1. What is Wave Speed?

Wave speed is the velocity at which a wave propagates through a medium. For ocean waves, this speed depends on gravity and wavelength, following the formula: \( v = \sqrt{\frac{g \lambda}{2\pi}} \), where g is gravity and λ is wavelength.

2. How Does the Calculator Work?

The calculator uses the wave speed formula:

Where:

• \( g \) — Gravitational acceleration (typically 9.81 m/s² on Earth)
• \( Wavelength \) — Distance between successive wave crests (meters)

Explanation: This formula calculates the phase speed of deep water waves where water depth is greater than half the wavelength.

3. Importance of Wave Speed Calculation

Details: Understanding wave speed is crucial for maritime navigation, coastal engineering, surfing, and studying ocean dynamics. It helps predict wave arrival times and energy transport in oceans.

4. Using the Calculator

Tips: Enter wavelength in meters and gravity in m/s² (Earth's gravity is 9.81 m/s²). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for all types of waves?
A: This formula specifically applies to deep water gravity waves where water depth is greater than half the wavelength.

Q2: How does water depth affect wave speed?
A: In shallow water, wave speed depends on depth rather than wavelength: \( v = \sqrt{g \times depth} \).

Q3: What are typical wave speeds in the ocean?
A: Ocean wave speeds typically range from 5-60 km/h, with tsunami waves traveling at 500-800 km/h in deep water.

Q4: Can I use this for waves other than water waves?
A: While the formula is derived for water waves, similar principles apply to other gravity waves with appropriate adjustments for the medium.

Q5: Why is gravity included in the formula?
A: Gravity is the restoring force that causes water to return to equilibrium, creating the wave motion and determining its speed.