Wave Speed Formula
The wave speed formula v = fλ relates the speed of a wave to its frequency and wavelength.
Essential for sound, light, and wave physics.
The Formula
The speed of a wave equals its frequency multiplied by its wavelength. This applies to all types of waves: sound, light, water, and more.
Variables
| Symbol | Meaning |
|---|---|
| v | Wave speed (measured in meters per second, m/s) |
| f | Frequency (measured in hertz, Hz, which means cycles per second) |
| λ | Wavelength (measured in meters, m) |
Example 1
A sound wave has a frequency of 440 Hz (the note A4). The speed of sound in air is 343 m/s. What is the wavelength?
Rearrange: λ = v / f
λ = 343 / 440
λ ≈ 0.78 m (about 78 cm)
Example 2
A radio station broadcasts at a frequency of 100 MHz. Radio waves travel at the speed of light (3 × 10⁸ m/s). What is the wavelength?
Convert frequency: 100 MHz = 100 × 10⁶ = 10⁸ Hz
Rearrange: λ = v / f = (3 × 10⁸) / (10⁸)
λ = 3 m
When to Use It
Use the wave speed formula for any problem relating wave speed, frequency, and wavelength.
- Sound wave calculations (music, acoustics, sonar)
- Light and electromagnetic wave problems
- Water wave analysis
- Telecommunications (radio, TV, Wi-Fi frequencies)
Key Notes
- Wave speed is a property of the medium, not the source — changing the frequency of a sound source changes its wavelength but not the speed; the speed of sound in air at 20°C is always 343 m/s regardless of pitch
- Sound speed increases with temperature: v ≈ 331 + 0.6T m/s (T in °C) — warm air carries sound faster; this temperature dependence causes outdoor sound to bend upward on hot days (higher layers are slower) creating "acoustic shadows"
- Electromagnetic waves all travel at c = 3×10⁸ m/s in a vacuum; in a medium with refractive index n, speed becomes c/n — light slows to about 0.75c in glass, which is why it bends at interfaces (Snell's law)
- The Doppler effect changes observed frequency, not wave speed: when a source moves toward you, waves bunch up (higher f, shorter λ) but still arrive at v = fλ in the medium — the formula always applies using the observed f and λ