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The Wave Speed Equation

Using v = f × λ to link speed, frequency and wavelength.

  • Define and explain The Wave Speed Equation in your own words
  • Use key terms such as wavelength accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on The Wave Speed Equation: using v = f × λ to link speed, frequency and wavelength.

Definition: The Wave Speed Equation

Using v = f × λ to link speed, frequency and wavelength.

Key ideas

Wave speed links frequency and wavelength

v = f × λ: speed equals frequency times wavelength. Higher frequency means more waves per second, so for a fixed speed the wavelength must shrink. Rearranging gives f = v ÷ λ and λ = v ÷ f — learn all three forms.

The electromagnetic spectrum is one family

All EM waves travel at 3 × 10⁸ m/s in a vacuum and differ only in wavelength and frequency. From longest to shortest: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. Long waves suit communications; short waves carry more energy per photon and can ionise atoms, making them hazardous.

Key term — wavelength: The distance between two matching points on neighbouring waves, e.g. crest to crest, in metres.

Speed of a water wave

A ripple tank wave has frequency 2 Hz and wavelength 3 m. Calculate the wave speed.

Use v = f × λ. Substitute: v = 2 × 3. v = 6.

Answer: 6 m/s.

Common mistakes
  • Thinking different EM waves travel at different speeds In a vacuum every EM wave travels at 3 × 10⁸ m/s — speed does not depend on wavelength.
  • Mixing up amplitude and wavelength on a diagram Amplitude is the vertical height from the middle line; wavelength is the horizontal repeat distance.

Practice

A wave has frequency 50 Hz and wavelength 4 m. Calculate its speed.
v = fλ.

50 × 4 = 200 m/s.

Red light has a longer wavelength than blue light. Which has the higher frequency?
v = fλ with v fixed.

Blue light — with speed constant, shorter wavelength means higher frequency.

An EM wave has wavelength 0.5 m. Calculate its frequency (c = 3 × 10⁸ m/s).
f = v ÷ λ.

3 × 10⁸ ÷ 0.5 = 6 × 10⁸ Hz.

Is a sound wave transverse or longitudinal? Explain.
Which way do air particles vibrate?

Longitudinal — air particles vibrate parallel to the direction the sound travels, in compressions and rarefactions.

Quick check

The Wave Speed Equation — quick check

Which of these best defines "wavelength"?

The distance between two matching points on neighbouring waves, e.g. crest to crest, in metres.

Name two uses of microwaves and one danger of excessive infrared exposure.

Microwaves: cooking food, mobile phone and satellite communication. Infrared: overexposure can cause skin burns.

A ray of light bends as it enters glass from air. Name the effect and explain why it happens.

Refraction — light slows down in glass, and the change in speed at the boundary bends the ray.
Key takeaways
  • The Wave Speed Equation: using v = f × λ to link speed, frequency and wavelength.
  • Wave speed links frequency and wavelength: v = f × λ: speed equals frequency times wavelength.
  • frequency: The number of waves passing a point per second, in hertz.
  • Watch out for: thinking different EM waves travel at different speeds
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