Relative Phase given coefficients Calculator

✖Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude.ⓘ Coefficient of Wave Component Amplitude [b_n]			+10% -10%
✖Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude.ⓘ Coefficient of Wave Component Amplitude [a_n]			+10% -10%

✖Relative Phase of the wave component is denoted by εv symbol.ⓘ Relative Phase given coefficients [ε_v]

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Formula

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Relative Phase given coefficients

Formula

`"ε"_{"v"} = atanh("b"_{"n"}/"a"_{"n"})`

Example

`"0.168236"=atanh("0.1"/"0.6")`

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Relative Phase given coefficients Solution

STEP 0: Pre-Calculation Summary

Formula Used

Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude)
ε_v = atanh(b_n/a_n)
This formula uses 2 Functions, 3 Variables

Functions Used

tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(Number)

Variables Used

Relative Phase - Relative Phase of the wave component is denoted by εv symbol.
Coefficient of Wave Component Amplitude - Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude.
Coefficient of Wave Component Amplitude - Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Wave Component Amplitude: 0.1 --> No Conversion Required
Coefficient of Wave Component Amplitude: 0.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_v = atanh(b_n/a_n) --> atanh(0.1/0.6)

Evaluating ... ...

ε_v = 0.168236118310607

STEP 3: Convert Result to Output's Unit

0.168236118310607 --> No Conversion Required

FINAL ANSWER

0.168236118310607 ≈ 0.168236 <-- Relative Phase

(Calculation completed in 00.004 seconds)

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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

Relative Phase given coefficients Formula

Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude)
ε_v = atanh(b_n/a_n)

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 Relative Phase given coefficients?

Relative Phase given coefficients calculator uses Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude) to calculate the Relative Phase, The Relative Phase given coefficients measured with respect to another waveform of the exact same constant frequency. Relative Phase is denoted by ε_v symbol.

How to calculate Relative Phase given coefficients using this online calculator? To use this online calculator for Relative Phase given coefficients, enter Coefficient of Wave Component Amplitude (b_n) & Coefficient of Wave Component Amplitude (a_n) and hit the calculate button. Here is how the Relative Phase given coefficients calculation can be explained with given input values -> 0.168236 = atanh(0.1/0.6).

FAQ

What is Relative Phase given coefficients?

The Relative Phase given coefficients measured with respect to another waveform of the exact same constant frequency and is represented as ε_v = atanh(b_n/a_n) or Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude). Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude & Coefficient of Wave Component Amplitude of wave profile time trace written as an infinite sum of sinusoids of amplitude.

How to calculate Relative Phase given coefficients?

The Relative Phase given coefficients measured with respect to another waveform of the exact same constant frequency is calculated using Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude). To calculate Relative Phase given coefficients, you need Coefficient of Wave Component Amplitude (b_n) & Coefficient of Wave Component Amplitude (a_n). With our tool, you need to enter the respective value for Coefficient of Wave Component Amplitude & Coefficient of Wave Component Amplitude 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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