Reflected Wave Period Given Water Surface Amplitude Calculator

Formula:

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

Time Elapsed (t):

Water Surface Amplitude (N):

Incident Wave Height (H_i):

Horizontal Ordinate (x):

Incident Wave Length in Deepwater (L_o):

Reflected Wave Period (T):

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1. What is Reflected Wave Period?

The Reflected Wave Period is the time interval between successive crests or troughs of a wave after it reflects off a surface, measured in seconds (s). It is an important parameter in wave dynamics and coastal engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the period of reflected waves based on time elapsed, water surface characteristics, and wave geometry.

3. Importance of Reflected Wave Period Calculation

Details: Accurate calculation of reflected wave period is crucial for coastal structure design, harbor resonance studies, and understanding wave-structure interactions in marine environments.

4. Using the Calculator

Tips: Enter all values in appropriate units. Time elapsed and wave measurements must be positive values. The horizontal ordinate can be positive or negative depending on the coordinate system used.

5. Frequently Asked Questions (FAQ)

Q1: What causes wave reflection?
A: Wave reflection occurs when waves encounter a barrier or boundary that they cannot pass through, such as seawalls, breakwaters, or steep seabed slopes.

Q2: How does reflected wave period differ from incident wave period?
A: The reflected wave period is typically equal to the incident wave period for perfect reflection, but can vary depending on the reflecting surface characteristics and wave conditions.

Q3: What are typical values for reflected wave periods?
A: Reflected wave periods typically range from 2-20 seconds for ocean waves, depending on the incident wave characteristics and reflection conditions.

Q4: When is this calculation most useful?
A: This calculation is particularly useful in coastal engineering for designing structures that minimize wave reflection or for studying wave patterns in harbors and marinas.

Q5: What are the limitations of this formula?
A: The formula assumes linear wave theory and may not accurately represent extreme wave conditions or complex reflection scenarios with multiple reflecting surfaces.