Water Surface Elevation of Two Sinusoidal Wave Calculator

✖Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Wave Height [H]			+10% -10%
✖Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes.ⓘ Spatial (Progressive Wave) [x]			+10% -10%
✖Wavelength of Component Wave 1. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough.ⓘ Wavelength of Component Wave 1 [L1]			+10% -10%
✖Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.ⓘ Temporal (Progressive Wave) [t]			+10% -10%
✖Wave Period of Component Wave 1. Wave Period is the time between successive peaks or troughs.ⓘ Wave Period of Component Wave 1 [T₁]			+10% -10%
✖Wavelength of Component Wave 2. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough.ⓘ Wavelength of Component Wave 2 [L2]			+10% -10%
✖Wave Period of Component Wave 2. Wave Period is the time between successive peaks or troughs.ⓘ Wave Period of Component Wave 2 [T₂]			+10% -10%

✖Elevation of Water Surface relative to the SWL, Standing Water Level recorded for the water well.ⓘ Water Surface Elevation of Two Sinusoidal Wave [η]

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Formula

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Water Surface Elevation of Two Sinusoidal Wave

Formula

`"η" = ("H"/2)*cos((2*pi*"x"/"L1")-(2*pi*"t"/"T"_{"1"}))+("H"/2)*cos((2*pi*"x"/"L2")-(2*pi*"t"/"T"_{"2"}))`

Example

`"1.5m"=("3m"/2)*cos((2*pi*"50"/"50")-(2*pi*"25"/"25s"))+("3m"/2)*cos((2*pi*"50"/"25")-(2*pi*"25"/"100s"))`

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Water Surface Elevation of Two Sinusoidal Wave Solution

STEP 0: Pre-Calculation Summary

Formula Used

Elevation of Water Surface = (Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 1)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 2)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 2))
η = (H/2)*cos((2*pi*x/L1)-(2*pi*t/T₁))+(H/2)*cos((2*pi*x/L2)-(2*pi*t/T₂))
This formula uses 1 Constants, 1 Functions, 8 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Elevation of Water Surface - (Measured in Meter) - Elevation of Water Surface relative to the SWL, Standing Water Level recorded for the water well.
Wave Height - (Measured in Meter) - Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough.
Spatial (Progressive Wave) - Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes.
Wavelength of Component Wave 1 - Wavelength of Component Wave 1. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough.
Temporal (Progressive Wave) - Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude.
Wave Period of Component Wave 1 - (Measured in Second) - Wave Period of Component Wave 1. Wave Period is the time between successive peaks or troughs.
Wavelength of Component Wave 2 - Wavelength of Component Wave 2. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough.
Wave Period of Component Wave 2 - (Measured in Second) - Wave Period of Component Wave 2. Wave Period is the time between successive peaks or troughs.

STEP 1: Convert Input(s) to Base Unit

Wave Height: 3 Meter --> 3 Meter No Conversion Required
Spatial (Progressive Wave): 50 --> No Conversion Required
Wavelength of Component Wave 1: 50 --> No Conversion Required
Temporal (Progressive Wave): 25 --> No Conversion Required
Wave Period of Component Wave 1: 25 Second --> 25 Second No Conversion Required
Wavelength of Component Wave 2: 25 --> No Conversion Required
Wave Period of Component Wave 2: 100 Second --> 100 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η = (H/2)*cos((2*pi*x/L1)-(2*pi*t/T₁))+(H/2)*cos((2*pi*x/L2)-(2*pi*t/T₂)) --> (3/2)*cos((2*pi*50/50)-(2*pi*25/25))+(3/2)*cos((2*pi*50/25)-(2*pi*25/100))

Evaluating ... ...

η = 1.5

STEP 3: Convert Result to Output's Unit

1.5 Meter --> No Conversion Required

FINAL ANSWER

1.5 Meter <-- Elevation of Water Surface

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Subsurface Pressure » Pressure Component » Water Surface Elevation of Two Sinusoidal Wave

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Coorg Institute of Technology (CIT), Coorg

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< 16 Pressure Component Calculators

Water Surface Elevation of Two Sinusoidal Wave

Go Elevation of Water Surface = (Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 1)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 2)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 2))

Phase Angle for Total or Absolute Pressure

Go Phase Angle = acos((Absolute Pressure+(Mass Density*[g]*Seabed Elevation)-(Atmospheric Pressure))/((Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))/(2*cosh(2*pi*Water Depth/Wavelength))))

Atmospheric Pressure given Total or Absolute Pressure

Go Atmospheric pressure = Absolute pressure-(Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))+(Mass Density*[g]*Seabed Elevation)

Total or Absolute Pressure

Go Absolute pressure = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength)*cos(Phase Angle)/2*cosh(2*pi*Water Depth/Wavelength))-(Mass Density*[g]*Seabed Elevation)+Atmospheric Pressure

Dynamic Component due to Acceleration from Absolute Pressure Equation

Go Dynamic Component due to Acceleration = (Mass Density*[g]*Wave Height*cosh(2*pi*(Distance above the Bottom)/Wavelength))*cos(Phase Angle)/(2*cosh(2*pi*Water Depth/Wavelength))

Height of Surface Waves based on Subsurface Measurements

Go Elevation of Water Surface = Correction Factor*(Pressure+(Mass Density*[g]*Depth below the SWL of Pressure Gauge))/(Mass Density*[g]*Pressure Response Factor)

