The Wave Speed Equation
Wave speed (v) equals frequency (f) multiplied by wavelength (λ). This universal relationship applies to all waves — electromagnetic, sound, water, and seismic.
Types of Waves and Their Speeds
Electromagnetic waves (light, radio, X-rays) travel at the speed of light c = 299,792,458 m/s in vacuum. In a medium with refractive index n, they slow to v = c/n.
Mechanical waves (sound, seismic, water waves) require a medium. Their speed depends on the medium's elasticity and density.
Sound waves in air travel at about 343 m/s (20°C). Speed increases with temperature and in denser/stiffer media like water and steel.
Wave Speed Reference Table
| Wave Type / Medium | Speed (m/s) | Notes |
|---|---|---|
| Light in vacuum | 299,792,458 | Exact (defined constant) |
| Light in water (n≈1.33) | ≈ 225,000,000 | v = c/n |
| Light in glass (n≈1.5) | ≈ 200,000,000 | v = c/n |
| Sound in air (20°C) | ≈ 343 | Varies with temperature |
| Sound in water | ≈ 1,480 | Freshwater at 20°C |
| Sound in seawater | ≈ 1,530 | Varies with salinity, depth |
| Sound in steel | ≈ 5,960 | Longitudinal waves |
| Sound in aluminum | ≈ 6,420 | Longitudinal waves |
| Sound in glass | ≈ 5,640 | Depends on glass type |
| Seismic P-wave (crust) | 4,000–8,000 | Depends on rock type |
Sound Speed and Temperature
The speed of sound in dry air increases linearly with temperature. At 0°C it is about 331 m/s; at 20°C about 343 m/s; at 40°C about 355 m/s. This approximation is valid from roughly −40°C to +60°C.
Worked Examples
FM Radio at 100 MHz
v = fλ → λ = v/f = 299,792,458 / 100,000,000 ≈ 2.998 m. FM radio waves in air travel at essentially the speed of light.
Sound of Middle C (262 Hz)
λ = v/f = 343 / 262 ≈ 1.31 m in air at 20°C. The wavelength is about the height of a guitar.
Light in glass (n = 1.52)
v = c/n = 299,792,458 / 1.52 ≈ 197,232,000 m/s. Light slows by about 34% in this glass.
Real-World Applications
| Application | Wave Type | How Speed Matters |
|---|---|---|
| Sonar / echolocation | Sound in water | Distance = v × t/2; needs accurate sound speed |
| Fiber optics | Light in glass | Signal delay depends on v = c/n |
| Seismology | Seismic P/S waves | Locating earthquakes by wave arrival times |
| Antenna design | EM / radio | Antenna length depends on λ = c/f |
| Medical ultrasound | Sound in tissue | Imaging resolution depends on v and f |
Accuracy and Limitations
This calculator uses ideal wave equations. Real-world considerations include: dispersion (speed varies with frequency in some media), nonlinear effects at high amplitudes, temperature/pressure/humidity effects on sound speed, and attenuation. Sound speed approximation v ≈ 331.3 + 0.606T is valid for dry air from −40°C to +60°C only.
Frequently Asked Questions
What is the wave speed equation?›
The fundamental wave equation is v = fλ, where v is wave speed in m/s, f is frequency in Hz, and λ (lambda) is wavelength in metres. This applies to all types of waves — sound, light, radio, water, and seismic.
What is the speed of light?›
The speed of light in vacuum is exactly c = 299,792,458 m/s. In a medium with refractive index n, light travels at v = c/n. For example, in glass (n ≈ 1.5), light travels at about 200,000 km/s.
What is the speed of sound in air?›
At 20°C in dry air, the speed of sound is approximately 343 m/s. It increases with temperature: v ≈ 331.3 + 0.606 × T(°C). At 0°C it is about 331 m/s; at 30°C about 349 m/s.
Does wave speed depend on frequency?›
For most waves in simple media, no — wave speed depends on the medium, not the frequency. This is called a non-dispersive medium. However, in dispersive media (like glass for light, or deep water for waves), speed does vary with frequency.
Why is the speed of sound different in water and steel?›
Sound speed depends on the medium's elasticity and density. Steel is much stiffer than water (higher bulk modulus), so longitudinal sound waves travel about 4× faster in steel (~5,960 m/s) than in water (~1,480 m/s).
What is a refractive index?›
The refractive index n = c/v is the ratio of the speed of light in vacuum to the speed of light in a medium. Higher n means slower light. Air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.
Can anything travel faster than light?›
No material object or information can travel faster than c in vacuum. However, the phase velocity of a wave can exceed c in certain media — this does not violate relativity because no energy or information travels faster than c.
How does temperature affect sound speed?›
Higher temperature means faster-moving air molecules, which transmit sound vibrations more quickly. The relationship is approximately linear: v ≈ 331.3 + 0.606 × T(°C) for dry air. Humidity also increases sound speed slightly.
