Wavelength As Function Of Water Depth And Wave Period Calculator

Wavelength Formula:

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

Wave Period (T):

Wave Angular Frequency (ω):

rad/s

Wave Number (k):

Water Depth (d):

Wavelength (λ):

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1. What is Wavelength Calculation?

Wavelength calculation determines the distance between two successive crests or troughs of a wave in water bodies. It's an essential parameter in oceanography, coastal engineering, and wave mechanics studies.

2. How Does the Calculator Work?

The calculator uses the wavelength formula:

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

Where:

\( \lambda \) — Wavelength (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( T \) — Wave period (s)
\( \omega \) — Wave angular frequency (rad/s)
\( k \) — Wave number
\( d \) — Water depth (m)
\( \tanh \) — Hyperbolic tangent function

Explanation: The formula accounts for wave dispersion in water of finite depth, where the hyperbolic tangent function models the effect of water depth on wave propagation.

3. Importance of Wavelength Calculation

Details: Accurate wavelength calculation is crucial for coastal structure design, ship navigation, offshore operations, and understanding wave energy distribution in marine environments.

4. Using the Calculator

Tips: Enter wave period in seconds, angular frequency in rad/s, wave number, and water depth in meters. All values must be positive (water depth can be zero for shallow water approximations).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the hyperbolic tangent function?
A: The tanh function accounts for the transition from deep water waves (where depth > λ/2) to shallow water waves (where depth < λ/20), providing accurate results across all depth regimes.

Q2: How does water depth affect wavelength?
A: In deep water, wavelength is determined solely by wave period. In shallow water, wavelength decreases with decreasing depth while wave speed decreases.

Q3: What are typical wavelength values in oceans?
A: Ocean wavelengths typically range from a few centimeters (capillary waves) to several hundred meters (tsunami waves and swell).

Q4: Can this formula be used for all wave types?
A: This formula applies to linear gravity waves. For nonlinear waves, breaking waves, or waves with significant amplitude, more complex models are needed.

Q5: How accurate is this calculation?
A: The formula provides excellent accuracy for most engineering applications involving small-amplitude waves in constant depth conditions.