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Q85.

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 454

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Short Answer

A water wave is a shallow-water wave if the water depth d is less than ≈ l/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v = 1gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than ≈ 10 m. Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.0 m at a distance of 100 m. How long does it take a wave to move the last 100 m to the shore? Assume that the waves are so small that they don’t break before reaching the shore

t = 28.571 sec

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Step by Step Solution

Given Info:

Given Info:

Depth increases from 0 to 5m from distance 0 to 100m.

Slope of this surface =

If x is the distance from shore, depth of water can directly be found as d(x) = 0.05x

similarly velocity can be stated as a function of x as

Finding time

We know that time taken can be found as integral of inverse of velocity.

Substituting values in above equation

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