Question

Some water waves reach the beach at a rate of one every 3.2 s, and the distance between their crests is 2.1 m. Calculate the speed of these waves.

Short answer

The speed of the water wave is 0.65 m/sec.

Step-by-step solution

Speed of wave 

Thewave equation gives the formula to calculate the speed of the wave shown as follows:

$\begin{array}{c}\mathrm{Speed}=\mathrm{wavelength}\times \mathrm{frequency}\\ =\lambda \times \upsilon \end{array}$

Speed of water wave

The formula to calculate the speed of the water wave is as follows:

$\mathrm{Speed}=\mathrm{wavelength}\left(\mathrm{\lambda }\right)\times \mathrm{frequency}\left(\mathrm{\upsilon }\right)$

The frequency of the wave is calculated as follows:

$\begin{array}{c}\mathrm{\upsilon }\text{\hspace{0.17em}=\hspace{0.17em}}\frac{\text{1}}{\text{T}}\\ \text{=}\frac{\text{1}}{\text{3.2\hspace{0.17em}sec}}\\ {\text{=\hspace{0.17em}0.312\hspace{0.17em}sec}}^{\text{-1}}\end{array}$

Here:

• The wavelength of the water wave is 2.1m.
• The frequency of the water wave is$0.312{\sec }^{-1}$.

Substituting the known value in the formula ofthe speed of the wave is done as follows:

$\begin{array}{c}\text{Speed\hspace{0.17em}=\hspace{0.17em}λ×\hspace{0.17em}}\mathrm{\upsilon }\\ {\text{=\hspace{0.17em}2.1\hspace{0.17em}m×0.312\hspace{0.17em}sec}}^{\text{-1}}\\ \text{=\hspace{0.17em}0.65\hspace{0.17em}m/sec}\end{array}$