Wave Speed Calculator

Wave speed is the rate at which a wave propagates through a medium. It represents how quickly the wave's energy and disturbance travel from one point to another. Unlike the motion of individual particles in the medium (which typically oscillate in place), wave speed describes the forward progress of the wave itself.

All waves, whether mechanical (like sound and water waves) or electromagnetic (like light and radio waves), have a characteristic speed that depends on the properties of the medium through which they travel. Understanding wave speed is fundamental to physics, engineering, and many practical applications from telecommunications to seismology.

The fundamental relationship between wave speed, frequency, and wavelength is expressed by the wave equation:

This equation applies to all types of waves and shows that:

• Wave speed = frequency × wavelength
• Frequency = wave speed ÷ wavelength (f = v / λ)
• Wavelength = wave speed ÷ frequency (λ = v / f)

The wave period (T), which is the time for one complete wave cycle, is related to frequency by T = 1 / f. This gives us an alternative form: v = λ / T.

Sound waves are mechanical compression waves that require a medium to propagate. The speed of sound depends on the medium's density and elasticity, varying significantly between gases, liquids, and solids.

In air, sound speed increases approximately 0.6 m/s for each 1°C increase in temperature. This is because higher temperatures increase molecular kinetic energy, allowing vibrations to propagate faster. Sound travels faster in denser solids because their molecules are closer together, enabling quicker energy transfer.

Water wave speed is more complex than other wave types because it depends on both wavelength and water depth. Two distinct regimes exist:

Tsunamis are shallow water waves even in deep ocean because their wavelengths (100-500 km) are much larger than ocean depth (~4 km). This allows them to travel at speeds over 200 m/s (700 km/h) across open ocean.

All electromagnetic waves—including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays—travel at the speed of light in a vacuum: approximately 299,792,458 m/s (about 300,000 km/s or 186,000 mi/s).

Unlike mechanical waves, electromagnetic waves don't require a medium and can propagate through the vacuum of space. They are oscillating electric and magnetic fields that generate each other as they travel.

In materials, electromagnetic wave speed decreases according to the refractive index (n): v = c/n. For example, light slows to about 225,000,000 m/s in water (n ≈ 1.33) and 124,000,000 m/s in diamond (n ≈ 2.42).

Earthquakes generate two main types of body waves that travel through Earth's interior: P-waves (primary/compression waves) and S-waves (secondary/shear waves). Their different speeds allow seismologists to determine earthquake locations and study Earth's internal structure.

The time difference between P-wave and S-wave arrivals helps determine the distance to an earthquake's epicenter. The fact that S-waves don't propagate through Earth's outer core (liquid) was key evidence that it's in a liquid state.

Comparing different wave types shows the vast range of wave speeds in nature: