Wave Length For Average Horizontal Velocity At Node Calculator

Formula Used:

\[ \lambda = \frac{V' \times \pi \times d \times T_n}{H_{wave}} \]

Average Horizontal Velocity at a Node (V'):

m/s

Water Depth at Harbor (d):

Natural Free Oscillating Period of a Basin (T_n):

Wave Height (H_wave):

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 average horizontal velocity at a node, water depth, natural oscillation period, and wave height.

2. How Does the Calculator Work?

The calculator uses the wavelength formula:

\[ \lambda = \frac{V' \times \pi \times d \times T_n}{H_{wave}} \]

Where:

\( \lambda \) — Wavelength (m)
\( V' \) — Average Horizontal Velocity at a Node (m/s)
\( \pi \) — Archimedes' constant (≈3.14159)
\( d \) — Water Depth at Harbor (m)
\( T_n \) — Natural Free Oscillating Period of a Basin (s)
\( H_{wave} \) — Wave Height (m)

Explanation: The formula calculates wavelength by considering the relationship between wave velocity, water depth, oscillation period, and wave height.

3. Importance of Wavelength Calculation

Details: Accurate wavelength calculation is crucial for harbor design, coastal engineering, wave energy estimation, and understanding wave behavior in confined basins.

4. Using the Calculator

Tips: Enter all values in appropriate units (m/s for velocity, m for depth and height, s for period). All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a node in wave mechanics?
A: A node is a point along a standing wave where the wave has zero amplitude due to destructive interference.

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

Q3: What is natural free oscillating period?
A: It's the time it takes for a wave to travel from one end of a basin to the other and back, representing the basin's natural resonance period.

Q4: Are there limitations to this formula?
A: This formula assumes ideal conditions and may need adjustments for complex bathymetry, nonlinear effects, or energy dissipation.

Q5: How accurate is this calculation for real-world applications?
A: While providing a good estimate, field measurements and additional factors should be considered for precise engineering applications.