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Water Surface Amplitude Formula

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Water Surface Amplitude is the maximum vertical distance between the highest and lowest points of a water surface wave. Check FAQs

N = H i \cdot \cos (\frac{2 \cdot π \cdot x}{L o}) \cdot \cos (\frac{2 \cdot π \cdot t}{T})

N - Water Surface Amplitude?H_i - Incident Wave Height?x - Horizontal Ordinate?L_o - Incident Wave Length in Deepwater?t - Time Elapsed?T - Reflected Wave Period?π - Archimedes' constant?

Water Surface Amplitude Example

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Here is how the Water Surface Amplitude equation looks like with Values.

Here is how the Water Surface Amplitude equation looks like with Units.

Here is how the Water Surface Amplitude equation looks like.

80.1716 = 160 \cdot \cos (\frac{2 \cdot 3.1416 \cdot 38.5}{16}) \cdot \cos (\frac{2 \cdot 3.1416 \cdot 12}{34})

80.1716m = 160m \cdot \cos (\frac{2 \cdot 3.1416 \cdot 38.5}{16m}) \cdot \cos (\frac{2 \cdot 3.1416 \cdot 12s}{34s})

80.1716 = 160 \cdot \cos (\frac{2 \cdot 3.1416 \cdot 38.5}{16}) \cdot \cos (\frac{2 \cdot 3.1416 \cdot 12}{34})

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Water Surface Amplitude Solution

Follow our step by step solution on how to calculate Water Surface Amplitude?

FIRST Step Consider the formula

N = H i \cdot \cos (\frac{2 \cdot π \cdot x}{L o}) \cdot \cos (\frac{2 \cdot π \cdot t}{T})

Next Step Substitute values of Variables

∴

N = 160m \cdot \cos (\frac{2 \cdot π \cdot 38.5}{16m}) \cdot \cos (\frac{2 \cdot π \cdot 12s}{34s})

Next Step Substitute values of Constants

∴

N = 160m \cdot \cos (\frac{2 \cdot 3.1416 \cdot 38.5}{16m}) \cdot \cos (\frac{2 \cdot 3.1416 \cdot 12s}{34s})

Next Step Prepare to Evaluate

∴

N = 160 \cdot \cos (\frac{2 \cdot 3.1416 \cdot 38.5}{16}) \cdot \cos (\frac{2 \cdot 3.1416 \cdot 12}{34})

Next Step Evaluate

∴

N = 80.1715819952553m

LAST Step Rounding Answer

∴

N = 80.1716m

Water Surface Amplitude Formula Elements

Variables

Constants

Functions

Water Surface Amplitude

Water Surface Amplitude is the maximum vertical distance between the highest and lowest points of a water surface wave.

Symbol: N

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Surface Amplitude

Incident Wave Height

Incident Wave Height is obtained as the arithmetic mean of the wave heights measured by two gauges separated by a quarter of a wavelength [length].

Symbol: H_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Incident Wave Height

Horizontal Ordinate

Horizontal Ordinate refers to the distance measured horizontally from a reference point or axis.

Symbol: x

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Horizontal Ordinate

Incident Wave Length in Deepwater

Incident Wave Length in Deepwater is the wave length of the wave that travels from the generating source towards the load.

Symbol: L_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Incident Wave Length in Deepwater

Time Elapsed

Time Elapsed is the total duration that has passed from the start of an event to a specific point in time, typically measured in seconds, minutes, or hours.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Elapsed

Reflected Wave Period

Reflected Wave Period is the time interval between successive crests or troughs of a wave after it reflects off a surface, measured in seconds (s).

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Reflected Wave Period

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Wave Transmission Coefficient and Water Surface Amplitude category

Go Wave Transmission Coefficient

C t = C \cdot (1 - (\frac{F}{R}))

Go Dimensionless Coefficient in Seelig Equation for Wave Transmission Coefficient

C = \frac{C t}{1 - (\frac{F}{R})}

Go Freeboard for given Wave Transmission Coefficient

F = R \cdot (1 - (\frac{C t}{C}))

Go Wave Runup above Mean Water Level for given Wave Transmission Coefficient

R = \frac{F}{1 - (\frac{C t}{C})}

How to Evaluate Water Surface Amplitude?

Water Surface Amplitude evaluator uses Water Surface Amplitude = Incident Wave Height*cos((2*pi*Horizontal Ordinate)/Incident Wave Length in Deepwater)*cos((2*pi*Time Elapsed)/Reflected Wave Period) to evaluate the Water Surface Amplitude, The Water Surface Amplitude is defined as the maximum vertical distance between the highest and lowest points of a water surface wave. Water Surface Amplitude is denoted by N symbol.

How to evaluate Water Surface Amplitude using this online evaluator? To use this online evaluator for Water Surface Amplitude, enter Incident Wave Height (H_i), Horizontal Ordinate (x), Incident Wave Length in Deepwater (L_o), Time Elapsed (t) & Reflected Wave Period (T) and hit the calculate button.

FAQs on Water Surface Amplitude

What is the formula to find Water Surface Amplitude?

The formula of Water Surface Amplitude is expressed as Water Surface Amplitude = Incident Wave Height*cos((2*pi*Horizontal Ordinate)/Incident Wave Length in Deepwater)*cos((2*pi*Time Elapsed)/Reflected Wave Period). Here is an example- 78.7881 = 160*cos((2*pi*38.5)/16)*cos((2*pi*12)/34).

How to calculate Water Surface Amplitude?

With Incident Wave Height (H_i), Horizontal Ordinate (x), Incident Wave Length in Deepwater (L_o), Time Elapsed (t) & Reflected Wave Period (T) we can find Water Surface Amplitude using the formula - Water Surface Amplitude = Incident Wave Height*cos((2*pi*Horizontal Ordinate)/Incident Wave Length in Deepwater)*cos((2*pi*Time Elapsed)/Reflected Wave Period). This formula also uses Archimedes' constant and Cosine function(s).

Can the Water Surface Amplitude be negative?

No, the Water Surface Amplitude, measured in Length cannot be negative.

Which unit is used to measure Water Surface Amplitude?

Water Surface Amplitude is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Water Surface Amplitude can be measured.

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Water Surface Amplitude Formula

Water Surface Amplitude Example

Water Surface Amplitude Solution

Water Surface Amplitude Formula Elements

Other formulas in Wave Transmission Coefficient and Water Surface Amplitude category

How to Evaluate Water Surface Amplitude?

FAQs on Water Surface Amplitude

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