Wavelength Formula

The Formula

\lambda = \frac{v}{f} (wave speed divided by frequency)

When to use: How 'long' one complete wave cycle is — the spatial size of a single repeating pattern.

Quick Example

Radio waves have wavelengths of meters; visible light has wavelengths of hundreds of nanometers.

Notation

\lambda (lambda) is the wavelength in metres (m), v is the wave speed in m/s, f is the frequency in hertz (Hz), and k is the wave number in rad/m.

What This Formula Means

Wavelength is the distance between two consecutive identical points on a wave, such as from one peak to the next peak or one trough to the next trough, measured in metres.

How 'long' one complete wave cycle is — the spatial size of a single repeating pattern.

Formal View

Wavelength \lambda is the spatial period of a sinusoidal wave: the smallest positive value satisfying y(x + \lambda, t) = y(x, t) for all x and t. It is related to the wave number by \lambda = 2\pi / k and to speed and frequency by \lambda = v / f.

Worked Examples

Example 1

easy
A wave has a speed of 340 \text{ m/s} and a frequency of 170 \text{ Hz}. What is the wavelength?

Solution

  1. 1
    Use the wave equation: v = f\lambda.
  2. 2
    Rearrange for wavelength: \lambda = \frac{v}{f}.
  3. 3
    \lambda = \frac{340}{170} = 2 \text{ m}

Answer

\lambda = 2 \text{ m}
Wavelength is the distance between consecutive identical points on a wave (e.g., crest to crest). It is inversely proportional to frequency for a given wave speed.

Example 2

medium
Red light has a wavelength of 700 \text{ nm} in a vacuum. What is its frequency? Use c = 3 \times 10^8 \text{ m/s}.

Example 3

medium
A sound wave has frequency 440 Hz and travels at 343 m/s. Find the wavelength.

Common Mistakes

  • Confusing wavelength with amplitude — wavelength is measured horizontally (peak to peak), while amplitude is measured vertically (equilibrium to peak).
  • Measuring from peak to trough instead of peak to peak — that gives only half a wavelength.
  • Forgetting to convert units: mixing centimetres for wavelength with metres per second for speed without converting.

Why This Formula Matters

Wavelength determines how waves interact with objects and what we perceive — it controls the colour of light we see, the pitch of sound we hear, and whether a wave can diffract around obstacles.

Frequently Asked Questions

What is the Wavelength formula?

Wavelength is the distance between two consecutive identical points on a wave, such as from one peak to the next peak or one trough to the next trough, measured in metres.

How do you use the Wavelength formula?

How 'long' one complete wave cycle is — the spatial size of a single repeating pattern.

What do the symbols mean in the Wavelength formula?

\lambda (lambda) is the wavelength in metres (m), v is the wave speed in m/s, f is the frequency in hertz (Hz), and k is the wave number in rad/m.

Why is the Wavelength formula important in Physics?

Wavelength determines how waves interact with objects and what we perceive — it controls the colour of light we see, the pitch of sound we hear, and whether a wave can diffract around obstacles.

What do students get wrong about Wavelength?

Wavelength is a spatial measurement in meters, not a time measurement like period.

What should I learn before the Wavelength formula?

Before studying the Wavelength formula, you should understand: waves.

Want the Full Guide?

This formula is covered in depth in our complete guide:

Forces, Motion, and Energy: A Concept Bridge Guide →
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Related Concepts

WavesFrequencyWave Speed