Question

An ocean wave as a wavelength of 10 meters. These waves pass by a stationary boat every 2.0 seconds. What is the speed of the waves?

Answer 1

`v=5m//s`

Explanation:

The speed of a wave can be found by using the equation `v=lambdanu` where `lambda` is the wavelength of the wave and `nu` its frequency.

The question already has given us the wavelength of these waves to be `10m` meaning `lambda=10m`
The task at hand is now to find the frequency of these waves.

Consider the information given with regard to frequency. We know that the frequency of a given wave is the number of cycles it takes in a set number of seconds. A wave passes through a stationary boat every 2 seconds. A wave passing through a boat implies that a crest or trough has passes through a boat, here it does so every 2 seconds. This implies that for every one cycle, 2 seconds pass.

We now know for each cycle 2 seconds pass, hence
`nu=1`cycle`/2` seconds `implies nu=1/2/s`

Substituting for `lambda` and `nu`,
`v=10/2m//s`

I'm sure the rest will be done smoothly.