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Phase Speed of Water Wave

The phase speed of a water wave is the rate at which the phase of the wave propagates through the water.

The wave propagation speed equals the square root of the gravitational acceleration times the tangent of the product of the depth of water and the wavenumber divided by the wavenumber. The wavenumber equals 2\[Pi] divided by the wavelength.

Formula

{QuantityVariable["v", "Speed"] == Sqrt[(QuantityVariable["g", "GravitationalAcceleration"]*Tanh[QuantityVariable["d", "Depth"]*QuantityVariable["k", "Wavenumber"]])/QuantityVariable["k", "Wavenumber"]], QuantityVariable["k", "Wavenumber"] == (2*Pi)/QuantityVariable["λ", "Wavelength"]}

symbol description physical quantity
v wave propagation speed "Speed"
g gravitational acceleration "GravitationalAcceleration"
k wavenumber "Wavenumber"
d depth of water "Depth"
λ wavelength "Wavelength"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Phase Speed of Water Wave"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Phase Speed of Water Wave"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Phase Speed of Water Wave"], {QuantityVariable["k","Wavenumber"] -> None, QuantityVariable["g","GravitationalAcceleration"] -> Quantity[9.81`, ("Meters")/("Seconds")^2], QuantityVariable["v","Speed"] -> Quantity[1.25`, ("Meters")/("Seconds")]}]
Out[3]=

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