## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) $t = 180~s$ (b) The signal is detected at a wavelength of 488 nm
(a) We can find the time it takes the signal to reach the planet: $t = \frac{d}{v}$ $t = \frac{54\times 10^6~km}{3.0\times 10^5~km/s}$ $t = 180~s$ (b) We can find the wavelength that the signal is detected: $\lambda' = \lambda_0~\frac{\sqrt{1-v/c}}{\sqrt{1+v/c}}$ $\lambda' = (540~nm)~\frac{\sqrt{1-0.1c/c}}{\sqrt{1+0.1c/c}}$ $\lambda' = (540~nm)~\frac{\sqrt{0.9}}{\sqrt{1.1}}$ $\lambda' = 488~nm$ The signal is detected at a wavelength of 488 nm.