Resonant Period for Helmholtz Mode Calculator

✖Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.ⓘ Channel Length [L_c]			+10% -10%
✖Additional Length of the Channel to account for Mass Outside each end of the Channel.ⓘ Additional Length of the Channel [l'_c]			+10% -10%
✖Surface Area of Bay is defined as a small body of water set off from the main body.ⓘ Surface Area of Bay [A_b]			+10% -10%
✖Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.ⓘ Channel Cross-sectional Area [A_C]			+10% -10%

✖Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity.ⓘ Resonant Period for Helmholtz Mode [T_H]

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Resonant Period for Helmholtz Mode

Formula

`"T"_{"H"} = (2*pi)*sqrt(("L"_{"c"}+"l'"_{"c"})*"A"_{"b"}/("[g]"*"A"_{"C"}))`

Example

`"6.019429s"=(2*pi)*sqrt(("40m"+"20m")*"1.5001m²"/("[g]"*"10m²"))`

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Resonant Period for Helmholtz Mode Solution

STEP 0: Pre-Calculation Summary

Formula Used

Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area))
T_H = (2*pi)*sqrt((L_c+l'_c)*A_b/([g]*A_C))
This formula uses 2 Constants, 1 Functions, 5 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

Resonant Period for Helmholtz Mode - (Measured in Second) - Resonant Period for Helmholtz Mode [time], Helmholtz resonance or wind throb is the phenomenon of air resonance in a cavity.
Channel Length - (Measured in Meter) - Channel Length is the measurement or extent of water wider than a strait, joining two larger areas of water.
Additional Length of the Channel - (Measured in Meter) - Additional Length of the Channel to account for Mass Outside each end of the Channel.
Surface Area of Bay - (Measured in Square Meter) - Surface Area of Bay is defined as a small body of water set off from the main body.
Channel Cross-sectional Area - (Measured in Square Meter) - Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.

STEP 1: Convert Input(s) to Base Unit

Channel Length: 40 Meter --> 40 Meter No Conversion Required
Additional Length of the Channel: 20 Meter --> 20 Meter No Conversion Required
Surface Area of Bay: 1.5001 Square Meter --> 1.5001 Square Meter No Conversion Required
Channel Cross-sectional Area: 10 Square Meter --> 10 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_H = (2*pi)*sqrt((L_c+l'_c)*A_b/([g]*A_C)) --> (2*pi)*sqrt((40+20)*1.5001/([g]*10))

Evaluating ... ...

T_H = 6.01942851535248

STEP 3: Convert Result to Output's Unit

6.01942851535248 Second --> No Conversion Required

FINAL ANSWER

6.01942851535248 ≈ 6.019429 Second <-- Resonant Period for Helmholtz Mode

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Harbor Oscillations » Resonant Period for Helmholtz Mode

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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National Institute of Technology Karnataka (NITK), Surathkal

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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]

Resonant Period for Helmholtz Mode Formula

Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area))
T_H = (2*pi)*sqrt((L_c+l'_c)*A_b/([g]*A_C))

What is the resonant frequency of a Helmholtz resonator?

Like a reed or like lips at the mouthpiece of a wind instrument, the vocal folds function acoustically as a closed end, so that the vocal column is a closed-tube resonator with resonant frequencies of about 500, 1,500, 2,500, and 3,500 hertz, and so on.

What are Open basins - Helmholtz resonance?

A harbor basin open to the sea through an inlet can resonate in a mode referred to as the Helmholtz or grave mode (Sorensen 1986b). This very long period mode appears to be particularly significant for harbors responding to tsunami energy and for several harbors on the Great Lakes that respond to long-wave energy spectra generated by storms (Miles 1974; Sorensen 1986; Sorensen and Seelig 1976).

How to Calculate Resonant Period for Helmholtz Mode?

Resonant Period for Helmholtz Mode calculator uses Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area)) to calculate the Resonant Period for Helmholtz Mode, The Resonant Period for Helmholtz Mode or wind throb is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle. Resonant Period for Helmholtz Mode is denoted by T_H symbol.

How to calculate Resonant Period for Helmholtz Mode using this online calculator? To use this online calculator for Resonant Period for Helmholtz Mode, enter Channel Length (L_c), Additional Length of the Channel (l'_c), Surface Area of Bay (A_b) & Channel Cross-sectional Area (A_C) and hit the calculate button. Here is how the Resonant Period for Helmholtz Mode calculation can be explained with given input values -> 6.019228 = (2*pi)*sqrt((40+20)*1.5001/([g]*10)).

FAQ

What is Resonant Period for Helmholtz Mode?

The Resonant Period for Helmholtz Mode or wind throb is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle and is represented as T_H = (2*pi)*sqrt((L_c+l'_c)*A_b/([g]*A_C)) or 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 Length is the measurement or extent of water wider than a strait, joining two larger areas of water, Additional Length of the Channel to account for Mass Outside each end of the Channel, Surface Area of Bay is defined as a small body of water set off from the main body & Channel Cross-sectional Area [length^2] is the cross sectional area of the channel.

How to calculate Resonant Period for Helmholtz Mode?

The Resonant Period for Helmholtz Mode or wind throb is the phenomenon of air resonance in a cavity, such as when one blows across the top of an empty bottle is calculated using Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length+Additional Length of the Channel)*Surface Area of Bay/([g]*Channel Cross-sectional Area)). To calculate Resonant Period for Helmholtz Mode, you need Channel Length (L_c), Additional Length of the Channel (l'_c), Surface Area of Bay (A_b) & Channel Cross-sectional Area (A_C). With our tool, you need to enter the respective value for Channel Length, Additional Length of the Channel, Surface Area of Bay & Channel Cross-sectional Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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