Wavelength As Function Of Depth And Wave Period Calculator

Wavelength Formula:

\[ \lambda = \frac{[g] \cdot T^2}{2\pi} \cdot \tanh(k \cdot d) \]

Wavelength (λ):

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1. What is the Wavelength Formula?

The wavelength formula calculates the distance between two successive crests or troughs of a wave based on wave period, wave number, and water depth. This equation is fundamental in wave mechanics and oceanography.

2. How Does the Calculator Work?

The calculator uses the wavelength formula:

\[ \lambda = \frac{[g] \cdot T^2}{2\pi} \cdot \tanh(k \cdot d) \]

Where:

\( \lambda \) — Wavelength (meters)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( T \) — Wave period (seconds)
\( \pi \) — Archimedes' constant (3.141592653589793)
\( k \) — Wave number
\( d \) — Water depth (meters)
\( \tanh \) — Hyperbolic tangent function

Explanation: The formula accounts for the dispersion relationship of water waves, where wavelength depends on wave period and water depth through the hyperbolic tangent function.

3. Importance of Wavelength Calculation

Details: Accurate wavelength calculation is crucial for coastal engineering, marine navigation, offshore structure design, and understanding wave behavior in different water depths.

4. Using the Calculator

Tips: Enter wave period in seconds, wave number, and water depth in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is wave number?
A: Wave number (k) is defined as 2π divided by wavelength, representing the number of wavelengths per unit distance along the wave propagation direction.

Q2: How does water depth affect wavelength?
A: In deep water, waves are less affected by the bottom and have longer wavelengths. In shallow water, wave speed and wavelength decrease due to bottom friction.

Q3: What is the significance of the hyperbolic tangent function?
A: The tanh function smoothly transitions between deep water and shallow water wave behavior, providing accurate results across all depth regimes.

Q4: What are typical wavelength values?
A: Ocean waves typically have wavelengths from tens to hundreds of meters, while tsunamis can have wavelengths of hundreds of kilometers.

Q5: Can this formula be used for all wave types?
A: This formula is specifically for surface gravity waves in water. Different equations apply for other wave types like sound waves or electromagnetic waves.