Speed of Water Waves

[SaintJude]

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If six ocean wave crests with a wavelength of 48 m crash into a harbor every minute, what is the speed of the waves?

2 Qs:

1.) Why can we use the v=f(lambda) equation, when velocity in a deformable medium is supposedly only affected by the medium's physical properties?

2.) Also , I interpreted six ocean waves having a total wavelength of 48 m. By definition, does the wavelength only pertain to the length of a single wave ?

Also six ocean waves hitting the crest is 5 cycles, not 6 cycles!! So frequency = 5 cycles/ 60 seconds OR 1/12 Hz. In general, the appearance of the nth wavelength represents the completion of "n-1" cycles. I've made this mistake 2x so far...

 

[chiddler]

Sorry i don't know how to answer #1. But for #2, It's by definition the length of the wave at which the wave repeats itself. Could be from wave to wave, could be from trough to trough, et cetera.

tricky, unusual wording: "6 ocean wave crests".

 

[Arctangent]

1. The v = f * lambda equation is applicable to any wave with constant frequency and wavelength. In describing waves, f can be thought of as waves/s, and wavelength is basically m/wave. By dimensional analysis, the product necessarily yields the velocity.

2. Wavelength itself does refer to the length of only one wave. As far as the number of cycles/waves that occur in one minute, I'd actually be inclined to think 6 cycles occurred. As the waves have a constant wavelength, and all the info you are given is that in any given time period of 60s, you have 6 crests/peaks, depending on where the time is taken, you can actually have 5 or 6 waves occur.

Assume the frequency is 5 waves/minute, or equivalently the period is 12s. Then if you count your first crest at 0s, you will actually count 6 crests (12, 24, 36, 48, 60). However, if this was your time frame, and say your next "minute" was 60s-120s, you would count crests at (60, 72, 84, 96, 108, 120), again 6 crests, but it can be argued that the 60s crest would be counted twice. If your first crest does not occur at t = 0s, then you will count 5 crests, which contradicts the question.

Considering the case where frequency is 6 waves/minute, or the period is 10s, you will similarly count 7 crests in a minute if there is a crest at t = 0 (though this could be argued to be 6 crests), whereas if there is not a crest at t = 0s, there will be 6 crests.

 

[dmf2682]

Suddenly I have this urge to brush my teeth!

I'd agree with arctan

 

[SaintJude]

Thanks--it's 5 cycles. Let's focus on the conceptual understanding b/c the mathematical proof you've outligned not only takes too long, but may lead to quick errors for some (maybe not you) under pressure like test day.

The problem is partially visualized here. You're on the beach front & have a stop watch and start watching for when the top of the crest hits (noted by the red line) the harbor again. How many complete cycles will you measure after seeing the second water crest hit the harbor ? 1.

And looked this up via another source and now understand that the v=f x lambda is still applicable in velocity on a string, like EK says, but it just does NOT depend on the frequency. So v =f x lambda can be used, but a change in frequency won't affect the velocity. Only the medium's physical properties will cause that change--and so using v=f (lambda) is no exception here.