Standing Wave Height given Maximum Horizontal Particle Excursion at Node Calculator

✖Maximum Horizontal Particle Excursion at a Node in a standing wave [length].ⓘ Maximum Horizontal Particle Excursion [X]			+10% -10%
✖Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.ⓘ Natural Free Oscillating Period of a Basin [T_n]			+10% -10%
✖Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.ⓘ Water Depth [d]			+10% -10%

✖Standing Wave Height result when two equal waves are going in opposite direction and in this case you get the usual up/down motion of the water surface but the waves don't progress [length].ⓘ Standing Wave Height given Maximum Horizontal Particle Excursion at Node [H]

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Standing Wave Height given Maximum Horizontal Particle Excursion at Node

Formula

`"H" = (2*pi*"X")/"T"_{"n"}*sqrt("[g]"/"d")`

Example

`"17.80545m"=(2*pi*"5.1m")/"5.5s"*sqrt("[g]"/"1.05m")`

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Standing Wave Height given Maximum Horizontal Particle Excursion at Node Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth)
H = (2*pi*X)/T_n*sqrt([g]/d)
This formula uses 2 Constants, 1 Functions, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Standing Wave Height - (Measured in Meter) - Standing Wave Height result when two equal waves are going in opposite direction and in this case you get the usual up/down motion of the water surface but the waves don't progress [length].
Maximum Horizontal Particle Excursion - (Measured in Meter) - Maximum Horizontal Particle Excursion at a Node in a standing wave [length].
Natural Free Oscillating Period of a Basin - (Measured in Second) - Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth.
Water Depth - (Measured in Meter) - Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

STEP 1: Convert Input(s) to Base Unit

Maximum Horizontal Particle Excursion: 5.1 Meter --> 5.1 Meter No Conversion Required
Natural Free Oscillating Period of a Basin: 5.5 Second --> 5.5 Second No Conversion Required
Water Depth: 1.05 Meter --> 1.05 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

H = (2*pi*X)/T_n*sqrt([g]/d) --> (2*pi*5.1)/5.5*sqrt([g]/1.05)

Evaluating ... ...

H = 17.8054536518346

STEP 3: Convert Result to Output's Unit

17.8054536518346 Meter --> No Conversion Required

FINAL ANSWER

17.8054536518346 ≈ 17.80545 Meter <-- Standing Wave Height

(Calculation completed in 00.004 seconds)

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< 22 Harbor Oscillations Calculators

Additional Length to account for Mass Outside each end of Channel

Go Additional Length of the Channel = (-Channel Width corresponding to Mean Water Depth/pi)*ln(pi*Channel Width corresponding to Mean Water Depth/(sqrt([g]*Channel Depth)*Resonant Period for Helmholtz Mode))

Resonant Period for Helmholtz Mode

Go Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area))

Channel Cross-sectional Area given Resonant Period for Helmholtz mode

Go Channel Cross-sectional Area = (Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*(Resonant Period for Helmholtz Mode/2*pi)^2)

Basin Surface Area given Resonant Period for Helmholtz mode

Go Surface Area of Bay = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/(Channel Length+Additional Length of the Channel))

Additional Length accounting for Mass Outside each End of Channel

Go Additional Length of the Channel = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Channel Length

Channel Length for Resonant Period for Helmholtz Mode

Go Channel Length = ([g]*Channel Cross-sectional Area*(Resonant Period for Helmholtz Mode/2*pi)^2/Surface Area of Bay)-Additional Length of the Channel

Standing Wave Height given Maximum Horizontal Particle Excursion at Node

Go Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth)

Maximum Horizontal Particle Excursion at Node

Go Maximum Horizontal Particle Excursion = (Standing Wave Height*Natural Free Oscillating Period of a Basin/2*pi)*sqrt([g]/Water Depth)

Standing Wave Height for Average Horizontal Velocity at Node

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

Water Depth given Average Horizontal Velocity at Node

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

Wave Length for Average Horizontal Velocity at Node

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

Average Horizontal Velocity at Node

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

Water Depth given Maximum Horizontal Particle Excursion at Node

Go Water Depth = [g]/(2*pi*Maximum Horizontal Particle Excursion/Standing Wave Height*Natural Free Oscillating Period of a Basin)^2

Standing Wave Height given Maximum Horizontal Velocity at Node

Go Standing Wave Height = (Maximum Horizontal Velocity at a Node/sqrt([g]/Water Depth))*2

Maximum Horizontal Velocity at Node

Go Maximum Horizontal Velocity at a Node = (Standing Wave Height/2)*sqrt([g]/Water Depth)

