Spectral Bandwidth Calculator

✖Moment of Wave Spectrum 2 in terms of cyclic frequency.ⓘ Moment of Wave Spectrum 2 [m₂]			+10% -10%
✖Zero-th Moment of Wave Spectrum in terms of cyclic frequency.ⓘ Zero-th Moment of Wave Spectrum [m₀]			+10% -10%
✖Moment of Wave Spectrum 4 in terms of cyclic frequency.ⓘ Moment of Wave Spectrum 4 [m₄]			+10% -10%

✖Spectral Width is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum.ⓘ Spectral Bandwidth [v]

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Formula

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Spectral Bandwidth

Formula

`"v" = sqrt(1-("m"_{"2"}^2/("m"_{"0"}*"m"_{"4"})))`

Example

`"0.993712"=sqrt(1-(("1.4")^2/("265"*"0.59")))`

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Spectral Bandwidth Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))
v = sqrt(1-(m₂^2/(m₀*m₄)))
This formula uses 1 Functions, 4 Variables

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

Spectral Width - Spectral Width is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum.
Moment of Wave Spectrum 2 - Moment of Wave Spectrum 2 in terms of cyclic frequency.
Zero-th Moment of Wave Spectrum - Zero-th Moment of Wave Spectrum in terms of cyclic frequency.
Moment of Wave Spectrum 4 - Moment of Wave Spectrum 4 in terms of cyclic frequency.

STEP 1: Convert Input(s) to Base Unit

Moment of Wave Spectrum 2: 1.4 --> No Conversion Required
Zero-th Moment of Wave Spectrum: 265 --> No Conversion Required
Moment of Wave Spectrum 4: 0.59 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = sqrt(1-(m₂^2/(m₀*m₄))) --> sqrt(1-(1.4^2/(265*0.59)))

Evaluating ... ...

v = 0.993712243572184

STEP 3: Convert Result to Output's Unit

0.993712243572184 --> No Conversion Required

FINAL ANSWER

0.993712243572184 ≈ 0.993712 <-- Spectral Width

(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 » Spectral Bandwidth

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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< 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

Spectral Bandwidth Formula

Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))
v = sqrt(1-(m₂^2/(m₀*m₄)))

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.

What is the definition of wave spectrum?

Wave Spectrum is a concept used to describe the distribution of energy among waves of different period. Wave speed increases with wave length, so distant storms may be detected by the increase of energy in long period waves.

How to Calculate Spectral Bandwidth?

Spectral Bandwidth calculator uses Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4))) to calculate the Spectral Width, The Spectral Bandwidth is defined as the band width of light at one-half the peak maximum used to determine the narrowness of a wave spectra . Spectral Width is denoted by v symbol.

How to calculate Spectral Bandwidth using this online calculator? To use this online calculator for Spectral Bandwidth, enter Moment of Wave Spectrum 2 (m₂), Zero-th Moment of Wave Spectrum (m₀) & Moment of Wave Spectrum 4 (m₄) and hit the calculate button. Here is how the Spectral Bandwidth calculation can be explained with given input values -> 0.987596 = sqrt(1-(1.4^2/(265*0.59))).

FAQ

What is Spectral Bandwidth?

The Spectral Bandwidth is defined as the band width of light at one-half the peak maximum used to determine the narrowness of a wave spectra and is represented as v = sqrt(1-(m₂^2/(m₀*m₄))) or Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4))). Moment of Wave Spectrum 2 in terms of cyclic frequency, Zero-th Moment of Wave Spectrum in terms of cyclic frequency & Moment of Wave Spectrum 4 in terms of cyclic frequency.

How to calculate Spectral Bandwidth?

The Spectral Bandwidth is defined as the band width of light at one-half the peak maximum used to determine the narrowness of a wave spectra is calculated using Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4))). To calculate Spectral Bandwidth, you need Moment of Wave Spectrum 2 (m₂), Zero-th Moment of Wave Spectrum (m₀) & Moment of Wave Spectrum 4 (m₄). With our tool, you need to enter the respective value for Moment of Wave Spectrum 2, Zero-th Moment of Wave Spectrum & Moment of Wave Spectrum 4 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 Spectral Width?

In this formula, Spectral Width uses Moment of Wave Spectrum 2, Zero-th Moment of Wave Spectrum & Moment of Wave Spectrum 4. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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