Water Depth given Wavelength, Wave Period and Wave Number Calculator

✖Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave.ⓘ Wavelength [L]			+10% -10%
✖Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).ⓘ Wave Angular Frequency [ω]			+10% -10%
✖Wave Period is the time it takes for successive wave crests or troughs to pass a fixed point.ⓘ Wave Period [T]			+10% -10%
✖The Wave Number for Water Waves quantifies the number of waves per unit length along the surface of the water.ⓘ Wave Number for Water Wave [k]			+10% -10%

✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth given Wavelength, Wave Period and Wave Number [d]

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Water Depth given Wavelength, Wave Period and Wave Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave
d = (atanh((L*ω)/([g]*T)))/k
This formula uses 1 Constants, 2 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)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.
Wavelength - (Measured in Meter) - Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave.
Wave Angular Frequency - (Measured in Radian per Second) - Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega).
Wave Period - (Measured in Second) - Wave Period is the time it takes for successive wave crests or troughs to pass a fixed point.
Wave Number for Water Wave - The Wave Number for Water Waves quantifies the number of waves per unit length along the surface of the water.

STEP 1: Convert Input(s) to Base Unit

Wavelength: 0.4 Meter --> 0.4 Meter No Conversion Required
Wave Angular Frequency: 6.2 Radian per Second --> 6.2 Radian per Second No Conversion Required
Wave Period: 0.622 Second --> 0.622 Second No Conversion Required
Wave Number for Water Wave: 0.2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = (atanh((L*ω)/([g]*T)))/k --> (atanh((0.4*6.2)/([g]*0.622)))/0.2

Evaluating ... ...

d = 2.15750500220341

STEP 3: Convert Result to Output's Unit

2.15750500220341 Meter --> No Conversion Required

FINAL ANSWER

2.15750500220341 ≈ 2.157505 Meter <-- Water Depth

(Calculation completed in 00.020 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Predicting Waves in Deep Water Calculators

Significant Wave Height from Bretschneider Empirical Relationships

LaTeX Go Wave Height for Deep Water = (Wind Speed^2*0.283*tanh(0.0125*(([g]*Fetch Length)/Wind Speed^2)^0.42))/[g]

Wave Number given Wavelength, Wave Period and Water Depth

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

Water Depth given Wavelength, Wave Period and Wave Number

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

Significant Wave Period from Bretschneider Empirical Relationships

LaTeX Go Wave Period = (Wind Speed*7.54*tanh(0.077*(([g]*Fetch Length)/Wind Speed^2)^0.25))/[g]

Water Depth given Wavelength, Wave Period and Wave Number Formula

LaTeX Go

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

What is Wave Number?

Wave Number is the spatial frequency of a wave in a given medium, typically measured in reciprocal units of distance, such as radians per meter or cycles per meter.

What is Time period of a Wave?

The time taken for one complete oscillation in the density of the medium is called the time period of the wave. It can also be defined as the time taken by two consecutive compressions (Trough) or rarefactions (Crest) to cross a fixed point. It is represented by the symbol T.

How to Calculate Water Depth given Wavelength, Wave Period and Wave Number?

Water Depth given Wavelength, Wave Period and Wave Number calculator uses Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave to calculate the Water Depth, The Water Depth given Wavelength, Wave Period and Wave Number formula is defined as the vertical distance from the water surface to the seabed, determined by the wavelength, wave period, and wave number of a propagating wave. Water Depth is denoted by d symbol.

How to calculate Water Depth given Wavelength, Wave Period and Wave Number using this online calculator? To use this online calculator for Water Depth given Wavelength, Wave Period and Wave Number, enter Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Wave Number for Water Wave (k) and hit the calculate button. Here is how the Water Depth given Wavelength, Wave Period and Wave Number calculation can be explained with given input values -> 2.157505 = (atanh((0.4*6.2)/([g]*0.622)))/0.2.

FAQ

What is Water Depth given Wavelength, Wave Period and Wave Number?

The Water Depth given Wavelength, Wave Period and Wave Number formula is defined as the vertical distance from the water surface to the seabed, determined by the wavelength, wave period, and wave number of a propagating wave and is represented as d = (atanh((L*ω)/([g]*T)))/k or Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave. Wavelength is the distance between successive crests, troughs, or any corresponding points on a wave, Wave Angular Frequency is the rate of change of the phase of the wave over time, given by the symbol ω (omega), Wave Period is the time it takes for successive wave crests or troughs to pass a fixed point & The Wave Number for Water Waves quantifies the number of waves per unit length along the surface of the water.

How to calculate Water Depth given Wavelength, Wave Period and Wave Number?

The Water Depth given Wavelength, Wave Period and Wave Number formula is defined as the vertical distance from the water surface to the seabed, determined by the wavelength, wave period, and wave number of a propagating wave is calculated using Water Depth = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Wave Number for Water Wave. To calculate Water Depth given Wavelength, Wave Period and Wave Number, you need Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Wave Number for Water Wave (k). With our tool, you need to enter the respective value for Wavelength, Wave Angular Frequency, Wave Period & Wave Number for Water Wave and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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