Wavelength as Function of Water Depth and Wave Period Calculator

✖Wave Period is the time between successive peaks or troughs.ⓘ Wave Period [T]			+10% -10%
✖Wave Angular Frequency is a measure of how quickly the phase of the wave changes over time.ⓘ Wave Angular Frequency [ω]			+10% -10%
✖Wave Number is the number of wavelengths per unit distance along the propagation of a wave.ⓘ Wave Number [k]			+10% -10%
✖Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%

✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength as Function of Water Depth and Wave Period [λ]

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Wavelength as Function of Water Depth and Wave Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
λ = (([g]*T)/ω)*tanh(k*d)
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)

Variables Used

Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Wave Period - (Measured in Second) - Wave Period is the time between successive peaks or troughs.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is a measure of how quickly the phase of the wave changes over time.
Wave Number - Wave Number is the number of wavelengths per unit distance along the propagation of a wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Wave Period: 3 Second --> 3 Second No Conversion Required
Wave Angular Frequency: 2.5 Radian per Second --> 2.5 Radian per Second No Conversion Required
Wave Number: 5 --> No Conversion Required
Water Depth: 1.55 Meter --> 1.55 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = (([g]*T)/ω)*tanh(k*d) --> (([g]*3)/2.5)*tanh(5*1.55)

Evaluating ... ...

λ = 11.7679756331591

STEP 3: Convert Result to Output's Unit

11.7679756331591 Meter --> No Conversion Required

FINAL ANSWER

11.7679756331591 ≈ 11.76798 Meter <-- Wavelength

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Wavelength Calculators

Wavelength given Wave Celerity and Wave Speed

LaTeX Go Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))

Wavelength as Function of Depth and Wave Period

LaTeX Go Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)

Deepwater Wavelength given Wave Celerity

LaTeX Go DeepWater Wavelength = Deepwater Wave Celerity*Wave Period

Wavelength given Wave Celerity

LaTeX Go Wavelength = Wave Celerity*Wave Period

Wavelength as Function of Water Depth and Wave Period Formula

LaTeX Go

Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
λ = (([g]*T)/ω)*tanh(k*d)

What are Water Waves & Wave Energy?

A wave, a ridge or swell on the surface of a body of water, normally having a forward motion distinct from the oscillatory motion of the particles that successively compose it. Water waves are considered oscillatory or nearly oscillatory if the motion described by the water particles is circular orbits that are closed or nearly closed for each wave period.
Wave energy (or wave power) is the transport and capture of energy by ocean surface waves. The energy captured is then used for all different kinds of useful work, including electricity generation, water desalination, and pumping of water.

How does Depth affect Wavelength?

The change from deep to shallow water waves occurs when the depth of the water, d, becomes less than one-half of the wavelength of the wave. The speed of deep-water waves depends on the wavelength of the waves. We say that deep-water waves show dispersion. A wave with a longer wavelength travel at a higher speed.

How to Calculate Wavelength as Function of Water Depth and Wave Period?

Wavelength as Function of Water Depth and Wave Period calculator uses Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth) to calculate the Wavelength, The Wavelength as Function of Water Depth and Wave Period formula is defined as the distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space given as the function of the time it takes for two successive crests or troughs of a wave to pass a specific point on the water surface. Wavelength is denoted by λ symbol.

How to calculate Wavelength as Function of Water Depth and Wave Period using this online calculator? To use this online calculator for Wavelength as Function of Water Depth and Wave Period, enter Wave Period (T), Wave Angular Frequency (ω), Wave Number (k) & Water Depth (d) and hit the calculate button. Here is how the Wavelength as Function of Water Depth and Wave Period calculation can be explained with given input values -> 11.76733 = (([g]*3)/2.5)*tanh(5*1.55).

FAQ

What is Wavelength as Function of Water Depth and Wave Period?

The Wavelength as Function of Water Depth and Wave Period formula is defined as the distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space given as the function of the time it takes for two successive crests or troughs of a wave to pass a specific point on the water surface and is represented as λ = (([g]*T)/ω)*tanh(k*d) or Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth). Wave Period is the time between successive peaks or troughs, Wave Angular Frequency is a measure of how quickly the phase of the wave changes over time, Wave Number is the number of wavelengths per unit distance along the propagation of a wave & Water Depth of the considered catchment is measured from the water level to the bottom of the considered water body.

How to calculate Wavelength as Function of Water Depth and Wave Period?

The Wavelength as Function of Water Depth and Wave Period formula is defined as the distance between identical points (adjacent crests) in adjacent cycles of waveform signal propagated in space given as the function of the time it takes for two successive crests or troughs of a wave to pass a specific point on the water surface is calculated using Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth). To calculate Wavelength as Function of Water Depth and Wave Period, you need Wave Period (T), Wave Angular Frequency (ω), Wave Number (k) & Water Depth (d). With our tool, you need to enter the respective value for Wave Period, Wave Angular Frequency, Wave Number & Water Depth and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Wavelength?

In this formula, Wavelength uses Wave Period, Wave Angular Frequency, Wave Number & Water Depth. We can use 3 other way(s) to calculate the same, which is/are as follows -

Wavelength = Wave Celerity*Wave Period
Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)

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