If 360 ocean water waves, each 20 meters long, hit the shore every hour, what is the wave speed? What is the wave period?

1 Answer
Steve J.
Apr 6, 2018

#v = 2 m/s and T = 10 s#

Explanation:

Wave speed:
So the crests of these waves are 20 m apart. (That is called wavelength.)360 of these come ashore every hour. Let's look at the waves that are on the way to the shore. When the first of those 360 waves hits the shore, the distance, s, from the shore to the last one that would hit the shore in the hour was

#s = (20 m)/(1 "wave")* 360 "waves" = 7200 m#

So the wave speed, v, is

#v = (7200 m)/(3600 s) = 2 m/s#

Wave period:
The formula that relates wavelength, #lambda#; frequency, #f#; and wave speed, #v#; is

#v = lambda*f#

Period, #T#, is the inverse of frequency, #f#. Therefore we can write that the above formula can be rewritten

#v = lambda/T#

Therefore,

#T = lambda/v = (20 m)/(2 m/s) = 10 s#

I hope this helps,
Steve

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