Correction Factor given Height of Surface Waves based on Subsurface Measurements

Go Correction Factor = Elevation of Water Surface*Mass Density*[g]*Pressure Response Factor/(Pressure+(Mass Density*[g]*Depth below the SWL of Pressure Gauge))

Depth below SWL of Pressure Gauge

Go Depth below the SWL of Pressure Gauge = ((Elevation of Water Surface*Mass Density*[g]*Pressure Response Factor/Correction Factor)-Pressure)/Mass Density*[g]

Friction Velocity given Dimensionless Time

Go Friction Velocity = ([g]*Time for Dimensionless Parameter Calculation)/Dimensionless Time

Water Surface Elevation

Go Elevation of Water Surface = (Wave Height/2)*cos(Phase Angle)

Wave celerity for shallow water given water depth

Go Celerity of the Wave = sqrt([g]*Water Depth)

Atmospheric Pressure given Gauge Pressure

Go Atmospheric Pressure = Absolute Pressure-Gauge Pressure

Total Pressure given Gauge Pressure

Go Total Pressure = Gauge Pressure+Atmospheric Pressure

Water Depth given Wave Celerity for Shallow Water

Go Water Depth = (Celerity of the Wave^2)/[g]

Radian Frequency given Wave Period

Go Wave Angular Frequency = 1/Mean Wave Period

Wave Period given average Frequency

Go Wave Period = 1/Wave Angular Frequency

Water Surface Elevation of Two Sinusoidal Wave Formula

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 Water Surface Elevation of Two Sinusoidal Wave?

Water Surface Elevation of Two Sinusoidal Wave calculator uses Elevation of Water Surface = (Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 1)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 2)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 2)) to calculate the Elevation of Water Surface, Water Surface Elevation of Two Sinusoidal Wave means the height, in relation to mean sea level, of floods of various magnitudes and frequencies in the floodplains of coastal or riverine areas. Elevation of Water Surface is denoted by η symbol.

How to calculate Water Surface Elevation of Two Sinusoidal Wave using this online calculator? To use this online calculator for Water Surface Elevation of Two Sinusoidal Wave, enter Wave Height (H), Spatial (Progressive Wave) (x), Wavelength of Component Wave 1 (L1), Temporal (Progressive Wave) (t), Wave Period of Component Wave 1 (T₁), Wavelength of Component Wave 2 (L2) & Wave Period of Component Wave 2 (T₂) and hit the calculate button. Here is how the Water Surface Elevation of Two Sinusoidal Wave calculation can be explained with given input values -> 1.5 = (3/2)*cos((2*pi*50/50)-(2*pi*25/25))+(3/2)*cos((2*pi*50/25)-(2*pi*25/100)).

FAQ

What is Water Surface Elevation of Two Sinusoidal Wave?

Water Surface Elevation of Two Sinusoidal Wave means the height, in relation to mean sea level, of floods of various magnitudes and frequencies in the floodplains of coastal or riverine areas and is represented as η = (H/2)*cos((2*pi*x/L1)-(2*pi*t/T₁))+(H/2)*cos((2*pi*x/L2)-(2*pi*t/T₂)) or Elevation of Water Surface = (Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 1)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 2)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 2)). Wave Height of a surface wave is the difference between the elevations of a crest and a neighboring trough, Spatial (Progressive Wave) is a wave that continuously travels in a medium in the same direction minus the changes, Wavelength of Component Wave 1. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough, Temporal (Progressive Wave) is a wave which generally travels continuously in a medium of the same direction without the change in its amplitude, Wave Period of Component Wave 1. Wave Period is the time between successive peaks or troughs, Wavelength of Component Wave 2. Wavelength is the horizontal distance between any two corresponding points on successive waveforms, such as from crest to crest or from trough to trough & Wave Period of Component Wave 2. Wave Period is the time between successive peaks or troughs.

How to calculate Water Surface Elevation of Two Sinusoidal Wave?

Water Surface Elevation of Two Sinusoidal Wave means the height, in relation to mean sea level, of floods of various magnitudes and frequencies in the floodplains of coastal or riverine areas is calculated using Elevation of Water Surface = (Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 1)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 1))+(Wave Height/2)*cos((2*pi*Spatial (Progressive Wave)/Wavelength of Component Wave 2)-(2*pi*Temporal (Progressive Wave)/Wave Period of Component Wave 2)). To calculate Water Surface Elevation of Two Sinusoidal Wave, you need Wave Height (H), Spatial (Progressive Wave) (x), Wavelength of Component Wave 1 (L1), Temporal (Progressive Wave) (t), Wave Period of Component Wave 1 (T₁), Wavelength of Component Wave 2 (L2) & Wave Period of Component Wave 2 (T₂). With our tool, you need to enter the respective value for Wave Height, Spatial (Progressive Wave), Wavelength of Component Wave 1, Temporal (Progressive Wave), Wave Period of Component Wave 1, Wavelength of Component Wave 2 & Wave Period of Component Wave 2 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 Elevation of Water Surface?

In this formula, Elevation of Water Surface uses Wave Height, Spatial (Progressive Wave), Wavelength of Component Wave 1, Temporal (Progressive Wave), Wave Period of Component Wave 1, Wavelength of Component Wave 2 & Wave Period of Component Wave 2. We can use 2 other way(s) to calculate the same, which is/are as follows -

Elevation of Water Surface = Correction Factor*(Pressure+(Mass Density*[g]*Depth below the SWL of Pressure Gauge))/(Mass Density*[g]*Pressure Response Factor)
Elevation of Water Surface = (Wave Height/2)*cos(Phase Angle)

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