or ${\lambda }^{\prime }=\frac{v}{f}.\left(\frac{v+v_s}{v}\right)$

where $\lambda =$ original wavelength of sound ,

$v_s=$ speed of source ,

$v=$ speed of sound ,

$f=$ frequency of sound ,

given $v=344m/s,v_s=30m/s,f=500Hz$ ,

therefore , ${\lambda }^{\prime }=\frac{344+30}{500}=374/500=0.748m$