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Resonant Period for Helmholtz Mode Formula

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Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance. Check FAQs

T H = (2 \cdot π) \cdot \sqrt{(L ch + l' c) \cdot \frac{A b}{[g] \cdot A C}}

T_H - Resonant Period for Helmholtz Mode?L_ch - Channel Length (Helmholtz Mode)?l'_c - Additional Length of the Channel?A_b - Surface Area of Bay?A_C - Cross Sectional Area?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

Resonant Period for Helmholtz Mode Example

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Here is how the Resonant Period for Helmholtz Mode equation looks like with Values.

Here is how the Resonant Period for Helmholtz Mode equation looks like with Units.

Here is how the Resonant Period for Helmholtz Mode equation looks like.

42.5638 = (2 \cdot 3.1416) \cdot \sqrt{(40 + 20) \cdot \frac{1.5001}{9.8066 \cdot 0.2}}

42.5638s = (2 \cdot 3.1416) \cdot \sqrt{(40m + 20m) \cdot \frac{1.5001m²}{9.8066m/s² \cdot 0.2m²}}

42.5638 = (2 \cdot 3.1416) \cdot \sqrt{(40 + 20) \cdot \frac{1.5001}{9.8066 \cdot 0.2}}

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Resonant Period for Helmholtz Mode Solution

Follow our step by step solution on how to calculate Resonant Period for Helmholtz Mode?

FIRST Step Consider the formula

T H = (2 \cdot π) \cdot \sqrt{(L ch + l' c) \cdot \frac{A b}{[g] \cdot A C}}

Next Step Substitute values of Variables

∴

T H = (2 \cdot π) \cdot \sqrt{(40m + 20m) \cdot \frac{1.5001m²}{[g] \cdot 0.2m²}}

Next Step Substitute values of Constants

∴

T H = (2 \cdot 3.1416) \cdot \sqrt{(40m + 20m) \cdot \frac{1.5001m²}{9.8066m/s² \cdot 0.2m²}}

Next Step Prepare to Evaluate

∴

T H = (2 \cdot 3.1416) \cdot \sqrt{(40 + 20) \cdot \frac{1.5001}{9.8066 \cdot 0.2}}

Next Step Evaluate

∴

T H = 42.5637872207341s

LAST Step Rounding Answer

∴

T H = 42.5638s

Resonant Period for Helmholtz Mode Formula Elements

Variables

Constants

Functions

Resonant Period for Helmholtz Mode

Resonant Period for Helmholtz Mode is the specific time period at which a resonant oscillation occurs in a system exhibiting Helmholtz resonance.

Symbol: T_H

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Resonant Period for Helmholtz Mode

Channel Length (Helmholtz Mode)

Channel Length (Helmholtz Mode) is the specific length of a coastal channel at which the natural frequency of the channel matches the frequency of incoming waves, leading to resonance.

Symbol: L_ch

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Channel Length (Helmholtz Mode)

Additional Length of the Channel

Additional Length of the Channel refers to the extra distance required in a channel or conduit to accommodate certain flow characteristics or conditions.

Symbol: l'_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Additional Length of the Channel

Surface Area of Bay

Surface Area of Bay is defined as a small body of water set off from the main body.

Symbol: A_b

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area of Bay

Cross Sectional Area

Cross Sectional Area is the area of the channel when viewed in a plane perpendicular to the direction of flow.

Symbol: A_C

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Cross Sectional Area

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 in Harbor Oscillations category

Go Maximum Horizontal Velocity at Node

V max = (\frac{H w}{2}) \cdot \sqrt{\frac{[g]}{D w}}

Go Standing Wave Height given Maximum Horizontal Velocity at Node

H w = (\frac{V max}{\sqrt{\frac{[g]}{D w}}}) \cdot 2

Go Water Depth given Maximum Horizontal Velocity at Node

D w = \frac{[g]}{{(\frac{V max}{\frac{H w}{2}})}^{2}}

Go Natural Free Oscillation Period for Closed Basin

T n = \frac{2 \cdot L B}{N \cdot \sqrt{[g] \cdot D w}}

How to Evaluate Resonant Period for Helmholtz Mode?

Resonant Period for Helmholtz Mode evaluator uses Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area of Bay/([g]*Cross Sectional Area)) to evaluate the Resonant Period for Helmholtz Mode, The Resonant Period for Helmholtz Mode formula is defined as the natural oscillation period of a submerged cavity or structure, such as a breakwater or coastal barrier, responding to wave action. Resonant Period for Helmholtz Mode is denoted by T_H symbol.

How to evaluate Resonant Period for Helmholtz Mode using this online evaluator? To use this online evaluator for Resonant Period for Helmholtz Mode, enter Channel Length (Helmholtz Mode) (L_ch), Additional Length of the Channel (l'_c), Surface Area of Bay (A_b) & Cross Sectional Area (A_C) and hit the calculate button.

FAQs on Resonant Period for Helmholtz Mode

What is the formula to find Resonant Period for Helmholtz Mode?

The formula of Resonant Period for Helmholtz Mode is expressed as Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area of Bay/([g]*Cross Sectional Area)). Here is an example- 42.56379 = (2*pi)*sqrt((40+20)*1.5001/([g]*0.2)).

How to calculate Resonant Period for Helmholtz Mode?

With Channel Length (Helmholtz Mode) (L_ch), Additional Length of the Channel (l'_c), Surface Area of Bay (A_b) & Cross Sectional Area (A_C) we can find Resonant Period for Helmholtz Mode using the formula - Resonant Period for Helmholtz Mode = (2*pi)*sqrt((Channel Length (Helmholtz Mode)+Additional Length of the Channel)*Surface Area of Bay/([g]*Cross Sectional Area)). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

Can the Resonant Period for Helmholtz Mode be negative?

Yes, the Resonant Period for Helmholtz Mode, measured in Time can be negative.

Which unit is used to measure Resonant Period for Helmholtz Mode?

Resonant Period for Helmholtz Mode is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Resonant Period for Helmholtz Mode can be measured.

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Resonant Period for Helmholtz Mode Formula

Resonant Period for Helmholtz Mode Example

Resonant Period for Helmholtz Mode Solution

Resonant Period for Helmholtz Mode Formula Elements

Other formulas in Harbor Oscillations category

How to Evaluate Resonant Period for Helmholtz Mode?

FAQs on Resonant Period for Helmholtz Mode

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