Probability Density of Wave Period Calculator

✖Wave Period is the time between successive peaks or troughs.ⓘ Wave Period [P]			+10% -10%
✖Mean Wave Period is the mean of all wave periods in a time-series representing a certain sea state.ⓘ Mean Wave Period [T']			+10% -10%

✖Probability of occurrence of an event (x ≥ xt), of how likely an event is to occur, or how likely it is that a proposition is true.ⓘ Probability Density of Wave Period [p]

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Formula

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Probability Density of Wave Period

Formula

`"p" = 2.7*("P"^3/"T'")*exp(-0.675*("P"/"T'")^4)`

Example

`"1.116046"=2.7*(("1.03")^3/"2.6s")*exp(-0.675*("1.03"/"2.6s")^4)`

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Probability Density of Wave Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4)
p = 2.7*(P^3/T')*exp(-0.675*(P/T')^4)
This formula uses 1 Functions, 3 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Probability - Probability of occurrence of an event (x ≥ xt), of how likely an event is to occur, or how likely it is that a proposition is true.
Wave Period - Wave Period is the time between successive peaks or troughs.
Mean Wave Period - (Measured in Second) - Mean Wave Period is the mean of all wave periods in a time-series representing a certain sea state.

STEP 1: Convert Input(s) to Base Unit

Wave Period: 1.03 --> No Conversion Required
Mean Wave Period: 2.6 Second --> 2.6 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

p = 2.7*(P^3/T')*exp(-0.675*(P/T')^4) --> 2.7*(1.03^3/2.6)*exp(-0.675*(1.03/2.6)^4)

Evaluating ... ...

p = 1.11604571411966

STEP 3: Convert Result to Output's Unit

1.11604571411966 --> No Conversion Required

FINAL ANSWER

1.11604571411966 ≈ 1.116046 <-- Probability

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Period Distribution and Wave Spectrum » Probability Density of Wave Period

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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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

Probability Density of Wave Period Formula

Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4)
p = 2.7*(P^3/T')*exp(-0.675*(P/T')^4)

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 Probability Density of Wave Period?

Probability Density of Wave Period calculator uses Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4) to calculate the Probability, The Probability Density of Wave Period by Bretschneider determines the distributions for wave periods, even under the assumptions that waves are linear and have narrow-band frequency spectrum. Probability is denoted by p symbol.

How to calculate Probability Density of Wave Period using this online calculator? To use this online calculator for Probability Density of Wave Period, enter Wave Period (P) & Mean Wave Period (T') and hit the calculate button. Here is how the Probability Density of Wave Period calculation can be explained with given input values -> 1.116046 = 2.7*(1.03^3/2.6)*exp(-0.675*(1.03/2.6)^4).

FAQ

What is Probability Density of Wave Period?

The Probability Density of Wave Period by Bretschneider determines the distributions for wave periods, even under the assumptions that waves are linear and have narrow-band frequency spectrum and is represented as p = 2.7*(P^3/T')*exp(-0.675*(P/T')^4) or Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4). Wave Period is the time between successive peaks or troughs & Mean Wave Period is the mean of all wave periods in a time-series representing a certain sea state.

How to calculate Probability Density of Wave Period?

The Probability Density of Wave Period by Bretschneider determines the distributions for wave periods, even under the assumptions that waves are linear and have narrow-band frequency spectrum is calculated using Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4). To calculate Probability Density of Wave Period, you need Wave Period (P) & Mean Wave Period (T'). With our tool, you need to enter the respective value for Wave Period & Mean Wave Period 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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