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Standing Wave Height given Maximum Horizontal Particle Excursion at Node Formula

GoStanding Wave Height for Average Horizontal Velocity at Node Formula

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Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress. Check FAQs

H wave = \frac{2 \cdot π \cdot X}{T n} \cdot \sqrt{\frac{[g]}{d}}

H_wave - Wave Height?X - Maximum Horizontal Particle Excursion?T_n - Natural Free Oscillating Period of a Basin?d - Water Depth at Harbor?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Example

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Here is how the Standing Wave Height given Maximum Horizontal Particle Excursion at Node equation looks like.

27.5112 = \frac{2 \cdot 3.1416 \cdot 7.88}{5.5} \cdot \sqrt{\frac{9.8066}{1.05}}

27.5112m = \frac{2 \cdot 3.1416 \cdot 7.88m}{5.5s} \cdot \sqrt{\frac{9.8066m/s²}{1.05m}}

27.5112 = \frac{2 \cdot 3.1416 \cdot 7.88}{5.5} \cdot \sqrt{\frac{9.8066}{1.05}}

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Standing Wave Height given Maximum Horizontal Particle Excursion at Node Solution

Follow our step by step solution on how to calculate Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

FIRST Step Consider the formula

H wave = \frac{2 \cdot π \cdot X}{T n} \cdot \sqrt{\frac{[g]}{d}}

Next Step Substitute values of Variables

∴

H wave = \frac{2 \cdot π \cdot 7.88m}{5.5s} \cdot \sqrt{\frac{[g]}{1.05m}}

Next Step Substitute values of Constants

∴

H wave = \frac{2 \cdot 3.1416 \cdot 7.88m}{5.5s} \cdot \sqrt{\frac{9.8066m/s²}{1.05m}}

Next Step Prepare to Evaluate

∴

H wave = \frac{2 \cdot 3.1416 \cdot 7.88}{5.5} \cdot \sqrt{\frac{9.8066}{1.05}}

Next Step Evaluate

∴

H wave = 27.5111715247954m

LAST Step Rounding Answer

∴

H wave = 27.5112m

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Formula Elements

Variables

Constants

Functions

Wave Height

Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress.

Symbol: H_wave

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wave Height

Maximum Horizontal Particle Excursion

Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Symbol: X

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Maximum Horizontal Particle Excursion

Natural Free Oscillating Period of a Basin

Natural Free Oscillating Period of a Basin referred to as the natural period or resonant period, is the time it takes for a wave to travel from one end of the basin to the other and back again.

Symbol: T_n

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Natural Free Oscillating Period of a Basin

Water Depth at Harbor

Water Depth at Harbor is the vertical distance from the water surface to the seabed or bottom of the harbor.

Symbol: d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Water Depth at Harbor

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Wave Height

Go Standing Wave Height for Average Horizontal Velocity at Node

H wave = \frac{V' \cdot π \cdot d \cdot T n}{λ}

Other formulas in Harbor Oscillations category

Go Maximum Oscillation Period corresponding to Fundamental Mode

T 1 = 2 \cdot \frac{L ba}{\sqrt{[g] \cdot D}}

Go Basin Length along axis given Maximum Oscillation Period corresponding to Fundamental Mode

L ba = T 1 \cdot \frac{\sqrt{[g] \cdot D}}{2}

Go Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

d = \frac{{(2 \cdot \frac{L ba}{T n})}^{2}}{[g]}

Go Period for Fundamental Mode

T n = \frac{4 \cdot L ba}{\sqrt{[g] \cdot d}}

How to Evaluate Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

Standing Wave Height given Maximum Horizontal Particle Excursion at Node evaluator uses Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth at Harbor) to evaluate the Wave Height, The Standing Wave Height given Maximum Horizontal Particle Excursion at Node formula is defined as the vertical distance between the crest (highest point) and the trough (lowest point) of a standing wave. In a standing wave, certain points (nodes) appear to be stationary while the rest of the wave oscillates, at the nodes of a standing wave, the vertical motion of water particles is zero, but they still experience horizontal movement. Wave Height is denoted by H_wave symbol.

How to evaluate Standing Wave Height given Maximum Horizontal Particle Excursion at Node using this online evaluator? To use this online evaluator for Standing Wave Height given Maximum Horizontal Particle Excursion at Node, enter Maximum Horizontal Particle Excursion (X), Natural Free Oscillating Period of a Basin (T_n) & Water Depth at Harbor (d) and hit the calculate button.

FAQs on Standing Wave Height given Maximum Horizontal Particle Excursion at Node

What is the formula to find Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

The formula of Standing Wave Height given Maximum Horizontal Particle Excursion at Node is expressed as Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth at Harbor). Here is an example- 27.51117 = (2*pi*7.88)/5.5*sqrt([g]/1.05).

How to calculate Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

With Maximum Horizontal Particle Excursion (X), Natural Free Oscillating Period of a Basin (T_n) & Water Depth at Harbor (d) we can find Standing Wave Height given Maximum Horizontal Particle Excursion at Node using the formula - Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth at Harbor). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Wave Height?

Here are the different ways to Calculate Wave Height-

Wave Height=(Average Horizontal Velocity at a Node*pi*Water Depth at Harbor*Natural Free Oscillating Period of a Basin)/Wavelength

Can the Standing Wave Height given Maximum Horizontal Particle Excursion at Node be negative?

No, the Standing Wave Height given Maximum Horizontal Particle Excursion at Node, measured in Length cannot be negative.

Which unit is used to measure Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

Standing Wave Height given Maximum Horizontal Particle Excursion at Node is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Standing Wave Height given Maximum Horizontal Particle Excursion at Node can be measured.

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Standing Wave Height given Maximum Horizontal Particle Excursion at Node Formula

​GoStanding Wave Height for Average Horizontal Velocity at Node Formula

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Example

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Solution

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Formula Elements

Other Formulas to find Wave Height

Other formulas in Harbor Oscillations category

How to Evaluate Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

FAQs on Standing Wave Height given Maximum Horizontal Particle Excursion at Node

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GoStanding Wave Height for Average Horizontal Velocity at Node Formula