γ°οΈ Wave Speed Calculator
Calculate v = fΓΞ»: wave speed from frequency and wavelength.
Result
How to Use This Calculator
This calculator solves the wave equation for any one variable. Choose what to solve for, enter the other two, and the missing value appears.
Use the Solve for dropdown to pick wave speed, frequency, or wavelength.
Enter the two known values: frequency in hertz, wavelength in meters, wave speed in meters per second.
Click Calculate. The missing quantity appears with its unit.
For sound in air, wave speed is about 343 m/s. For light in vacuum, use 3.00 x 10^8 m/s.
The Wave Equation
The wave equation says one wavelength passes a fixed point every period. Frequency counts how many cycles pass per second, wavelength measures each cycle's length, and multiplying them gives how fast the pattern travels. It is beautifully general: sound waves, light waves, water ripples, and stadium waves all obey v = f x wavelength.
In a given medium the speed is fixed, so frequency and wavelength trade off inversely. That is why a piccolo and a tuba playing in the same hall produce wildly different wavelengths from the same air. Change the medium and the speed changes: sound moves about four times faster in water than in air, while light slows down in glass.
Worked Example
Where This Comes Up
Acoustic engineers place speakers and design halls with wavelength math: bass traps must be a quarter wavelength deep to absorb low notes, which is why they are huge. Radio engineers pick antenna lengths as fractions of the wavelength. Ultrasound imaging chooses frequency to trade penetration against resolution, since higher frequency means shorter wavelength and finer detail.
The common slip is unit scale: nanometers for light, megahertz for radio. Convert to meters and hertz before calculating, or the powers of ten will ambush you. And remember the medium rule: 343 m/s is air at room temperature, not a universal constant. Underwater or in steel, look up the right speed.
Frequently Asked Questions
Does the frequency change when a wave enters a new medium?
No. Frequency is set by the source and stays constant across the boundary. What changes is the wavelength: it stretches or compresses to match the new wave speed.
What is the speed of sound in air?
About 343 m/s at 20 degrees C. It rises roughly 0.6 m/s per degree Celsius, so cold air carries sound noticeably slower.
Why do bass notes have such long wavelengths?
Wavelength equals speed divided by frequency, so low frequencies mean long waves. A 50 Hz bass note in air spans 343/50 = 6.9 m, longer than a car.
Does this formula work for light?
Yes. Light obeys c = f x wavelength with c = 3.00 x 10^8 m/s in vacuum. A green 550 nm photon has frequency 3.00 x 10^8 / 5.5 x 10^-7 = 5.45 x 10^14 Hz.
What is the relationship between period and frequency?
They are reciprocals: T = 1/f. A 440 Hz tone repeats every 1/440 = 2.27 ms.