Wavelength given wave celerity and wave speed Calculator

✖Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%
✖Wave Celerity is the speed at which an individual wave advances or propagates.ⓘ Wave Celerity [C]			+10% -10%
✖Wave Period is the time between successive peaks or troughs.ⓘ Wave Period [T]			+10% -10%

✖Wavelength can be defined as the distance between two successive crests or troughs of a wave.ⓘ Wavelength given wave celerity and wave speed [λ]

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Formula

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Wavelength given wave celerity and wave speed

Formula

`"λ" = (2*pi*"d")/(atanh((2*"C"*pi)/("[g]"*"T")))`

Example

`"10.06874m"=(2*pi*"1.55m")/(atanh((2*"3.5m/s"*pi)/("[g]"*"3s")))`

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Wavelength given wave celerity and wave speed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
λ = (2*pi*d)/(atanh((2*C*pi)/([g]*T)))
This formula uses 2 Constants, 2 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Wavelength - (Measured in Meter) - Wavelength can be defined as the distance between two successive crests or troughs of a wave.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body.
Wave Celerity - (Measured in Meter per Second) - Wave Celerity is the speed at which an individual wave advances or propagates.
Wave Period - (Measured in Second) - Wave Period is the time between successive peaks or troughs.

STEP 1: Convert Input(s) to Base Unit

Water Depth: 1.55 Meter --> 1.55 Meter No Conversion Required
Wave Celerity: 3.5 Meter per Second --> 3.5 Meter per Second No Conversion Required
Wave Period: 3 Second --> 3 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

λ = (2*pi*d)/(atanh((2*C*pi)/([g]*T))) --> (2*pi*1.55)/(atanh((2*3.5*pi)/([g]*3)))

Evaluating ... ...

λ = 10.0687411343781

STEP 3: Convert Result to Output's Unit

10.0687411343781 Meter --> No Conversion Required

FINAL ANSWER

10.0687411343781 ≈ 10.06874 Meter <-- Wavelength

(Calculation completed in 00.004 seconds)

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Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 14 Wavelength Calculators

Water depth given wave celerity and wavelength

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

Wavelength given wave celerity and wave speed

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

Eckert's equation for Wavelength

Go Wavelength = Deep-Water Wavelength*sqrt(tanh((2*pi*Water Depth)/Deep-Water Wavelength))

Wavelength as Function of Water Depth and Wave Period

Go Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)

Wavelength as Function of Depth and Wave Period

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

Wavelength given Deepwater Wavelength

Go Wavelength = Deep-Water Wavelength*tanh(Wave Number*Water Depth)

Long Wave simplification for Wavelength

Go Wavelength = Wave Period*sqrt([g]*Water Depth)

Wavelength given Deepwater celerity and Deepwater wavelength

Go Wavelength = (Deep-Water Wavelength*Wave Celerity)/Deepwater Wave Celerity

Deepwater wavelength given Deepwater celerity

Go Deep-Water Wavelength = (Wavelength*Deepwater Wave Celerity)/Wave Celerity

Deepwater Wavelength given Celerity of Deepwater Wave

Go Deep-Water Wavelength = (Deepwater Wave Celerity^2*2*pi)/[g]

Deepwater Wavelength given Wave Celerity

Go Deep-Water Wavelength = Deepwater Wave Celerity*Wave Period

Wavelength given wave celerity

Go Wavelength = Wave Celerity*Wave Period

Deepwater Wavelength given Units of Feet

Go Deep-Water Wavelength in Feet = 5.12*Wave Period^2

Deepwater Wavelength when SI systems Units of meters is considered

Go Deep-Water Wavelength = 1.56*Wave Period^2

Wavelength given wave celerity and wave speed Formula

Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period)))
λ = (2*pi*d)/(atanh((2*C*pi)/([g]*T)))

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, λ. 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 travels at higher speed.

How to Calculate Wavelength given wave celerity and wave speed?

Wavelength given wave celerity and wave speed calculator uses Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period))) to calculate the Wavelength, The Wavelength given wave celerity and wave speed is defined as the distance between two identical points on successive waves. Wavelength is denoted by λ symbol.

How to calculate Wavelength given wave celerity and wave speed using this online calculator? To use this online calculator for Wavelength given wave celerity and wave speed, enter Water Depth (d), Wave Celerity (C) & Wave Period (T) and hit the calculate button. Here is how the Wavelength given wave celerity and wave speed calculation can be explained with given input values -> 6.82076 = (2*pi*1.55)/(atanh((2*3.5*pi)/([g]*3))).

FAQ

What is Wavelength given wave celerity and wave speed?

The Wavelength given wave celerity and wave speed is defined as the distance between two identical points on successive waves and is represented as λ = (2*pi*d)/(atanh((2*C*pi)/([g]*T))) or Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period))). Water Depth of the considered catchment. Water depth means the depth as measured from the water level to the bottom of the considered water body, Wave Celerity is the speed at which an individual wave advances or propagates & Wave Period is the time between successive peaks or troughs.

How to calculate Wavelength given wave celerity and wave speed?

The Wavelength given wave celerity and wave speed is defined as the distance between two identical points on successive waves is calculated using Wavelength = (2*pi*Water Depth)/(atanh((2*Wave Celerity*pi)/([g]*Wave Period))). To calculate Wavelength given wave celerity and wave speed, you need Water Depth (d), Wave Celerity (C) & Wave Period (T). With our tool, you need to enter the respective value for Water Depth, Wave Celerity & Wave Period 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 Water Depth, Wave Celerity & Wave Period. We can use 7 other way(s) to calculate the same, which is/are as follows -

Wavelength = Wave Celerity*Wave Period
Wavelength = (([g]*Wave Period^2)/(2*pi))*tanh(Wave Number*Water Depth)
Wavelength = (([g]*Wave Period)/Wave Angular Frequency)*tanh(Wave Number*Water Depth)
Wavelength = (Deep-Water Wavelength*Wave Celerity)/Deepwater Wave Celerity
Wavelength = Deep-Water Wavelength*tanh(Wave Number*Water Depth)
Wavelength = Deep-Water Wavelength*sqrt(tanh((2*pi*Water Depth)/Deep-Water Wavelength))
Wavelength = Wave Period*sqrt([g]*Water Depth)

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