Standing Wave Height Given Maximum Horizontal Particle Excursion At Node Calculator

Standing Wave Height Formula:

\[ H_{wave} = \frac{2\pi X}{T_n} \sqrt{\frac{[g]}{d}} \]

Maximum Horizontal Particle Excursion (X):

Natural Free Oscillating Period (Tₙ):

Water Depth at Harbor (d):

Wave Height (Hₐᵥₑ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Standing Wave Height?

Standing Wave Height is formed when two equal waves are going in opposite direction and create the usual up/down motion of the water surface, but the waves don't progress. It represents the maximum vertical distance between the crest and trough of a standing wave.

2. How Does the Calculator Work?

The calculator uses the standing wave height formula:

\[ H_{wave} = \frac{2\pi X}{T_n} \sqrt{\frac{[g]}{d}} \]

Where:

\( H_{wave} \) — Wave Height (m)
\( X \) — Maximum Horizontal Particle Excursion (m)
\( T_n \) — Natural Free Oscillating Period of a Basin (s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( d \) — Water Depth at Harbor (m)
\( \pi \) — Archimedes' constant (3.14159)

Explanation: The formula calculates wave height based on particle motion characteristics and basin properties, incorporating gravitational effects and water depth.

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 confined basins. It helps predict potential wave impacts on structures and vessels.

4. Using the Calculator

Tips: Enter maximum horizontal particle excursion in meters, natural oscillating period in seconds, and water depth in meters. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is maximum horizontal particle excursion?
A: Maximum Horizontal Particle Excursion refers to the maximum distance that a particle can travel horizontally from its initial position under the influence of a wave or current.

Q2: What is natural free oscillating period?
A: Natural Free Oscillating Period of a Basin is 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 characteristics.

Q3: Why is water depth important in this calculation?
A: Water depth affects wave propagation speed and energy distribution. Deeper water allows waves to travel faster and with different energy characteristics than shallow water.

Q4: What are typical values for wave height in harbors?
A: Wave heights in harbors typically range from a few centimeters to several meters, depending on basin size, water depth, and external wave conditions.

Q5: Are there limitations to this equation?
A: This equation assumes ideal conditions and may be less accurate for very shallow water, complex basin geometries, or when non-linear wave effects become significant.