Frequency and wavelength are two fundamental properties of waves. Frequency (measured in Hz) is how many times per second a wave repeats. Wavelength is the physical distance between consecutive peaks or troughs. They are inversely related through the wave's speed in the medium, allowing conversion between them.
The Formula
Wavelength = Speed / Frequency
λ = v / f
Or:
Frequency = Speed / Wavelength
f = v / λ
Where:
- λ (lambda) = wavelength (meters)
- f = frequency (Hertz, Hz)
- v = speed of the wave in the medium
For electromagnetic waves (light) in vacuum: v = 3 × 10⁸ m/s (speed of light).
Worked Example: Light
Visible light has wavelengths around 500 nm (green). What is its frequency?
500 nm = 500 × 10⁻⁹ m = 5 × 10⁻⁷ m
f = (3 × 10⁸ m/s) / (5 × 10⁻⁷ m)
f = 6 × 10¹⁴ Hz
This green light oscillates 600 trillion times per second. Human eyes respond to frequencies roughly between 4 × 10¹⁴ Hz (red) and 8 × 10¹⁴ Hz (violet).
Speed Varies by Medium
Light travels at different speeds in different media:
| Medium | Speed | Relative to c |
|---|---|---|
| Vacuum | 3.0 × 10⁸ m/s | 1.0 |
| Air | 3.0 × 10⁸ m/s | ≈1.0 |
| Water | 2.25 × 10⁸ m/s | 0.75 |
| Glass | 2.0 × 10⁸ m/s | 0.67 |
In water, the same frequency light has a shorter wavelength because it travels slower.
Worked Example: Sound
A sound wave with frequency 440 Hz (musical note A) travels through air at 343 m/s (at 20°C).
λ = 343 m/s / 440 Hz = 0.78 m = 78 cm
The wavelength is about 78 cm. In water (speed 1,480 m/s):
λ = 1,480 m/s / 440 Hz = 3.36 m
The wavelength is 3.36 m in water — much longer because sound travels faster there.
Applications
Understanding frequency-wavelength relationships is essential for:
- Radio transmission: Different frequencies require different antenna sizes (λ/4 or λ/2)
- Optics: Lens design depends on wavelength
- Acoustics: Room dimensions affect which frequencies resonate
- Astronomy: Redshift (wavelength change) reveals distant object velocities
Tips
Remember that frequency doesn't change when a wave enters a different medium — but wavelength does. The higher the frequency, the shorter the wavelength (inverse relationship). Also, when comparing waves of different types (light vs sound), always specify the medium because speed varies.
Use our Frequency-Wavelength Converter to convert between frequency and wavelength instantly.