Wave Number given Wavelength, Wave Period and Water Depth 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%
✖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%

✖The wave number for water waves quantifies the number of waves per unit length along the surface of the water.ⓘ Wave Number given Wavelength, Wave Period and Water Depth [k]

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Wave Number given Wavelength, Wave Period and Water Depth

Formula

`"k" = (atanh(("L"*"ω")/("[g]"*"T")))/"d"`

Example

`"0.200698"=(atanh(("0.4m"*"6.2rad/s")/("[g]"*"0.622s")))/"2.15m"`

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Wave Number given Wavelength, Wave Period and Water Depth Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.
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.

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
Water Depth: 2.15 Meter --> 2.15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = (atanh((L*ω)/([g]*T)))/d --> (atanh((0.4*6.2)/([g]*0.622)))/2.15

Evaluating ... ...

k = 0.200698139739852

STEP 3: Convert Result to Output's Unit

0.200698139739852 --> No Conversion Required

FINAL ANSWER

0.200698139739852 ≈ 0.200698 <-- Wave Number for Water Wave

(Calculation completed in 00.004 seconds)

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< 4 Predicting Waves in Deep Water Calculators

Significant Wave Height from Bretschneider Empirical Relationships

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

Water Depth given Wavelength, Wave Period and Water Number

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

Wave Number given Wavelength, Wave Period and Water Depth

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

Significant Wave Period from Bretschneider Empirical Relationships

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

Wave Number given Wavelength, Wave Period and Water Depth Formula

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

What is Wave Number?

Wave Number is the distance between corresponding points of two consecutive waves. “Corresponding points” refers to two points or particles in the same phase—i.e., points that have completed identical fractions of their periodic motio

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 Wave Number given Wavelength, Wave Period and Water Depth?

Wave Number given Wavelength, Wave Period and Water Depth calculator uses Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth to calculate the Wave Number for Water Wave, Wave number given wavelength, wave period and water depth is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Wave Number for Water Wave is denoted by k symbol.

How to calculate Wave Number given Wavelength, Wave Period and Water Depth using this online calculator? To use this online calculator for Wave Number given Wavelength, Wave Period and Water Depth, enter Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Water Depth (d) and hit the calculate button. Here is how the Wave Number given Wavelength, Wave Period and Water Depth calculation can be explained with given input values -> 0.200698 = (atanh((0.4*6.2)/([g]*0.622)))/2.15.

FAQ

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

Wave number given wavelength, wave period and water depth is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance and is represented as k = (atanh((L*ω)/([g]*T)))/d or Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth. 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 & 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.

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

Wave number given wavelength, wave period and water depth is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance is calculated using Wave Number for Water Wave = (atanh((Wavelength*Wave Angular Frequency)/([g]*Wave Period)))/Water Depth. To calculate Wave Number given Wavelength, Wave Period and Water Depth, you need Wavelength (L), Wave Angular Frequency (ω), Wave Period (T) & Water Depth (d). With our tool, you need to enter the respective value for Wavelength, Wave Angular Frequency, Wave Period & Water Depth 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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