Wave Speed Calculator
Calculate wave speed, frequency, or wavelength using the wave equation.
Works for sound, light, and water waves.
Wave Calculation
The wave equation relates the speed, frequency, and wavelength of any wave. It is one of the fundamental relationships in physics.
Formula:
v = f × λ
Where:
- v = wave speed (meters per second, m/s)
- f = frequency (hertz, Hz — cycles per second)
- λ (lambda) = wavelength (meters, m)
Rearranged forms:
f = v / λ(find frequency)λ = v / f(find wavelength)
What each variable means:
- Speed — how fast the wave travels through a medium
- Frequency — how many complete wave cycles pass a point per second
- Wavelength — the distance between two consecutive peaks (or troughs)
Common wave speeds:
| Wave Type | Medium | Speed |
|---|---|---|
| Light | Vacuum | 299,792,458 m/s (186,282 mi/s) |
| Sound | Air (20°C/68°F) | 343 m/s (767 mph / 1,125 ft/s) |
| Sound | Water | 1,480 m/s (3,310 mph) |
| Sound | Steel | 5,960 m/s (13,330 mph) |
| Radio waves | Air | ~300,000,000 m/s |
| Water wave | Deep ocean | 5–25 m/s (depends on wavelength) |
When to use this calculator:
- Physics homework and exam preparation
- Audio engineering (speaker design, room acoustics)
- Radio and telecommunications calculations
- Seismology and earthquake wave analysis
- Musical instrument design
Practical example: Middle C on a piano has a frequency of 261.6 Hz. In air at 20°C, the speed of sound is 343 m/s. The wavelength of Middle C is: 343 / 261.6 = 1.31 meters (4.3 feet). This means the sound wave is about the height of a child.
Tips:
- Sound speed increases with temperature: approximately 0.6 m/s per degree Celsius.
- Higher frequency means shorter wavelength (and vice versa) at the same speed.
- The wave equation applies to all types of waves: mechanical, electromagnetic, and water.
- In a guitar string, changing tension changes wave speed, which changes the pitch (frequency).