Spectral Width Calculator

✖Zero-th Moment of Wave Spectrum is a measure of the total energy contained in the wave spectrum. It represents the integral of the wave spectrum over all frequencies.ⓘ Zero-th Moment of Wave Spectrum [m₀]			+10% -10%
✖Moment of Wave Spectrum 2 in terms of cyclic frequency are used to characterize its shape and intensity.ⓘ Moment of Wave Spectrum 2 [m₂]			+10% -10%
✖Moment of Wave Spectrum 1 are used to characterize its shape and intensity.ⓘ Moment of Wave Spectrum 1 [m₁]			+10% -10%

✖Spectral Width refers to the range of frequencies over which significant wave energy is distributed. It provides a measure of the spread of the spectrum or width.ⓘ Spectral Width [v]

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Spectral Width Solution

STEP 0: Pre-Calculation Summary

Formula Used

Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1)
v = sqrt((m₀*m₂/m₁^2)-1)
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 refers to the range of frequencies over which significant wave energy is distributed. It provides a measure of the spread of the spectrum or width.
Zero-th Moment of Wave Spectrum - Zero-th Moment of Wave Spectrum is a measure of the total energy contained in the wave spectrum. It represents the integral of the wave spectrum over all frequencies.
Moment of Wave Spectrum 2 - Moment of Wave Spectrum 2 in terms of cyclic frequency are used to characterize its shape and intensity.
Moment of Wave Spectrum 1 - Moment of Wave Spectrum 1 are used to characterize its shape and intensity.

STEP 1: Convert Input(s) to Base Unit

Zero-th Moment of Wave Spectrum: 265 --> No Conversion Required
Moment of Wave Spectrum 2: 1.4 --> No Conversion Required
Moment of Wave Spectrum 1: 2 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = sqrt((m₀*m₂/m₁^2)-1) --> sqrt((265*1.4/2^2)-1)

Evaluating ... ...

v = 9.57862203033401

STEP 3: Convert Result to Output's Unit

9.57862203033401 --> No Conversion Required

FINAL ANSWER

9.57862203033401 ≈ 9.578622 <-- Spectral Width

(Calculation completed in 00.020 seconds)

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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!

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NSS College of Engineering (NSSCE), Palakkad

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< Wave Period Distribution and Wave Spectrum Calculators

Most Probable Maximum Wave Period

LaTeX 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

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

Mean Zero-upcrossing Period

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

Mean Crest Period

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

Spectral Width Formula

LaTeX Go

Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1)
v = sqrt((m₀*m₂/m₁^2)-1)

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 Width?

Spectral Width calculator uses Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1) to calculate the Spectral Width, The Spectral Width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value. Spectral Width is denoted by v symbol.

How to calculate Spectral Width using this online calculator? To use this online calculator for Spectral Width, enter Zero-th Moment of Wave Spectrum (m₀), Moment of Wave Spectrum 2 (m₂) & Moment of Wave Spectrum 1 (m₁) and hit the calculate button. Here is how the Spectral Width calculation can be explained with given input values -> 9.578622 = sqrt((265*1.4/2^2)-1).

FAQ

What is Spectral Width?

The Spectral Width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value and is represented as v = sqrt((m₀*m₂/m₁^2)-1) or Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1). Zero-th Moment of Wave Spectrum is a measure of the total energy contained in the wave spectrum. It represents the integral of the wave spectrum over all frequencies, Moment of Wave Spectrum 2 in terms of cyclic frequency are used to characterize its shape and intensity & Moment of Wave Spectrum 1 are used to characterize its shape and intensity.

How to calculate Spectral Width?

The Spectral Width is the wavelength interval over which the magnitude of all spectral components is equal to or greater than a specified fraction of the magnitude of the component having the maximum value is calculated using Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1). To calculate Spectral Width, you need Zero-th Moment of Wave Spectrum (m₀), Moment of Wave Spectrum 2 (m₂) & Moment of Wave Spectrum 1 (m₁). With our tool, you need to enter the respective value for Zero-th Moment of Wave Spectrum, Moment of Wave Spectrum 2 & Moment of Wave Spectrum 1 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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