One relation ties speed, frequency and wavelength
Speed v is in metres per second, frequency f in hertz (cycles per second), and wavelength λ in metres. Know any two and the third follows. A 343 m/s sound at 1 metre wavelength has a frequency of 343 Hz; double the frequency and the wavelength halves to keep the product the same.
Speed is a property of the medium, not the wave
Sound travels about four times faster in water than in air because water is denser and stiffer. Light does the opposite, slowing as it passes into denser matter. The speed you plug in depends entirely on what the wave is travelling through.
The same 1,000 Hz tone has a 0.34 m wavelength in air but a 1.48 m wavelength in water — the frequency is unchanged, only the speed and wavelength shift.
Common wave speeds
| Wave in… | Speed | Note |
|---|---|---|
| Air (20°C) | 343 m/s | Sound at sea level |
| Air (0°C) | 331 m/s | Cold air is slower |
| Fresh water | 1,440 m/s | Sound |
| Sea water | 1,482 m/s | Sound (used by sonar) |
| Steel | 5,960 m/s | Sound |
| Vacuum | 299,792,458 m/s | Light and all EM waves (c) |
| Water | 225,000,000 m/s | Light (n = 1.33) |
The speed of sound in air rises about 0.6 m/s for every 1°C: v = 331.3 + 0.606 × T. So 343 m/s only holds near 20°C.
Where people slip up
- Frequency and wavelength are inversely proportional. For a fixed speed, doubling one halves the other. They only rise together if the speed itself changes.
- The medium moves, the wave travels. Particles oscillate in place; the disturbance is what propagates, not the particles themselves.
- Light in matter is not c. The 299,792,458 m/s figure is the vacuum speed. Light drops to about 225,000 km/s in water and 200,000 km/s in glass.
Common questions
What is the wave speed formula?
Speed equals frequency times wavelength: v = f x lambda. It works for every wave, sound, light, water or seismic. Rearrange it to f = v divided by lambda, or lambda = v divided by f, to solve for whichever value is missing.
Does a wave speed up when its frequency rises?
No. In a given medium the speed is fixed by the medium itself. Raising the frequency shortens the wavelength by the same factor, so their product stays constant.
What happens to a wave when it moves into a new medium?
Its frequency stays the same because that is set by the source. The speed changes to match the new medium, so the wavelength changes with it. This is why light bends as it enters water or glass.
