The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake withn a speed of `2 m//s` and a wavelength of `1.5 m`. When these waves move into a shallower part of the lake, their speed decreases to `1.6 m//s`, though their frequency remains the same. Find the wavelength of the wave in the shallower water.

Explanation

In the first case, as `v_1 = 2 m//s, lamda_1 = 1.5 m, v = (v)/(lamda) = (2 m//s)/(1.5 m) = (4)/(3) Hz`
In the second case, when the waves move into a shallower part of the lake, `v_2 = 1.6 m//s`
Since `v` remains the same, wavelength of the waves in the shallower water, i.e.,
`lamda_2 = (v_2)/(v) = (1.6 m//s)/((4//3) Hz) = 1.2 m`.