## College Physics (4th Edition)

The relative speed between the source and the receiver is $\frac{c}{2}$. Since the observed wavelength is longer than the emitted wavelength, the source and observer are moving farther apart.
Let $f_1$ be the frequency of the source. Let $f_2$ be the observed frequency. We can find the speed $v$ when $\lambda_2 = 2~\lambda_1$: $f_2 = f_1~(1-\frac{v}{c})$ $\frac{c}{\lambda_2} = \frac{c}{\lambda_1}~(1-\frac{v}{c})$ $\frac{c}{2\lambda_1} = \frac{c}{\lambda_1}~(1-\frac{v}{c})$ $\frac{1}{2} = 1-\frac{v}{c}$ $v = \frac{c}{2}$ The relative speed between the source and the receiver is $\frac{c}{2}$. Since the observed wavelength is longer than the emitted wavelength, the source and observer are moving farther apart.