Water Surface Amplitude Calculator

Water Surface Amplitude Formula:

\[ N = H_i \times \cos\left(\frac{2\pi x}{L_o}\right) \times \cos\left(\frac{2\pi t}{T}\right) \]

Incident Wave Height (Hi):

Horizontal Ordinate (x):

Incident Wave Length in Deepwater (Lo):

Time Elapsed (t):

Reflected Wave Period (T):

Water Surface Amplitude (N):

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1. What is Water Surface Amplitude?

Water Surface Amplitude is the maximum vertical distance between the highest and lowest points of a water surface wave. It represents the magnitude of wave oscillation at a specific point on the water surface.

2. How Does the Calculator Work?

The calculator uses the Water Surface Amplitude formula:

\[ N = H_i \times \cos\left(\frac{2\pi x}{L_o}\right) \times \cos\left(\frac{2\pi t}{T}\right) \]

Where:

\( N \) — Water Surface Amplitude (m)
\( H_i \) — Incident Wave Height (m)
\( x \) — Horizontal Ordinate (m)
\( L_o \) — Incident Wave Length in Deepwater (m)
\( t \) — Time Elapsed (s)
\( T \) — Reflected Wave Period (s)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the amplitude of water surface waves by considering the incident wave characteristics, spatial position, and time evolution of the wave pattern.

3. Importance of Water Surface Amplitude Calculation

Details: Accurate water surface amplitude calculation is crucial for coastal engineering, offshore structure design, wave energy assessment, and understanding wave behavior in various marine environments.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for length, seconds for time). Ensure all input values are positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the cosine terms in the formula?
A: The cosine terms represent the spatial and temporal variations of the wave pattern, accounting for wave position and time-dependent behavior.

Q2: How does horizontal ordinate affect the amplitude?
A: The horizontal ordinate determines the phase of the wave at a specific location, influencing the amplitude through the cosine function.

Q3: What is the difference between incident and reflected waves?
A: Incident waves travel from the source, while reflected waves bounce back from obstacles or boundaries, creating interference patterns.

Q4: Are there limitations to this equation?
A: This formula assumes ideal wave conditions and may not account for complex wave interactions, nonlinear effects, or energy dissipation.

Q5: When is this calculation most applicable?
A: This calculation is particularly useful for standing wave patterns, harbor resonance studies, and wave interference analysis in coastal engineering.