Angular Frequency of Wave Calculator

Angular Frequency of Wave Formula:

\[ \omega_c = \sqrt{[g] \times k \times \tanh(k \times d)} \]

Angular Frequency of Wave (ωc):

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1. What is Angular Frequency of Wave?

Angular Frequency of Wave (ωc) is the rate of change of phase of a sinusoidal waveform, typically measured in radians per second. It represents how rapidly the wave oscillates in space and time.

2. How Does the Calculator Work?

The calculator uses the Angular Frequency of Wave formula:

\[ \omega_c = \sqrt{[g] \times k \times \tanh(k \times d)} \]

Where:

\( \omega_c \) — Angular Frequency of Wave (rad/s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( k \) — Wave Number for Water Wave (m⁻¹)
\( d \) — Coastal Mean Depth (m)
\( \tanh \) — Hyperbolic tangent function

Explanation: The equation calculates the angular frequency of water waves considering gravitational acceleration, wave number, and water depth through the hyperbolic tangent function.

3. Importance of Angular Frequency Calculation

Details: Angular frequency is crucial for understanding wave dynamics, predicting wave behavior in coastal areas, designing marine structures, and studying oceanographic phenomena.

4. Using the Calculator

Tips: Enter wave number in m⁻¹ and coastal mean depth in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of angular frequency?
A: Angular frequency determines how many radians a wave completes per second, directly relating to the wave's temporal oscillation characteristics.

Q2: How does water depth affect angular frequency?
A: In shallow water (small d), waves are depth-limited and frequency decreases. In deep water, waves are less affected by bottom conditions.

Q3: What are typical values for wave number?
A: Wave number typically ranges from 0.01 to 10 m⁻¹, depending on wavelength (k = 2π/λ).

Q4: Why use hyperbolic tangent in the formula?
A: The tanh function smoothly transitions between deep water (tanh(kd)≈1) and shallow water (tanh(kd)≈kd) wave dispersion relationships.

Q5: Can this formula be used for all types of waves?
A: This formula is specifically for surface gravity waves in water. Other wave types (acoustic, electromagnetic) have different dispersion relations.