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Wave Equation Calculator

Use the wave equation v = fλ to find wave speed, frequency, or wavelength. Works for any wave type — sound, light, water, or radio waves.

Solve the wave equation v = f × λ — enter any two known values.

Sound in air ≈ 343 m/s · Light in vacuum ≈ 299,792,458 m/s

1 kHz = 1,000 Hz · 1 MHz = 1,000,000 Hz

Wavelength (λ)

0.779545 m

Period T = 0.002273 s

Wave equation reference

Wavelengthλ = v / f
Frequencyf = v / λ
PeriodT = 1 / f

Quick answer

The wave equation is v = fλ, where v is wave speed in metres per second, f is frequency in hertz, and λ (lambda) is wavelength in metres. To find wavelength, divide speed by frequency: λ = v/f. To find frequency, divide speed by wavelength: f = v/λ. Sound travels at about 343 m/s in air at 20°C, while light and radio waves travel at 3×10⁸ m/s in a vacuum.

Formula & method

v = f × λ
  • v — Wave speed in metres per second (m/s)
  • f — Frequency in hertz (Hz)
  • λ — Wavelength in metres (m)

Wave speed equals frequency multiplied by wavelength.

λ = v / f
  • λ — Wavelength in metres (m)
  • v — Wave speed in metres per second (m/s)
  • f — Frequency in hertz (Hz)

Wavelength is found by dividing wave speed by frequency.

f = v / λ
  • f — Frequency in hertz (Hz)
  • v — Wave speed in metres per second (m/s)
  • λ — Wavelength in metres (m)

Frequency is found by dividing wave speed by wavelength.

T = 1 / f
  • T — Period in seconds (s)
  • f — Frequency in hertz (Hz)

Period T is the reciprocal of frequency.

Examples

Example 1: Wavelength of concert A note (440 Hz) in air
Input
v = 343 m/s, f = 440 Hz
Result
λ = 0.7795 m
Why
Using λ = v/f: λ = 343 / 440 = 0.7795 m. Middle A at 440 Hz has a wavelength of about 78 cm in air at 20°C.
Example 2: Frequency of green light (λ = 550 nm) in a vacuum
Input
v = 3.00×10⁸ m/s, λ = 550 nm = 5.50×10⁻⁷ m
Result
f = 5.45×10¹⁴ Hz
Why
Using f = v/λ: f = 3.00×10⁸ / 5.50×10⁻⁷ = 5.4545×10¹⁴ Hz ≈ 5.45×10¹⁴ Hz. Green light oscillates about 545 trillion times per second.
Example 3: Speed of an ocean swell (f = 0.1 Hz, λ = 15 m)
Input
f = 0.1 Hz, λ = 15 m
Result
v = 1.5 m/s
Why
Using v = f × λ: v = 0.1 × 15 = 1.5 m/s. A gentle ocean swell with a 10-second period and 15 m crest spacing travels at 1.5 metres per second.
Example 4: Wavelength of an FM radio station at 100 MHz
Input
v = 3.00×10⁸ m/s, f = 100×10⁶ Hz = 1.00×10⁸ Hz
Result
λ = 3 m
Why
Using λ = v/f: λ = 3.00×10⁸ / 1.00×10⁸ = 3.00 m. An FM radio station broadcasting at 100 MHz has a wavelength of exactly 3 metres.

Frequently asked questions

What is the wave equation?

The wave equation v = fλ relates three properties of any periodic wave: wave speed v (m/s), frequency f (Hz), and wavelength λ (m). If you know any two values, you can calculate the third.

What is the speed of sound in air?

Sound travels at approximately 343 m/s in dry air at 20°C (68°F). Speed increases with temperature — roughly 0.6 m/s for every 1°C rise. In water, sound travels about 4 times faster at ~1480 m/s.

What is the speed of light?

Light and all electromagnetic waves (radio, X-rays, gamma rays) travel at 299,792,458 m/s ≈ 3.00×10⁸ m/s in a vacuum. In other media such as glass or water, speed is reduced by the refractive index.

How do frequency and wavelength relate?

For a wave travelling at a fixed speed, frequency and wavelength are inversely proportional. Doubling the frequency halves the wavelength, and vice versa. High-frequency waves (like gamma rays) have very short wavelengths; low-frequency waves (like AM radio) have very long wavelengths.

What is the period of a wave and how is it related to frequency?

Period T is the time (in seconds) for one complete oscillation. It is the reciprocal of frequency: T = 1/f. A wave at 440 Hz has a period of 1/440 ≈ 0.00227 s (about 2.27 milliseconds).

Can this calculator be used for light and electromagnetic waves?

Yes. Enter the speed of light (3×10⁸ m/s or 299,792,458 m/s) as the wave speed. For visible light, wavelengths range from about 380 nm (violet) to 700 nm (red). Make sure to convert nanometres to metres by multiplying by 10⁻⁹.

Sources & references

External references open in a new tab. We are independent and not affiliated with these organizations.

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Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.

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