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Instructions
Write down the equation for idealized ocean wave speed, which is as follows:
velocity = ( (gλ / 2π) (tanh (2πd / λ) ) )^1/2
where g is 9.8 meters per second squared, λ is the wavelength of the waves, d is the depth and you take the square root of everything inside the parentheses; tanh is an algebraic expression such that tanh x = (e^2x - 1)/(e^2x + 1).
Calculate 2π d / λ. Plug in the depth, divide it by the wavelength and multiply by 2π.
Example: If depth is 6 meters and λ is 10 meters, (6/10) * 2π = 3.769.
Take your result from the last step and substitute it for x in the following equation:
(e^2x - 1)/(e^2x + 1)
Example: You found 3.769 in the last step, so multiply by 2 to get 7.538 and raise e to this power. (Remember that e is a number in math. Most calculators have an e^x button on them, so just enter 7.538 on your calculator and hit the e^x button.) If you subtract 1 from this result, then divide by this result plus 1, you get 0.9989.
Calculate gλ/2π by plugging in your figure for λ.
Example: You know that g is 9.8 meters per second squared. In our example, λ is 10, so (9.8)(10)/2π = 15.597.
Multiply the result for gλ/2π by the result from step 3, then take the square root.
Example: (15.597)(0.9989) = 15.579. The square root of this # is 3.947 meters per second. This is the speed of the wave with respect to stationary water.
Add the velocity of the current in the direction of the wave to the number you found in the last step if the water at the beach is not stationary -- if there is a current flowing that affects the behavior of the wave.
Example: If a current flows towards the shore with a net water velocity of 0.2 meters per second, add 0.2 meters per second to the number from the last step.