Standing Wave Height For Average Horizontal Velocity At Node Calculator

Formula Used:

\[ Wave\ Height = \frac{(Average\ Horizontal\ Velocity\ at\ a\ Node \times \pi \times Water\ Depth\ at\ Harbor \times Natural\ Free\ Oscillating\ Period\ of\ a\ Basin)}{Wavelength} \]

Average Horizontal Velocity at a Node (V'):

m/s

Water Depth at Harbor (d):

Natural Free Oscillating Period of a Basin (Tn):

Wavelength (λ):

Wave Height (Hwave):

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1. What is the Standing Wave Height Formula?

The Standing Wave Height formula calculates the height of standing waves formed when two equal waves travel in opposite directions, creating the characteristic up/down motion of the water surface without wave progression.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( H_{wave} \) — Wave Height (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)
\( \lambda \) — Wavelength (m)

Explanation: This formula calculates wave height based on the relationship between horizontal velocity, water depth, oscillation period, and wavelength.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for harbor design, coastal engineering, navigation safety, and understanding wave behavior in enclosed basins.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is a standing wave?
A: A standing wave is formed when two waves of equal frequency and amplitude travel in opposite directions, creating stationary nodes and antinodes.

Q2: How does water depth affect wave height?
A: Water depth influences wave behavior through shoaling effects - as waves approach shallower water, their height typically increases while wavelength decreases.

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

Q4: When is this formula most applicable?
A: This formula is particularly useful for harbor resonance studies, seiche analysis, and understanding wave behavior in enclosed or semi-enclosed water bodies.

Q5: Are there limitations to this equation?
A: The formula assumes ideal conditions and may be less accurate in complex bathymetries, with irregular basin shapes, or under strong external forcing conditions.