# Waves and Wave Speeds

1. Dec 4, 2006

### mmiller39

I am trying to work through this problem to no avail.

1. The problem statement, all variables and given/known data

A water-skier is moving at a speed of 12.5 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.498 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.305 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.

2. Relevant equations

we know that v = wavelength/ period

and that wavelength equals V/f

3. The attempt at a solution

I am having trouble deriving period from the given data. I know that the speed of the wave is propotional to the speed of the water skier, but I am not sure about the correct ratio to use.

any help is appreciated.

-Matt

2. Dec 4, 2006

### Staff: Mentor

The speed of the wave has nothing to do with the speed of the water skier. The rate at which the skier hits the wave peaks is related to both the speed of the skier and the wave speed. What is the apparent wavelength of the water wave from the skier's point of view ("reference frame") in each direction? And how can you use those wavelengths to get you your answers?