Question

A wave of water behaves like a plane wave with a frequency of 12 Hz breaks as it passes a sharp barrier between deep and shallow water. The velocity of the wave's propagation in the deep water is 24 cm/s, the angle of the wave reaching the barrier is 60^o and the breaking wave angle at the barrier is 40^o.

a. What is the velocity of propagation of the wave in shallow water?

b. What is the wavelength in the shallow water and what is the wavelength in the deep water?

Answer 1

For a plane wave incident at an angle

_d/_s = Sin_d /Sin_s

_d, wave speed in deep waters = 24 m/s

_s wave speed in shallow waters

_d , angle of incidence in deep waters = 90-60 =30 deg

_s  , angle of transmission in shallow waters = 90-40 = 50 deg

The wave approaches the barrier at 60 deg, it makes an angle (90-60) with the normal and the same with transmitted wave (90-40) with the normal

24/_s = Sin30 / Sin50

wave speed in shallow waters  _s = 24 * Sin50 /Sin30 = 36.77 m/s

frequency of the wave f = 12 Hz, frequency of the wave remains same in both media for a plane wave

= f

wave length in shallow waters = 36.77 /12 = 3.06 m

wave length in deep waters = 24/12 = 2.0 m