1. What is Wave Celerity?

Definition: Wave celerity is the speed at which a wave propagates through a medium, in this case, water.

Purpose: This calculator determines the speed of water waves based on depth and gravitational acceleration, important for oceanography and coastal engineering.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( c \) — Wave celerity (meters per second, m/s)
• \( g \) — Gravitational acceleration (9.81 m/s² on Earth)
• \( d \) — Water depth (meters, m)

Explanation: The speed of water waves increases with both water depth and gravitational acceleration.

3. Importance of Wave Celerity Calculation

Details: Understanding wave speed is crucial for tsunami warnings, ship navigation, coastal construction, and understanding ocean energy transport.

4. Using the Calculator

Tips: Enter water depth in meters and gravitational acceleration (default 9.81 m/s² for Earth). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for all water waves?
A: This is the simplified formula for shallow water waves where depth is less than 1/20th of wavelength.

Q2: What's a typical celerity value?
A: In 10m depth, waves travel about 9.9 m/s (35.6 km/h). In 100m depth, about 31.3 m/s (113 km/h).

Q3: When would I change the gravity value?
A: Only if calculating for other celestial bodies (e.g., 1.62 m/s² for the Moon, 3.71 m/s² for Mars).

Q4: How does this relate to wave period?
A: Wave period (T) can be calculated from celerity (c) and wavelength (L) as T = L/c.

Q5: What about deep water waves?
A: For deep water (depth > 1/2 wavelength), use c = √(gL/2π).