Question

An observer is approaching with a speed v, towards a stationary source emitting sound waves of wavelength ${\lambda }_0$.The wavelength shift detected by the observer is [Velocity of Sound: $c$ ]

• A. $\frac{{\lambda }_{o}v}{c}$
• B. $\frac{{\lambda }_{o}c}{v}$
• C. $\frac{{\lambda }_o{v}^2}{c^2}$
• D. Zero

Answer 1

The correct option is A $\frac{{\lambda }_{o}v}{c}$

Doppler shift for a sound wave when the observer is moving towards a stationary source can be given as:

$f^{\prime }=\frac{f_0(c+v)}{c}$

$\Rightarrow f^{\prime }c=f_{0}c+f_{0}v$

$\Rightarrow (f^{\prime }-f_0)c=f_{0}v$
$(\frac{c}{{\lambda }^{\prime }}-\frac{c}{{\lambda }_0})c=f_{0}v$
$\frac{({\lambda }_0-{\lambda }^{\prime })}{{\lambda }^{\prime }{\lambda }_0}{c}^2\approx \frac{\Delta \lambda }{{\lambda }_0^2}{c}^2=f_{0}v=\frac{c}{{\lambda }_0}v$
$\Delta \lambda =\frac{{\lambda }_{0}v}{c}$

The correct option is $\left(A\right)$.