Trough to Crest Wave Height Calculator

✖Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.ⓘ Water Depth for Cnoidal Wave [d_c]			+10% -10%
✖Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.ⓘ Distance from the Bottom to the Crest [y_c]			+10% -10%
✖Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.ⓘ Distance from the Bottom to the Wave Trough [y_t]			+10% -10%

✖Height of the Wave is the difference between the elevations of a crest and a neighboring trough.ⓘ Trough to Crest Wave Height [H_w]

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Trough to Crest Wave Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))
H_w = d_c*((y_c/d_c)-(y_t/d_c))
This formula uses 4 Variables

Variables Used

Height of the Wave - (Measured in Meter) - Height of the Wave is the difference between the elevations of a crest and a neighboring trough.
Water Depth for Cnoidal Wave - (Measured in Meter) - Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.
Distance from the Bottom to the Crest - (Measured in Meter) - Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.
Distance from the Bottom to the Wave Trough - (Measured in Meter) - Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

STEP 1: Convert Input(s) to Base Unit

Water Depth for Cnoidal Wave: 16 Meter --> 16 Meter No Conversion Required
Distance from the Bottom to the Crest: 35 Meter --> 35 Meter No Conversion Required
Distance from the Bottom to the Wave Trough: 21 Meter --> 21 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H_w = d_c*((y_c/d_c)-(y_t/d_c)) --> 16*((35/16)-(21/16))

Evaluating ... ...

H_w = 14

STEP 3: Convert Result to Output's Unit

14 Meter --> No Conversion Required

FINAL ANSWER

14 Meter <-- Height of the Wave

(Calculation completed in 00.020 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Cnoidal Wave Theory Calculators

Complete Elliptic Integral of Second Kind

LaTeX Go Complete Elliptic Integral of the Second Kind = -((((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave)-1)*(3*Wavelength of Wave^2)/((16*Water Depth for Cnoidal Wave^2)*Complete Elliptic Integral of the First Kind))-Complete Elliptic Integral of the First Kind)

Distance from Bottom to Wave Trough

LaTeX Go Distance from the Bottom to the Wave Trough = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Height of the Wave/Water Depth for Cnoidal Wave))

Distance from Bottom to Crest

LaTeX Go Distance from the Bottom to the Crest = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)+(Height of the Wave/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height

LaTeX Go Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave))

Trough to Crest Wave Height Formula

LaTeX Go

What Causes Waves?

Waves are most commonly caused by wind. Wind-driven waves, or surface waves, are created by the friction between wind and surface water. As wind blows across the surface of the ocean or a lake, the continual disturbance creates a wave crest. The gravitational pull of the sun and moon on the earth also causes waves.

How to Calculate Trough to Crest Wave Height?

Trough to Crest Wave Height calculator uses Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)) to calculate the Height of the Wave, The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave. Height of the Wave is denoted by H_w symbol.

How to calculate Trough to Crest Wave Height using this online calculator? To use this online calculator for Trough to Crest Wave Height, enter Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Distance from the Bottom to the Wave Trough (y_t) and hit the calculate button. Here is how the Trough to Crest Wave Height calculation can be explained with given input values -> 14 = 16*((35/16)-(21/16)).

FAQ

What is Trough to Crest Wave Height?

The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave and is represented as H_w = d_c*((y_c/d_c)-(y_t/d_c)) or Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)). Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating, Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave & Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

How to calculate Trough to Crest Wave Height?

The Trough to Crest Wave Height formula is defined as the total stretch from the trough to the crest of the wave is calculated using Height of the Wave = Water Depth for Cnoidal Wave*((Distance from the Bottom to the Crest/Water Depth for Cnoidal Wave)-(Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)). To calculate Trough to Crest Wave Height, you need Water Depth for Cnoidal Wave (d_c), Distance from the Bottom to the Crest (y_c) & Distance from the Bottom to the Wave Trough (y_t). With our tool, you need to enter the respective value for Water Depth for Cnoidal Wave, Distance from the Bottom to the Crest & Distance from the Bottom to the Wave Trough 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 Height of the Wave?

In this formula, Height of the Wave uses Water Depth for Cnoidal Wave, Distance from the Bottom to the Crest & Distance from the Bottom to the Wave Trough. We can use 1 other way(s) to calculate the same, which is/are as follows -

Height of the Wave = -Water Depth for Cnoidal Wave*((Distance from the Bottom to the Wave Trough/Water Depth for Cnoidal Wave)-1-((16*Water Depth for Cnoidal Wave^2/(3*Wavelength of Wave^2))*Complete Elliptic Integral of the First Kind*(Complete Elliptic Integral of the First Kind-Complete Elliptic Integral of the Second Kind)))

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