Wave Speed Calculator
v = fλ — wave speed from frequency and wavelength
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Working out v = fλ is easier with Wave Speed Calculator, which answers as you type. Just enter Frequency (Hz) and Wavelength (m); Wave Speed updates the result as you type. Wave Speed displays each intermediate figure as well. Use Wave Speed for a reliable number, fast. Nothing typed into Wave Speed leaves your device or the tab. Looking for wave speed calculator frequency wavelength or free online wave speed calculator? Wave Speed covers both. Wave Speed is great for comparing scenarios. Change one value and watch. Try Wave Speed now and keep it handy.
What the defaults give
440 Hz at 0.78 m gives a wave speed of 343.20 m/s.
That is the speed of sound in air at roughly 20 °C — which is why 440 Hz, the tuning A, has a wavelength close to three quarters of a metre.
The formula
v = f × λ — speed equals frequency times wavelength.
440 × 0.78 = 343.20 m/s. The period, 1 ÷ 440, is 0.0023 s, so the wave repeats about 440 times a second.
Worked examples
440 Hz × 0.78 m → 343.20 m/s (sound in air)
20 Hz × 17 m → 340 m/s (a very low bass note)
2.4 GHz × 0.125 m → 300,000 km/s (a Wi-Fi signal in vacuum)
100 Hz × 15 m → 1,500 m/s (sound in water)
Why the speed depends on the medium
Frequency is set by the source and does not change when the wave crosses into another material. Wavelength and speed do. Sound travels at about 343 m/s in air, 1,480 m/s in water and 5,000 m/s in steel, so the same 440 Hz tone has a wavelength of 0.78 m in air and 11 m in steel. Light behaves the same way: its speed in glass is about two thirds of its speed in vacuum, so the wavelength shortens while the colour, which is the frequency, stays the same.
Practical uses
- Antenna design. A quarter-wave antenna is a quarter of the wavelength, which is why FM and Wi-Fi antennas differ in size by an order of magnitude.
- Room acoustics. Wavelengths comparable to room dimensions cause standing waves and boomy bass notes.
- Medical imaging. Ultrasound wavelength sets the resolution limit, which is why higher frequencies give sharper images but penetrate less deeply.
- Radio planning. Lower frequencies diffract around obstacles; higher ones need line of sight.
Keep the units consistent: frequency in hertz and wavelength in metres give speed in metres per second.
The 343 m/s result is the speed of sound in dry air at about 20 °C, and it is a property of the medium rather than of the wave. Change the medium and the speed changes: roughly 1,480 m/s in water and 5,000 m/s in steel, which is why a train can be heard through the rail long before it arrives. At a fixed speed, frequency and wavelength trade against each other, so a 440 Hz tone in water has a wavelength three times longer than in air.
Frequently Asked Questions
What is the wavelength of 440 Hz?
About 0.78 m in air at 20 °C, because 343 m/s divided by 440 Hz is 0.7795 m.
Does frequency change when a wave enters another medium?
No. Frequency is fixed by the source; speed and wavelength change together to keep f × λ consistent.
How fast does sound travel in water?
Roughly 1,480 m/s at room temperature — about four times the speed in air, so wavelengths are four times longer.
What is the difference between wave speed and particle speed?
The wave moves through the medium carrying energy; the particles only oscillate around a resting position and do not travel with the wave.
How do I find the period?
Period is one divided by frequency. At 440 Hz that is 0.00227 seconds, so the wave completes a cycle every 2.3 milliseconds.
Can I use this for light?
Yes, with the right speed. In vacuum v is about 3 × 10⁸ m/s, so a 500 nm wavelength corresponds to 600 THz.
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