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Trough to Crest Wave Height Formula

GoWave Height given Distance from Bottom to Wave Trough and Water Depth Formula

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Height of the Wave is the difference between the elevations of a crest and a neighboring trough. Check FAQs

H w = d c \cdot ((\frac{y c}{d c}) - (\frac{y t}{d c}))

H_w - Height of the Wave?d_c - Water Depth for Cnoidal Wave?y_c - Distance from the Bottom to the Crest?y_t - Distance from the Bottom to the Wave Trough?

Trough to Crest Wave Height Example

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Here is how the Trough to Crest Wave Height equation looks like with Values.

Here is how the Trough to Crest Wave Height equation looks like with Units.

Here is how the Trough to Crest Wave Height equation looks like.

14 = 16 \cdot ((\frac{35}{16}) - (\frac{21}{16}))

14m = 16m \cdot ((\frac{35m}{16m}) - (\frac{21m}{16m}))

14 = 16 \cdot ((\frac{35}{16}) - (\frac{21}{16}))

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Trough to Crest Wave Height Solution

Follow our step by step solution on how to calculate Trough to Crest Wave Height?

FIRST Step Consider the formula

H w = d c \cdot ((\frac{y c}{d c}) - (\frac{y t}{d c}))

Next Step Substitute values of Variables

∴

H w = 16m \cdot ((\frac{35m}{16m}) - (\frac{21m}{16m}))

Next Step Prepare to Evaluate

∴

H w = 16 \cdot ((\frac{35}{16}) - (\frac{21}{16}))

LAST Step Evaluate

∴

H w = 14m

Trough to Crest Wave Height Formula Elements

Variables

Height of the Wave

Height of the Wave is the difference between the elevations of a crest and a neighboring trough.

Symbol: H_w

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Height of the Wave

Water Depth for Cnoidal Wave

Water Depth for Cnoidal Wave refers to the depth of the water in which the cnoidal wave is propagating.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth for Cnoidal Wave

Distance from the Bottom to the Crest

Distance from the Bottom to the Crest is defined as the total stretch from the bottom to the crest of the wave.

Symbol: y_c

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from the Bottom to the Crest

Distance from the Bottom to the Wave Trough

Distance from the Bottom to the Wave Trough is defined as the total stretch from the bottom to the trough of the wave.

Symbol: y_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from the Bottom to the Wave Trough

Other Formulas to find Height of the Wave

Go Wave Height given Distance from Bottom to Wave Trough and Water Depth

H w = - d c \cdot ((\frac{y t}{d c}) - 1 - ((16 \cdot \frac{{d c}^{2}}{3 \cdot λ^{2}}) \cdot K k \cdot (K k - E k)))

Other formulas in Cnoidal Wave Theory category

Go Distance from Bottom to Wave Trough

y t = d c \cdot ((\frac{y c}{d c}) - (\frac{H w}{d c}))

Go Distance from Bottom to Crest

y c = d c \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}))

Go Complete Elliptic Integral of Second Kind

E k = - ((((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1) \cdot \frac{3 \cdot λ^{2}}{(16 \cdot {d c}^{2}) \cdot K k}) - K k)

Go Wavelength for Distance from Bottom to Wave Trough

λ = \sqrt{\frac{16 \cdot {d c}^{2} \cdot K k \cdot (K k - E k)}{3 \cdot ((\frac{y t}{d c}) + (\frac{H w}{d c}) - 1)}}

How to Evaluate Trough to Crest Wave Height?

Trough to Crest Wave Height evaluator 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 evaluate 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 evaluate Trough to Crest Wave Height using this online evaluator? To use this online evaluator 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.

FAQs on Trough to Crest Wave Height

What is the formula to find Trough to Crest Wave Height?

The formula of Trough to Crest Wave Height is expressed as 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)). Here is an example- 14 = 16*((35/16)-(21/16)).

How to calculate Trough to Crest Wave Height?

With 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) we can find Trough to Crest Wave Height using the formula - 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)).

What are the other ways to Calculate Height of the Wave?

Here are the different ways to Calculate Height of the Wave-

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)))

Can the Trough to Crest Wave Height be negative?

Yes, the Trough to Crest Wave Height, measured in Length can be negative.

Which unit is used to measure Trough to Crest Wave Height?

Trough to Crest Wave Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Trough to Crest Wave Height can be measured.

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Trough to Crest Wave Height Formula

​GoWave Height given Distance from Bottom to Wave Trough and Water Depth Formula

Trough to Crest Wave Height Example

Trough to Crest Wave Height Solution

Trough to Crest Wave Height Formula Elements

Other Formulas to find Height of the Wave

Other formulas in Cnoidal Wave Theory category

How to Evaluate Trough to Crest Wave Height?

FAQs on Trough to Crest Wave Height

Variable Name

GoWave Height given Distance from Bottom to Wave Trough and Water Depth Formula