A crest of a water wave requires 5.2 s to travel between two points on a fishing pier located 19 m apart. It is noted in a series of waves that 20 crests pass the first point in 17 s. What is the wavelength of the waves?

Question

I know the steps required to solve the problem. My question is: why is 20 crests considered 20 waves? I thought that 1 wavelength = distance from crest to crest. So, why isn't the answer 10 waves? PLEASE help!

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Answer 1 · 2017-04-12T11:50:14

Here is what I think

It has been given that the water wave travels 19 m in 5.2s.

Hence velocity of the water wave is #v="distance traveled"/"time"=19/5.2=95/26m"/"s#

It is also given that 20 crests pass the first point in 17s.

The distance in between two consecutive crests are known as wave length. So 20 crests in a row will be composed of 19 waves.

As 20 crests pass the first point in 17 sec then distance traveled by the wave in 17s will be #=17xxvm=17xx95/26m#

So this will be length of 19 waves.

Hence wave length #lambda=(17xx95/26)/19# m

#=85/26# m

#~~3.27# m