Recall and use the equation for wave speed v = f λ

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – 3.1 General properties of waves

3.1 General properties of waves

Key concepts

Waves transfer energy without the permanent movement of matter. The main quantities used to describe a wave are:

  • Amplitude (A) – maximum displacement from the rest position.
  • Wavelength (λ) – distance between two consecutive points in phase (e.g., crest to crest).
  • Frequency (f) – number of complete cycles that pass a given point each second (measured in hertz, Hz).
  • Period (T) – time for one complete cycle (T = 1/f).
  • Wave speed (v) – how fast a wave travels through a medium.

Wave terminology table

QuantitySymbolUnitDefinition
AmplitudeAmetre (m)Maximum displacement from equilibrium
Wavelengthλmetre (m)Distance between two successive points in phase
Frequencyfhertz (Hz)Number of cycles per second
PeriodTsecond (s)Time for one complete cycle (T = 1/f)
Wave speedvmetre per second (m s⁻¹)Distance a wave travels per unit time

Relationship between wave speed, frequency and wavelength

The fundamental equation linking the three quantities is

\$v = f \, \lambda\$

where

  • \$v\$ is the wave speed,
  • \$f\$ is the frequency, and
  • \$\lambda\$ is the wavelength.

Re‑arranging the equation allows you to solve for any one of the three variables:

  • \$v = f\lambda\$  (find speed)
  • \$f = \dfrac{v}{\lambda}\$  (find frequency)
  • \$\lambda = \dfrac{v}{f}\$  (find wavelength)

Suggested diagram: A transverse wave showing crest, trough, wavelength (λ) and direction of travel (v).

Using the equation – Worked example

Question: A sound wave travels through air at \$340\ \text{m s}^{-1}\$ and has a frequency of \$680\ \text{Hz}\$. Calculate its wavelength.

  1. Write down the known values:

    \$v = 340\ \text{m s}^{-1}\$, \$f = 680\ \text{Hz}\$.

  2. Use the rearranged form \$\lambda = \dfrac{v}{f}\$.
  3. Substitute the numbers:

    \$\lambda = \dfrac{340}{680}\ \text{m} = 0.5\ \text{m}\$.

  4. Answer: The wavelength is \$0.5\ \text{m}\$.

Practice questions

  1. A wave on a string has a wavelength of \$0.25\ \text{m}\$ and a frequency of \$12\ \text{Hz}\$. What is its speed?
  2. The speed of a water wave is \$2.0\ \text{m s}^{-1}\$ and its frequency is \$0.5\ \text{Hz}\$. Find its wavelength.
  3. If the wavelength of a radio wave is \$3.0\ \text{m}\$ and its speed is \$3.0\times10^{8}\ \text{m s}^{-1}\$, calculate its frequency.

Summary

  • The wave speed, frequency and wavelength are linked by \$v = f\lambda\$.
  • Increasing the frequency while keeping speed constant shortens the wavelength, and vice‑versa.
  • Remember to keep units consistent (metres for distance, seconds for time, hertz for frequency).