Answer to Question #219387 in Physics for yourmom

Question

The speed and wavelength of coastal water waves are 4.0 m/s and 6.0 m respectively. When the waves enter a shallower region, the speed decreases to 1.7 m/s. What is the wavelength in the shallower region?

Answer 1

The frequency of the waves is given as follows:

$$f = \dfrac{v_1}{\lambda_1}$$

where $v_1 = 4m/s, \lambda_1 = 6m$. Assuming the frequency did not change, the wavelength in the shallower region is given as follows:

$$\lambda_2 = \dfrac{v_2}{f} = \dfrac{v_2\lambda_1}{v_1}$$

where $v_2 = 1.7m/s$. Thus, obtain:

$$\lambda_2 = \dfrac{1.7\cdot 6}{4} \approx 2.6m$$

Answer. 2.6 m.