Question

In the case of sound waves, wind is blowing from source to receiver with speed $U_w$. Both source and receiver are statiolnary. If ${\lambda }_0$ is the oriqinal wavelength with no wind and $V$ is speed of sound in air then wavelength as received by the receiver is given by

• A. ${\lambda }_0$
• B. $\left(\frac{V+U_w}{V}\right){\lambda }_0$
• C. $\left(\frac{V-U_w}{V}\right){\lambda }_0$
• D. $\left(\frac{V}{V+U_w}\right){\lambda }_0$

Answer 1

The correct option is B $\left(\frac{V+U_w}{V}\right){\lambda }_0$

When no wind,

$V=f{\lambda }_0-----\left(1\right)$

When velocity of wind is $U_w$,

$V+U_w=f{\lambda }^{\prime }-----\left(2\right)$

Dividing (1) by (2),

$V=f{\lambda }_0$

$V+U_w=f{\lambda }^{\prime }$

${\lambda }^{\prime }=\left(\frac{V+U_w}{V}\right){\lambda }_0$