Question

A sound source emits waves of frequency $f_0$ and wavelength $\lambda_0$ in still air. When there is a wind blowing with speed u from left to right what will be wavelength of sound to the right of the source and to the left of the source.

Answer 1

The wavelength of sound to the right of the source is $\lambda_0 + \frac{u}{f_0}$. The wavelength of sound to the left of the source is $\lambda_0 - \frac{u}{f_0}$.

Answer 2

To the right: Effective speed $v_{ground, right} = v + u$. Wavelength $\lambda_{right} = \frac{v + u}{f_0} = \frac{f_0 \lambda_0 + u}{f_0} = \lambda_0 + \frac{u}{f_0}$.

To the left: Effective speed $v_{ground, left} = v - u$. Wavelength $\lambda_{left} = \frac{v - u}{f_0} = \frac{f_0 \lambda_0 - u}{f_0} = \lambda_0 - \frac{u}{f_0}$.