# You are standing on a beach and 5 wave crests land on shore in 50 seconds. Each wave is 32m...

## Question:

You are standing on a beach and 5 wave crests land on shore in 50 seconds. Each wave is 32m apart. Find Frequency, period, wavelength and speed.

## Periodic wave

A periodic wave can be characterized by its frequency {eq}f {/eq} or period {eq}T {/eq}, wavelength {eq}\lambda {/eq} and wave speed {eq}v {/eq}. The frequency and period are related via {eq}f = 1/T {/eq}. While, the wave speed, frequency and wavelength are related via {eq}v = \lambda f {/eq}.

A crest to crest of a wave constitute a single cycle. When a crest land on the shore followed by another crest, that is a single cycle. Hence, 5 wave crests landing on shore in 50 seconds means 4 cycles in 50 seconds and so the frequency (which is a measure of number of cycles per unit time) is

{eq}f = \dfrac{4 \ \text{ cycles}}{50 \ \text{s}} = 0.08 \ \text{Hz}. {/eq}

The period is then

{eq}T = \dfrac{1}{f} = \dfrac{1}{0.08 \ \text{Hz}} = 12.5 \ \text{s}. {/eq}

Since each wave is 32 m apart, then the wavelength {eq}\lambda =32 \ \text{m} {/eq}. Finally, the wave speed is

{eq}v = \lambda f = (32 \ \text{m})(0.08 \ \text{Hz}) = 2.56 \ \text{m}/\text{s}. {/eq}

Therefore, the wave's frequency is 0.08 Hz, its period is 12.5 s, its wavelength is 32 m, and the wave speed is 2.56 m/s.