IGCSE Physics 0625 – 3.1 General properties of waves3.1 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
| Quantity | Symbol | Unit | Definition |
|---|
| Amplitude | A | metre (m) | Maximum displacement from equilibrium |
| Wavelength | λ | metre (m) | Distance between two successive points in phase |
| Frequency | f | hertz (Hz) | Number of cycles per second |
| Period | T | second (s) | Time for one complete cycle (T = 1/f) |
| Wave speed | v | metre 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.
- Write down the known values:
\$v = 340\ \text{m s}^{-1}\$, \$f = 680\ \text{Hz}\$.
- Use the rearranged form \$\lambda = \dfrac{v}{f}\$.
- Substitute the numbers:
\$\lambda = \dfrac{340}{680}\ \text{m} = 0.5\ \text{m}\$.
- Answer: The wavelength is \$0.5\ \text{m}\$.
Practice questions
- A wave on a string has a wavelength of \$0.25\ \text{m}\$ and a frequency of \$12\ \text{Hz}\$. What is its speed?
- The speed of a water wave is \$2.0\ \text{m s}^{-1}\$ and its frequency is \$0.5\ \text{Hz}\$. Find its wavelength.
- 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).