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Wave Period given Wavelength and Water Depth Formula

GoWave period given wave depth and wavelength Formula

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Wave Period is the time between successive peaks or troughs. Check FAQs

P = 2 \cdot \frac{π}{{((2 \cdot π \cdot \frac{[g]}{λ}) \cdot \tanh (2 \cdot π \cdot \frac{D}{λ}))}^{0.5}}

P - Wave Period?λ - Wavelength?D - Water Depth?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Wave Period given Wavelength and Water Depth Example

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Here is how the Wave Period given Wavelength and Water Depth equation looks like with Values.

Here is how the Wave Period given Wavelength and Water Depth equation looks like with Units.

Here is how the Wave Period given Wavelength and Water Depth equation looks like.

7.129 = 2 \cdot \frac{3.1416}{{((2 \cdot 3.1416 \cdot \frac{9.8066}{26.8}) \cdot \tanh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8}))}^{0.5}}

7.129 = 2 \cdot \frac{3.1416}{{((2 \cdot 3.1416 \cdot \frac{9.8066m/s²}{26.8m}) \cdot \tanh (2 \cdot 3.1416 \cdot \frac{1.5m}{26.8m}))}^{0.5}}

7.129 = 2 \cdot \frac{3.1416}{{((2 \cdot 3.1416 \cdot \frac{9.8066}{26.8}) \cdot \tanh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8}))}^{0.5}}

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Wave Period given Wavelength and Water Depth Solution

Follow our step by step solution on how to calculate Wave Period given Wavelength and Water Depth?

FIRST Step Consider the formula

P = 2 \cdot \frac{π}{{((2 \cdot π \cdot \frac{[g]}{λ}) \cdot \tanh (2 \cdot π \cdot \frac{D}{λ}))}^{0.5}}

Next Step Substitute values of Variables

∴

P = 2 \cdot \frac{π}{{((2 \cdot π \cdot \frac{[g]}{26.8m}) \cdot \tanh (2 \cdot π \cdot \frac{1.5m}{26.8m}))}^{0.5}}

Next Step Substitute values of Constants

∴

P = 2 \cdot \frac{3.1416}{{((2 \cdot 3.1416 \cdot \frac{9.8066m/s²}{26.8m}) \cdot \tanh (2 \cdot 3.1416 \cdot \frac{1.5m}{26.8m}))}^{0.5}}

Next Step Prepare to Evaluate

∴

P = 2 \cdot \frac{3.1416}{{((2 \cdot 3.1416 \cdot \frac{9.8066}{26.8}) \cdot \tanh (2 \cdot 3.1416 \cdot \frac{1.5}{26.8}))}^{0.5}}

Next Step Evaluate

∴

P = 7.12903697703261

LAST Step Rounding Answer

∴

P = 7.129

Wave Period given Wavelength and Water Depth Formula Elements

Variables

Constants

Functions

Wave Period

Wave Period is the time between successive peaks or troughs.

Symbol: P

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Wave Period

Wavelength

Wavelength is the distance between two successive crests or troughs of a wave.

Symbol: λ

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Wavelength

Water Depth

Water Depth means the depth as measured from the water level to the bottom of the considered water body.

Symbol: D

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Water Depth

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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

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).

Syntax: tanh(Number)

Other Formulas to find Wave Period

Go Wave period given wave depth and wavelength

P = \frac{λ \cdot ω}{[g]} \cdot \tanh (k \cdot D)

Other formulas in Wave Period category

Go Wave Period given Radian Frequency of Wave

T = \frac{2 \cdot π}{ω}

Go Wave Period given Wave Celerity

T = \frac{λ}{C}

Go Wave Period given Wave Celerity and Wavelength

p = \frac{C \cdot 2 \cdot π}{[g] \cdot \tanh (2 \cdot π \cdot \frac{D}{λ})}

Go Wave Period for Known Deepwater Celerity

p = \frac{C \cdot 2 \cdot π}{[g]}

How to Evaluate Wave Period given Wavelength and Water Depth?

Wave Period given Wavelength and Water Depth evaluator uses Wave Period = 2*pi/((2*pi*[g]/Wavelength)*tanh(2*pi*Water Depth/Wavelength))^0.5 to evaluate the Wave Period, The Wave Period given Wavelength and Water Depth formula is defined as time for particle on medium to make one complete vibrational cycle. Wave Period is denoted by P symbol.

How to evaluate Wave Period given Wavelength and Water Depth using this online evaluator? To use this online evaluator for Wave Period given Wavelength and Water Depth, enter Wavelength (λ) & Water Depth (D) and hit the calculate button.

FAQs on Wave Period given Wavelength and Water Depth

What is the formula to find Wave Period given Wavelength and Water Depth?

The formula of Wave Period given Wavelength and Water Depth is expressed as Wave Period = 2*pi/((2*pi*[g]/Wavelength)*tanh(2*pi*Water Depth/Wavelength))^0.5. Here is an example- 7.129037 = 2*pi/((2*pi*[g]/26.8)*tanh(2*pi*1.5/26.8))^0.5.

How to calculate Wave Period given Wavelength and Water Depth?

With Wavelength (λ) & Water Depth (D) we can find Wave Period given Wavelength and Water Depth using the formula - Wave Period = 2*pi/((2*pi*[g]/Wavelength)*tanh(2*pi*Water Depth/Wavelength))^0.5. This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Hyperbolic Tangent (tanh) function(s).

What are the other ways to Calculate Wave Period?

Here are the different ways to Calculate Wave Period-

Wave Period=(Wavelength*Wave Angular Frequency)/[g]*tanh(Wave Number*Water Depth)

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