Question

A train is moving at $30\text{ }m{{s}^{-1}}$ in still air. The frequency of the locomotive whistle is $500\, Hz$ and the speed of sound is $345\text{ }m{{s}^{-1}}$ . The apparent wavelength of sound in front of and behind the locomotive are respectively

• A. 0.80 m, 0.63 m
• B. 0.63 m, 0.80 m
• C. 0.50 m, 0.85 m
• D. 0.63 m, 0.75 m

Answer 1

Answer: (D)

0.63 m, 0.75 m

Answer 2

Apparent wavelength, in front of locomotive
$\lambda =\frac{\lambda (v-{{v}_{s}})}{v}$
Or $\lambda =\frac{v-{{v}_{s}}}{v}$
$=\frac{345-30}{500}=\frac{315}{500}=0.63\,m$
Behind locomotive, $\lambda \,\,=\frac{\lambda (v+{{v}_{s}})}{v}$
$=\frac{v+{{v}_{s}}}{v}$
$=\frac{345+30}{500}$
$=\frac{375}{500}$
$=0.75\,m$