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Old Oct 18th 2012, 11:18 AM   #1
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Determining speed and wavelength of wave

I'm a little stuck on a problem, and would really appreciate some help. The problem is as follows:

A water-skier is moving at a speed of 12.0 m/s. When she skis in the same direction as a travelling wave, she springs upward every 0.600 s because of the wave crests. When she skis in the direction opposite to the direction in which the wave moves, she springs upward every 0.500 s in response to the crests. The speed of the skier is greater than the speed of the wave. Determine a) the speed and b) the wavelength of the wave.

OK, so here I suppose we are supposed to use the formula:

v = fλ

I figured that when the skier is travelling with the wave, the frequency is: f_1 = 1/T_1 = 1/0.6 = 1.67 Hz

And when the skier is travelling against the wave, the frequency is: f_2 = 1/T_2 = 1/0.5 = 2 Hz

I then assume that we are supposed to have two separate equations such that:

v_1 = 1.67λ

v_2 = 2λ

However, I have a hard time finding a way to express the velocities in the two different scenarios. If anyone can help me along here, I would really appreciate it!
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Old Nov 4th 2013, 11:45 PM   #2
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Last edited by Aena44; Dec 17th 2014 at 11:54 PM.
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Old Nov 5th 2013, 07:37 AM   #3
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Your expressions for V1 and V2 are correct, so now the next step is to develop a formula for what v1 and v2 are. V1 is the relative velocity of the skier versus the wave when traveling in the same direction, and V2 is the relative velocity when traveling in opposite directions. So if we let V = velocity of wave, then:

v1 = 12 m/s - V
v2 = 12 m/s + V

Now you have two equations in two unknowns and can solve for both V and λ.
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Old Nov 10th 2013, 10:38 AM   #4
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If the skier is on a crest, the next crest is a distance lambda away from him.The skier moves a distance 12 X 0.6 m in 0.6 secs. In this time the crest in front would have traveled a distance = v x 0.6.away Thus in 0.6 secs, The skier has traveled a distance of lambda + 0.6v = 12 x 0.6
When the skier and the wave move in opposite directions, the equation would be lambda - 0.6 v = 12 x 0.5 as he meets the crest sooner as it is traveling towards him. Solve for the two unknowns
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Old Feb 1st 2014, 03:46 AM   #5
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