Most Probable Maximum Wave Period Calculator

✖Spectral Width is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum.ⓘ Spectral Width [v]			+10% -10%
✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%

✖Maximum Wave Period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point.ⓘ Most Probable Maximum Wave Period [T_max]

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Formula

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Most Probable Maximum Wave Period

Formula

`"T"_{"max"} = 2*sqrt(1+"v"^2)/1+sqrt(1+(16*"v"^2/pi*"H"^2))`

Example

`"87.80989s"=2*sqrt(1+("10")^2)/1+sqrt(1+(16*("10")^2/pi*("3m")^2))`

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Most Probable Maximum Wave Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2))
T_max = 2*sqrt(1+v^2)/1+sqrt(1+(16*v^2/pi*H^2))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Maximum Wave Period - (Measured in Second) - Maximum Wave Period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point.
Spectral Width - Spectral Width is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.

STEP 1: Convert Input(s) to Base Unit

Spectral Width: 10 --> No Conversion Required
Wave Height: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_max = 2*sqrt(1+v^2)/1+sqrt(1+(16*v^2/pi*H^2)) --> 2*sqrt(1+10^2)/1+sqrt(1+(16*10^2/pi*3^2))

Evaluating ... ...

T_max = 87.8098860895937

STEP 3: Convert Result to Output's Unit

87.8098860895937 Second --> No Conversion Required

FINAL ANSWER

87.8098860895937 ≈ 87.80989 Second <-- Maximum Wave Period

(Calculation completed in 00.006 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Period Distribution and Wave Spectrum » Most Probable Maximum Wave Period

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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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< 12 Wave Period Distribution and Wave Spectrum Calculators

Equilibrium Form of PM Spectrum for Fully-Developed Seas

Go Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4)

Most Probable Maximum Wave Period

Go Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2))

Probability Density of Wave Period

Go Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4)

Wave Component Amplitude

Go Wave Amplitude = sqrt(0.5*sqrt(Coefficient of Wave Component Amplitude^2+Coefficient of Wave Component Amplitude bn^2))

Spectral Bandwidth

Go Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))

Spectral Width

Go Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1)

Mean Zero-upcrossing Period

Go Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2)

Relative Phase given coefficients

Go Relative Phase = atanh(Coefficient of Wave Component Amplitude bn/Coefficient of Wave Component Amplitude)

Mean Crest Period

Go Wave Crest Period = 2*pi*(Moment of Wave Spectrum 2/Moment of Wave Spectrum 4)

Mean Wave Period

Go Wave Period = 2*pi*(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1)

Normal Distribution with Wave Period

Go Wave Period = Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1

Maximum Wave Period

Go Maximum Wave Period = Coefficient Eckman*Mean Wave Period

Most Probable Maximum Wave Period Formula

Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2))
T_max = 2*sqrt(1+v^2)/1+sqrt(1+(16*v^2/pi*H^2))

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Most Probable Maximum Wave Period?

Most Probable Maximum Wave Period calculator uses Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2)) to calculate the Maximum Wave Period, Most Probable Maximum Wave Period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point. Wave regimes that are dominated by wind waves tend to have smaller peak wave periods, and regimes that are dominated by swell tend to have larger peak wave periods. Maximum Wave Period is denoted by T_max symbol.

How to calculate Most Probable Maximum Wave Period using this online calculator? To use this online calculator for Most Probable Maximum Wave Period, enter Spectral Width (v) & Wave Height (H) and hit the calculate button. Here is how the Most Probable Maximum Wave Period calculation can be explained with given input values -> 87.80989 = 2*sqrt(1+10^2)/1+sqrt(1+(16*10^2/pi*3^2)).

FAQ

What is Most Probable Maximum Wave Period?

Most Probable Maximum Wave Period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point. Wave regimes that are dominated by wind waves tend to have smaller peak wave periods, and regimes that are dominated by swell tend to have larger peak wave periods and is represented as T_max = 2*sqrt(1+v^2)/1+sqrt(1+(16*v^2/pi*H^2)) or Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2)). Spectral Width is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum & Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.

How to calculate Most Probable Maximum Wave Period?

Most Probable Maximum Wave Period is defined as the wave period associated with the most energetic waves in the total wave spectrum at a specific point. Wave regimes that are dominated by wind waves tend to have smaller peak wave periods, and regimes that are dominated by swell tend to have larger peak wave periods is calculated using Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2)). To calculate Most Probable Maximum Wave Period, you need Spectral Width (v) & Wave Height (H). With our tool, you need to enter the respective value for Spectral Width & Wave Height 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 Maximum Wave Period?

In this formula, Maximum Wave Period uses Spectral Width & Wave Height. We can use 1 other way(s) to calculate the same, which is/are as follows -

Maximum Wave Period = Coefficient Eckman*Mean Wave Period

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