How Does Skier Speed Affect Wave Frequency and Wavelength?

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SUMMARY

The discussion focuses on determining the speed and wavelength of a wave based on the motion of a water-skier traveling at 12.5 m/s. The skier experiences wave crests every 0.498 seconds when moving with the wave and every 0.305 seconds when moving against it. The relationship between wave speed, wavelength, and period is established through the equations v = wavelength/period and wavelength = V/f. The key insight is that the apparent wavelength perceived by the skier varies based on her speed relative to the wave.

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  • Calculate the speed of the wave using the given periods and skier's speed
  • Determine the wavelength of the wave using the derived wave speed
  • Explore the concept of apparent wavelength in different reference frames
  • Review related physics problems involving wave motion and relative speed
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mmiller39
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I am trying to work through this problem to no avail.

Homework Statement



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.


Homework Equations



we know that v = wavelength/ period

and that wavelength equals V/f




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
 
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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?
 

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