Wave speed, frequency and wavelength are linked by one equation that holds for any wave — sound, light, water, a plucked string. Only the speed itself differs by medium and wave type; the relationship between the three is universal.
How it works
The wave equation
v = f λ
v is wave speed in metres per second, f is frequency in hertz (cycles per second), λ (lambda) is wavelength in metres. The speed of sound in dry air at 20°C is commonly taken as 343 m/s.
Why pitch changes but a sound’s speed does not
In a fixed medium — air at a given temperature, say — wave speed stays constant. So if frequency goes up, wavelength must come down to keep v = fλ true, and vice versa. This is why a higher musical note is a shorter wavelength, not a faster-travelling sound: the sound from a piccolo and a tuba both cross a room at the same speed, they just pack their oscillations differently in space. Changing the medium — sound in water instead of air, for instance — is the thing that actually changes v, at fixed frequency and wavelength.
How to use this calculator
- Choose which quantity you want solved — speed, frequency or wavelength.
- Enter the other two.
- Read the solved value.
Frequently asked questions
Does this equation work for light as well as sound?
Yes — it is a general property of waves, not specific to sound. For light in a vacuum, the speed is the universal constant c (roughly 299,792,458 m/s), and the same v = fλ relationship holds between its frequency and wavelength.
Why is concert pitch A 440 Hz?
440 Hz is a widely adopted tuning standard — a convention, not a physical necessity — chosen historically for reasons of consistency between instruments and orchestras, not because that particular frequency has special physical significance.
Why does sound travel faster in water than in air?
Wave speed depends on the medium’s properties — how tightly its particles are packed and how they transmit the disturbance. Water is denser and less compressible than air in the relevant sense, which lets sound waves propagate through it considerably faster — roughly four times faster than in air.
What happens if wavelength is zero?
Solving for frequency with a zero wavelength is declined here — dividing speed by zero wavelength is mathematically undefined, not an infinitely high frequency, and zero wavelength does not correspond to any physically meaningful wave.
Is 343 m/s the exact speed of sound everywhere?
No — it is a commonly cited approximate value for dry air at 20°C. The speed of sound in air actually depends on temperature (and, to a lesser extent, humidity), so a colder or warmer room gives a measurably different figure.
