Velocity of a wave decreases as the water gets shallow

[kusal]

Velocity of a wave decreases as the water gets shallow. As described in-

v*v=gh
(v=velocity
g=gravity
h=depth)

as v=fλ

(λ=wave length
f=frequency)

Either f or λ has to decrease.
But as f is a constant where the same emitter is concerned the wavelength decreases.
Velocity is lower in the front of the wave than the back of it because sea gets shallow near the shore. So the wavelength decreases as it gets to the shore. But the amount of water is the same. So the amplitude has to rise. Water is pushed upwards.

What are yor comments?

 

[OlderDan]

There may be some fine points in the equations, but the basic idea is correct. Waves do travel slower in shallow water causing the back end of the wave to squeze toward the front and raise the amplitude. The slowing of the front is what causes the familiar "breaking" of ordinary waves at the shoreline.

The slowing of waves at shallower depth is the basis for "ripple tank" demonstrations of wave phenonomna.

 

[charng]

As the water gets shallow, the velocity of the wave decreases due to the change in depth. This change in velocity can be explained by the equation v = fλ, where v is the velocity, f is the frequency, and λ is the wavelength. As the water gets shallower, the wavelength decreases while the frequency remains constant. This means that the velocity must decrease in order to maintain the relationship between wavelength and frequency.

Additionally, the decrease in velocity may also be influenced by the equation v^2 = gh, where v is the velocity, g is the acceleration due to gravity, and h is the depth of the water. As the depth decreases, the acceleration due to gravity may also decrease, resulting in a lower velocity for the wave.

It is also important to note that the decrease in velocity may not be uniform throughout the wave. As mentioned, the front of the wave may have a lower velocity than the back of the wave due to the shallower water near the shore. This can also lead to an increase in amplitude as the water is pushed upwards.

In conclusion, the decrease in velocity of a wave as the water gets shallow can be explained by the relationship between wavelength, frequency, and depth, as well as the influence of gravity. Observing and understanding these changes in velocity can provide valuable insights for scientists studying wave behavior and coastal environments.