Question

A woman is standing in the ocean, and she notices that after a wave crest passes by, five more crests pass in a time of 74.9 s. The distance between two successive crests is 33.5 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed?

Answer 1

(a) Time period is 14.98 s

(b) Frequency is 0.667 Hz

(c) Wavelength is 33.5 m

(d) Speed is 22.34 m/s

Solution:

As per the question:

No. of wave crest, n = 5

Time taken, t = 74.9 s

Distance between two successive crest, d = 33.5 m

Now,

To calculate:

(a) Time period of the wave, T can be calculated as:

`T = (1)/(f)` (1)

where

f = frequency of the wave

The frequency of the wave is given by the no. of wave crest passed in time t:

`f = (n)/(t) = (5)/(74.9) = 0.667\ Hz`

Substitute f = 0.667 Hz in eqn (1):

`T = (1)/(0.667) = 14.98\ s`

(b) Wave's frequency is calculated as:

`f = (n)/(t) = (5)/(74.9) = 0.667\ Hz`

(c) Wavelength of the wave,
`\lambda`:

The wavelength of the wave can be defined as the distance between two successive crests of the wave.

Thus

Distance between the two successive crests of the wave, d = 33.5 m

Hence, the wavelength,
`\lambda = d = 33.5\ m`

(d) The speed of the wave can be given by the relation:

`c = \lambda f = 33.5* 0.667 = 22.34\ m/s`