Wave Speed Formula
Reference for v = f × λ wave speed formula.
Covers sound, light, and water waves with worked examples, Hz to kHz conversions, and speed in different media.
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)
Key Notes
- Formula: v = fλ: Wave speed equals frequency times wavelength. Frequency f (Hz) is the number of complete cycles per second; wavelength λ (m) is the distance between equivalent points on consecutive cycles. Rearranged: λ = v/f; f = v/λ.
- Wave speed depends on the medium, not the source: When a wave passes from one medium to another, its speed and wavelength change, but its frequency remains constant (determined by the source). This is why light bends at interfaces — wavelength adjusts, frequency stays fixed.
- Transverse wave in a string: v = √(T/μ): Speed increases with tension T and decreases with linear mass density μ (kg/m). Guitar and violin tuning works by adjusting T — higher tension raises pitch by increasing wave speed and thus frequency for a given string length.
- Speed of light: c = fλ = 3×10⁸ m/s in vacuum: In a medium with refractive index n, speed = c/n. AM radio (1 MHz): λ ≈ 300 m. FM radio (100 MHz): λ ≈ 3 m. Visible light (500 THz): λ ≈ 600 nm. All obey v = fλ.
- Applications: Wave speed calculations are used in sonar (sound speed in water for depth finding), seismology (P-wave and S-wave speeds to locate earthquakes), radio and antenna design, optical fiber communications, and musical instrument physics.