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 is the wavelength interval. Spectral Bandwidth is defined as the band width of light at one-half the peak maximum.
Zero-th Moment of Wave Spectrum - Zero-th Moment of Wave Spectrum in terms of cyclic frequency.
Moment of Wave Spectrum 2 - Moment of Wave Spectrum 2 in terms of cyclic frequency.
Moment of Wave Spectrum 1 - Moment of Wave Spectrum 1 in terms of cyclic frequency.
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 00.004 seconds)

Credits

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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^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/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 Width Formula

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 in terms of cyclic frequency, Moment of Wave Spectrum 2 in terms of cyclic frequency & Moment of Wave Spectrum 1 in terms of cyclic frequency.
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.
How many ways are there to calculate Spectral Width?
In this formula, Spectral Width uses Zero-th Moment of Wave Spectrum, Moment of Wave Spectrum 2 & Moment of Wave Spectrum 1. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))
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