Question

In the case of sound waves, wind is blowing from source to receiver with speed U_w. Both the source and the receiver are stationary. If λ₀is the original wavelength with no wind and V is speed of sound in air then the wavelength as received by the receiver is given by:

• A. λ₀
• 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

Answer: (B)

$\left( \frac{V + U_{w}}{V} \right)\lambda_{0}$

Answer 2

If f₀ is frequency of source then in ∆t time, it sends N = f₀t waves. These are now contained in distance (V + U_w)∆t.

Thus λ' = $\frac{\left( V + U_{w} \right)\Delta t}{f_{0}\Delta t}$

$\frac{\left( V + U_{w} \right)}{f_{0}} = \frac{\left( V + U_{w} \right)}{V}\lambda_{0}$