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?

1 Answer
Rohan A.K
Feb 12, 2017

#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.

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