If a water wave with length L moves with velocity v in a body of water with depth d, then
where g is the acceleration due to gravity. (See Figure 5.)
Explain why the approximation
is appropriate in deep water.
To explain: The approximation
The length of the water wave is L and d is the depth of the water.
The velocity .
The hyperbolic functions .
The velocity of the water wave .
Here, the hyperbolic function occur and the value of is very large if water is deep.
Obtain the approximation value of the velocity when is large value.
The value of is computed as follows,
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