Wave Speed Formula
The wave speed equation relates velocity, frequency, and wavelength.
Learn v = f x lambda with worked examples.
The Formula
The wave speed equation applies to all types of waves: sound, light, water, seismic, and more. It connects how fast a wave travels with how often it oscillates and how long each wave cycle is.
Variables
| Symbol | Meaning |
|---|---|
| v | Wave speed (m/s) |
| f | Frequency (Hz, cycles per second) |
| λ (lambda) | Wavelength (m) |
Useful Rearrangements
λ = v / f
Example 1 — Sound Wave
A tuning fork vibrates at 440 Hz (the note A4). The speed of sound in air is 343 m/s. What is the wavelength?
λ = v / f = 343 / 440
λ ≈ 0.780 m (about 78 cm)
Example 2 — Radio Wave
An FM radio station broadcasts at 101.1 MHz. The speed of electromagnetic waves is 3 × 10⁸ m/s. What is the wavelength?
f = 101.1 × 10⁶ Hz
λ = v / f = (3 × 10⁸) / (101.1 × 10⁶)
λ ≈ 2.97 m
Example 3 — Water Wave
Ocean waves arrive at a beach with a wavelength of 12 m and a frequency of 0.25 Hz. How fast are they traveling?
v = f × λ = 0.25 × 12
v = 3 m/s
Reference Speeds
| Wave Type | Speed |
|---|---|
| Light (vacuum) | 3.00 × 10⁸ m/s |
| Sound (air, 20°C) | 343 m/s |
| Sound (water) | ~1,480 m/s |
| Sound (steel) | ~5,960 m/s |
When to Use It
- Calculating wavelengths of sound or radio signals
- Sonar and ultrasound applications
- Antenna design (antenna length is related to wavelength)
- Musical acoustics (pipe and string instruments)