A person sitting on a pier observes incoming waves that have a sinusoidal form with a distance of 2.5 m between the crests. Of a wave laps against the pier every 5.0 s, what are (a) the frequency and (b) the speed of the wave?

Part(a): The frequency is .

Part(b): The speed of the wave is .

Explanation:

Given:

The distance between the crests of the wave, .

The time required for the wave to laps against the pier,

The distance between any two crests of a wave is known as the wavelength of the wave. So the wavelength of the wave is .

Also, the time required for the wave for each laps is the time period of oscillation and it is given by .

Part(a):

The relation between the frequency and time period is given by

Substituting the value of in equation (1), we have

Part(b):

The relation between the velocity of a wave to its frequency is given by

Substituting the value of and in equation (2), we have