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Homework Statement
I have sinusoidal waves traveling along the surface of the water. I'm given the relation [tex]v=\sqrt{gh}[/tex] where h is the depth of the water. I'm given that when the water is 5 m deep the wavelengt of the waves is 1.4 m. I"m asked how far apart the wave crests are near the shore.
Homework Equations
[tex]v=λf[/tex]
The Attempt at a Solution
Basically the wave starts somewhere in the middle of the pond and travels towards the shore, I need to find the wavelength as it approaches the shore, near the shore the water depth is only .5 m, so depth is decreasing, but not continuously, just see the pic, the upper right hand corner represents the shore.
The velocity therefore declines two times before it reaches the shore. I don't know how to find the wavelength when it's at the .5 m depth.
I've attempted to use the bolded data point to relate the wavelength to the velocity:
[tex]λ=\frac{1}{1.4 Hz}\sqrt{gh}[/tex]
But this relationship is almost certainly wrong because it assumes constant frequency.
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