Period for Fundamental Mode

Go Natural Free Oscillating Period of a Basin = (4*Length of Basin)/sqrt([g]*Water Depth)

Basin Length along Axis for given Period of Fundamental Mode

Go Length of Basin = Natural Free Oscillating Period of a Basin*sqrt([g]*Water Depth)/4

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

Go Length of Basin = Maximum Oscillation Period*sqrt([g]*Water Depth)/2

Maximum Oscillation Period corresponding to Fundamental Mode

Go Maximum Oscillation Period = 2*Length of Basin/sqrt([g]*Water Depth)

Water Depth given Maximum Horizontal Velocity at Node

Go Water Depth = [g]/(Maximum Horizontal Velocity at a Node/(Standing Wave Height/2))^2

Water Depth for given Period for Fundamental Mode

Go Water Depth = ((4*Length of Basin/Natural Free Oscillating Period of a Basin)^2)/[g]

Water Depth given Maximum Oscillation Period corresponding to Fundamental Mode

Go Water Depth = (2*Length of Basin/Natural Free Oscillating Period of a Basin)^2/[g]

Standing Wave Height given Maximum Horizontal Particle Excursion at Node Formula

Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth)
H = (2*pi*X)/T_n*sqrt([g]/d)

What are Open Basins?

Open Basins are Exorheic, or open lakes drain into a river, or other body of water that ultimately drains into the ocean.

What are Closed Basins?

Enclosed basins can experience oscillations due to a variety of causes. Lake oscillations are usually the result of a sudden change, or a series of intermittent-periodic changes, in atmospheric pressure or wind velocity. Oscillations in canals can be initiated by suddenly adding or subtracting large quantities of water. Harbor oscillations are usually initiated by forcing through the entrance; hence, they deviate from a true closed basin. Local seismic activity can also create oscillations in an enclosed basin.

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

Standing Wave Height given Maximum Horizontal Particle Excursion at Node calculator uses Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth) to calculate the Standing Wave Height, Standing Wave Height given Maximum Horizontal Particle Excursion at Node result when two equal waves are going in opposite direction and in this case you get usual up/down motion of water surface but waves don't progress. These are common in coastal areas where waves reflect off seawalls, ship's hulls, or breakwaters. Standing Wave Height is denoted by H symbol.

How to calculate Standing Wave Height given Maximum Horizontal Particle Excursion at Node using this online calculator? To use this online calculator 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 (d) and hit the calculate button. Here is how the Standing Wave Height given Maximum Horizontal Particle Excursion at Node calculation can be explained with given input values -> 18.24516 = (2*pi*5.1)/5.5*sqrt([g]/1.05).

FAQ

What is Standing Wave Height given Maximum Horizontal Particle Excursion at Node?

Standing Wave Height given Maximum Horizontal Particle Excursion at Node result when two equal waves are going in opposite direction and in this case you get usual up/down motion of water surface but waves don't progress. These are common in coastal areas where waves reflect off seawalls, ship's hulls, or breakwaters and is represented as H = (2*pi*X)/T_n*sqrt([g]/d) or Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth). Maximum Horizontal Particle Excursion at a Node in a standing wave [length], Natural Free Oscillating Period of a Basin have a period equal to the natural resonant period of the basin which is determined by the basin's geometry and depth & Water Depth of the considered catchment is the depth as measured from the water level to the bottom of the considered water body.

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

Standing Wave Height given Maximum Horizontal Particle Excursion at Node result when two equal waves are going in opposite direction and in this case you get usual up/down motion of water surface but waves don't progress. These are common in coastal areas where waves reflect off seawalls, ship's hulls, or breakwaters is calculated using Standing Wave Height = (2*pi*Maximum Horizontal Particle Excursion)/Natural Free Oscillating Period of a Basin*sqrt([g]/Water Depth). To calculate Standing Wave Height given Maximum Horizontal Particle Excursion at Node, you need Maximum Horizontal Particle Excursion (X), Natural Free Oscillating Period of a Basin (T_n) & Water Depth (d). With our tool, you need to enter the respective value for Maximum Horizontal Particle Excursion, Natural Free Oscillating Period of a Basin & Water Depth 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 Standing Wave Height?

In this formula, Standing Wave Height uses Maximum Horizontal Particle Excursion, Natural Free Oscillating Period of a Basin & Water Depth. We can use 2 other way(s) to calculate the same, which is/are as follows -

Standing Wave Height = (Maximum Horizontal Velocity at a Node/sqrt([g]/Water Depth))*2
Standing Wave Height = (Average Horizontal Velocity at a Node*pi*Water Depth*Natural Free Oscillating Period of a Basin)/Wavelength

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