When wind blows over the sea, it excites a range of wavelengths.
Why do longer wavelengths travel faster?
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- deep water limit : when the wavelength of the mode/wave is much less than the depth of the water
- shallow water limit : when the wavelength of the mode/wave is much larger than the water depth
Answer
Why do longer wavelengths travel faster?
In the deep water limit, the phase speed of, say, a gravity wave is $V_{ph} \propto \sqrt{\lambda}$, where $\lambda$ is the wavelength. This is because the waves are dispersive, i.e., their frequency depends upon their wavenumber/wavelength.
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