Question

A fisherman notices that wave crests pass the bow of his anchored boat every 3.4 s. He measures the distance between two crests to be 8.2 m. How fast are the waves traveling?

Answer 1

Concepts and reason

The concepts used to solve this question is the speed of the wave.

Initially, determine the frequency of the wave and later use the relation between speed and the wavelength to determine the speed of the wave.

Fundamentals

A wave is a form of disturbance which transfers energy through space or matter. The distance between two crests or troughs is called a wavelength of the wave. It is measured in meters.

The number of cycles completed by the wave per second is called a frequency of the wave. It is measured in Hertz.

The wave speed is defined as,

$v = \lambda f$

Here, $\lambda$ is the wavelength and $f$ is the frequency of the wave.

The frequency of the wave is defined as,

$f = \frac{1}{T}$ …… (1)

Here, $T$ is the time period of the wave.

Substitute $3.4{\rm{ s}}$ for $T$ in the equation (1).

$\begin{array}{c}\\f = \frac{1}{T}\\\\ = \frac{1}{{3.4{\rm{ s}}}}\\\\ = 0.294{\rm{ Hz}}\\\end{array}$

The relation between wave speed and frequency is,

$v = \lambda f$ …… (2)

Substitute $8.2{\rm{ m}}$ for $\lambda$ and $0.294{\rm{ Hz}}$ for $f$ in the equation (2).

$\begin{array}{c}\\v = \lambda f\\\\ = \left( {8.2{\rm{ m}}} \right)\left( {0.294{\rm{ Hz}}} \right)\\\\ = 2.41{\rm{ m/s}}\\\end{array}$

Ans:

The speed of the waves is $2.41{\rm{ m/s}}$