CalculateY CalculateY

Wavelength Calculator

The wave equation v = f x lambda (wavelength) connects wave velocity, frequency, and wavelength. Light with a frequency of 5.0 x 10^14 Hz traveling at 3.0 x 10^8 m/s has a wavelength of 6.0 x 10^-7 m (600 nm, orange light). Select which variable to solve for, choose a wave medium (light, sound, or custom velocity), and enter the known values to get instant results.

Quick Answer

Light at a frequency of 5.0 x 10^14 Hz has a wavelength of approximately 6.0 x 10^-7 m (600 nm). A 440 Hz sound wave in air (343 m/s) has a wavelength of approximately 0.78 m.

Use scientific notation, e.g. 5e-7 for 500 nm

Use scientific notation, e.g. 5e14 for 500 THz

Common Examples

Input Result
f = 5.0e14 Hz, v = 3.0e8 m/s (light) Wavelength = 6.0000e-7 m (600 nm)
f = 440 Hz, v = 343 m/s (sound in air) Wavelength = 0.7795 m
lambda = 0.02 m, v = 343 m/s (sound) Frequency = 17,150.00 Hz
lambda = 5.0e-7 m, v = 3.0e8 m/s (light) Frequency = 6.0000e14 Hz
f = 1000 Hz, lambda = 1.5 m Velocity = 1,500.00 m/s

How It Works

This calculator uses the universal wave equation:

v = f x lambda

Where:

  • v = wave velocity (speed) in meters per second (m/s)
  • f = frequency in hertz (Hz, cycles per second)
  • lambda = wavelength in meters (m), the distance between consecutive wave crests

Rearranged:

  • Wavelength: lambda = v / f
  • Frequency: f = v / lambda
  • Velocity: v = f x lambda

Wave Speed by Medium

Different types of waves travel at different speeds:

  • Light in vacuum: 299,792,458 m/s (approximately 3.0 x 10^8 m/s)
  • Sound in air (20 C): 343 m/s
  • Sound in water: approximately 1,480 m/s
  • Sound in steel: approximately 5,960 m/s

The Electromagnetic Spectrum

Electromagnetic waves range from radio waves (wavelengths of meters to kilometers) to gamma rays (wavelengths shorter than 10^-12 m). Visible light occupies a narrow band from about 380 nm (violet) to 700 nm (red), where 1 nm = 10^-9 m.

Frequency and Wavelength Relationship

For a given wave speed, frequency and wavelength are inversely proportional. Higher frequency means shorter wavelength, and lower frequency means longer wavelength. This is why radio waves have long wavelengths and gamma rays have extremely short ones.

Worked Example

An FM radio station broadcasts at 98.5 MHz (98,500,000 Hz). Radio waves travel at the speed of light. Wavelength = 3.0 x 10^8 / 98,500,000 = 3.045 m. For sound: a tuning fork vibrates at 440 Hz (the note A4). In air at 20 C, the wavelength is lambda = 343 / 440 = 0.7795 m, about 78 cm.

Related Calculators

Acceleration Calculator

Calculate acceleration, velocity, or time using the kinematic formula a = (v2 - v1) / t.

Velocity Calculator

Calculate velocity, distance, or time for uniform and accelerated motion using v = d/t and v = v0 + at.

Frequently Asked Questions

What is wavelength?
Wavelength is the distance between two consecutive identical points on a wave, such as crest to crest or trough to trough. It is measured in meters (m) for most physics applications. For light, wavelengths are often expressed in nanometers (nm, 10^-9 m). For radio waves, wavelengths may be in meters or kilometers.
What is the relationship between wavelength and color?
In visible light, wavelength determines color. Violet light has the shortest visible wavelength (about 380 nm), and red light has the longest (about 700 nm). In between: blue is approximately 450 nm, green approximately 520 nm, yellow approximately 580 nm, and orange approximately 600 nm. Wavelengths outside this range are invisible to human eyes.
Does wavelength change when a wave enters a different medium?
Yes. When a wave enters a medium where it travels at a different speed, the wavelength changes but the frequency stays the same. For example, light slows down in glass, so its wavelength becomes shorter in glass than in air. The relationship v = f x lambda holds in each medium with the appropriate velocity.
What is the difference between wavelength and frequency?
Wavelength is a spatial measurement (distance per cycle), while frequency is a temporal measurement (cycles per second). They are inversely related for a given wave speed: doubling the frequency halves the wavelength, and vice versa. Both describe the same wave from different perspectives.
Can I use this for sound waves?
Yes. Select 'Sound in air at 20 C' for the standard speed of 343 m/s, or choose 'Custom velocity' to enter the speed of sound in other media (water, steel, etc.). The wave equation applies to all types of mechanical and electromagnetic waves.