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 50.2 s. The distance between two successive crests is 30.2 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed

Answer 1

Explanation:

(a) The period of a wave is the time required for one complete cycle. In this case, we have the time of five cycles. So:

$T=\frac{t}{n}\\\\T=\frac{50.2s}{5}\\T=10.04s$

(b) The frequency of a wave is inversely proportional to its period:

$f=\frac{1}{T}\\f=\frac{1}{10.04s}\\f=0.01Hz$

(c) The wavelength is the distance between two successive crests, so:

$\lambda=30.2m$

(d) The speed of a wave is defined as:

$v=f\lambda\\v=(0.1Hz)(30.2m)\\v=3.02\frac{m}{s}$