1. What is the Long Wave Simplification for Wavelength?

The Long Wave Simplification formula calculates wavelength from wave period and water depth, using the gravitational acceleration constant. This simplified approach is particularly useful for long waves where the water depth is much smaller than the wavelength.

2. How Does the Calculator Work?

The calculator uses the Long Wave Simplification formula:

Where:

• \( \lambda \) — Wavelength (m)
• \( T \) — Wave Period (s)
• \( g \) — Gravitational acceleration (9.80665 m/s²)
• \( d \) — Water Depth (m)

Explanation: This formula simplifies the dispersion relationship for water waves under the assumption that the waves are long compared to the water depth.

3. Importance of Wavelength Calculation

Details: Accurate wavelength calculation is crucial for coastal engineering, wave energy estimation, navigation safety, and understanding wave behavior in shallow water conditions.

4. Using the Calculator

Tips: Enter wave period in seconds and water depth in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "long wave" in this context?
A: Waves are considered long when the water depth is much smaller than the wavelength (d/λ < 0.05), typically including tidal waves and tsunamis.

Q2: Why is gravitational acceleration constant used?
A: Gravitational acceleration (g) is a fundamental constant that governs wave propagation in fluids and is essential for accurate wavelength calculations.

Q3: What are typical wavelength values in oceanography?
A: Wavelengths can range from centimeters (capillary waves) to hundreds of kilometers (tidal waves), with most wind-generated waves having wavelengths of 10-300 meters.

Q4: Are there limitations to this simplified formula?
A: This simplification is less accurate for shorter waves or when the water depth is not significantly smaller than the wavelength. For general cases, the full dispersion relationship should be used.

Q5: How does water depth affect wavelength?
A: In shallow water, wavelength decreases with decreasing water depth, while wave period remains constant. This formula captures this relationship for long waves.