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

Answer:

(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:

$T = \frac{1}{f}$                    (1)

where

f = frequency of the wave

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

$f = \frac{n}{t} = \frac{5}{74.9} = 0.667\ Hz$

Substitute f = 0.667 Hz in eqn (1):

$T = \frac{1}{0.667} = 14.98\ s$

(b) Wave's frequency is calculated as:

$f = \frac{n}{t} = \frac{5}{74.9} = 0.667\ Hz$

(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:

$c = \lambda f = 33.5\times 0.667 = 22.34\ m/s$