Answer to Question #122351 in Physics for Lilly

Question

In deep water, a wave has a speed of 53 cm/s and a wavelength of 4.1 cm. When it enters
into shallow water, its wavelength decreases to 1.6 cm. Find the speed of the water wave
in shallow water. (Hint: Which property remains the same?)

Answer 1

At different medium the frequency of wave is the same, so

$$f=\frac{v_1}{\lambda_1}=\frac{v_2}{\lambda_2}.$$

Hence, the speed of the water wave in shallow water

$$v_2=v_1\frac{\lambda_2}{\lambda_1}=53\:\rm cm/s\times \frac{1.6\;\rm cm}{4.1\;\rm cm}=21\:\rm cm/s$$