Wave Period Given Wave Celerity And Wavelength Calculator

Formula Used:

\[ p = \frac{C \times 2\pi}{g \times \tanh\left(\frac{2\pi D}{\lambda}\right)} \]

Coastal Wave Period (p):

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1. What is the Wave Period Formula?

The wave period formula calculates the time between successive peaks or troughs of coastal waves using wave celerity, water depth, and wavelength. It's based on the dispersion relationship for water waves.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ p = \frac{C \times 2\pi}{g \times \tanh\left(\frac{2\pi D}{\lambda}\right)} \]

Where:

\( p \) — Coastal wave period (seconds)
\( C \) — Celerity of the wave (m/s)
\( D \) — Water depth (meters)
\( \lambda \) — Wavelength (meters)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( \pi \) — Pi constant (3.141592653589793)
\( \tanh \) — Hyperbolic tangent function

Explanation: The formula accounts for wave dispersion in varying water depths using the hyperbolic tangent function.

3. Importance of Wave Period Calculation

Details: Wave period is crucial for coastal engineering, navigation safety, beach erosion studies, and offshore structure design. It helps predict wave behavior and energy distribution.

4. Using the Calculator

Tips: Enter wave celerity in m/s, water depth in meters, and wavelength in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is wave celerity?
A: Wave celerity is the speed at which a wave propagates through a medium, measured as the distance a wave crest travels per unit time.

Q2: How does water depth affect wave period?
A: In shallow water, waves slow down and their period remains relatively constant, while in deep water, wave period is more dependent on wavelength.

Q3: What are typical wave period values?
A: Ocean waves typically have periods between 5-20 seconds, with longer periods indicating more energetic swell waves.

Q4: Why use the hyperbolic tangent function?
A: The tanh function smoothly transitions between deep water and shallow water wave behavior in the dispersion relationship.

Q5: Can this formula be used for all wave types?
A: This formula applies to linear waves in water of constant depth. For nonlinear waves or rapidly varying depths, more complex models are needed.