Question

When source and detector are stationary but the wind is blowing at speed , the apparent wavelength ${\lambda }^{\prime }$ on the wind side is related to actual wavelength $\lambda$ by [take speed of sound in air as v]

• A. ${\lambda }^{\prime }=\lambda$
• B. ${\lambda }^{\prime }=\frac{v_w}{v}\lambda$
• C. ${\lambda }^{\prime }=\frac{v_w+v}{v}\lambda$
• D. ${\lambda }^{\prime }=\frac{v}{v-v_w}\lambda$

Answer 1

The correct option is C ${\lambda }^{\prime }=\frac{v_w+v}{v}\lambda$

${\lambda }^{\prime }=\frac{Wavespeedrelativetolistener}{f}\Rightarrow {\lambda }^{\prime }=\frac{v+v_{\omega }}{f}=\frac{v+v_{\omega }}{f}\lambda$