Wave Behaviour
Types of Wave
Waves transfer energy from one place to another without transferring matter. The particles of the medium vibrate about their rest positions but do not travel along with the wave. There are two main categories of wave:
• Transverse waves — the vibrations are perpendicular (at right angles) to the direction of energy transfer. The wave forms crests (peaks) and troughs. Examples include light waves, water surface ripples, all electromagnetic waves, and waves on a string.
• Longitudinal waves — the vibrations are parallel to the direction of energy transfer. Instead of crests and troughs, longitudinal waves have compressions (particles pushed close together) and rarefactions (particles spread apart). Sound waves are the main example at GCSE.
An important distinction: mechanical waves (such as sound and water waves) require a medium (solid, liquid or gas) to travel through. Electromagnetic waves (such as light) do not need a medium and can travel through a vacuum.
Waves transfer energy without transferring matter. Transverse: vibrations perpendicular to travel (crests and troughs). Longitudinal: vibrations parallel to travel (compressions and rarefactions).
Wave Properties
All waves — whether transverse or longitudinal — can be described using four key properties:
• Amplitude — the maximum displacement from the rest (equilibrium) position. Measured in metres. A larger amplitude means the wave carries more energy. For sound, greater amplitude means a louder sound; for light, it means brighter light.
• Wavelength (\(\lambda\)) — the distance from one point on a wave to the same point on the next wave (e.g. crest to crest, or compression to compression). Measured in metres.
• Frequency (\(f\)) — the number of complete waves passing a fixed point per second, measured in hertz (Hz). For sound, higher frequency means a higher pitch.
• Period (\(T\)) — the time for one complete wave to pass a point, measured in seconds. Period and frequency are reciprocals: \(T = \frac{1}{f}\). A wave with a frequency of 50 Hz has a period of \(\frac{1}{50} = 0.02 \text{ s}\).
The Wave Speed Equation
The relationship between wave speed, frequency and wavelength is:
$$v = f \times \lambda$$
Where \(v\) is wave speed (m/s), \(f\) is frequency (Hz), and \(\lambda\) is wavelength (m). This equation applies to all waves. You can rearrange it to find frequency (\(f = \frac{v}{\lambda}\)) or wavelength (\(\lambda = \frac{v}{f}\)).
Question: A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. Calculate the wave speed.
Answer: \(v = f \times \lambda = 500 \times 0.68 = 340 \text{ m/s}\). This is the speed of sound in air at room temperature.
Reflection, Refraction and Diffraction
Waves can interact with boundaries and obstacles in three important ways:
• Reflection — a wave bounces off a surface. The angle of incidence equals the angle of reflection (both measured from the normal — an imaginary line perpendicular to the surface). The wave speed, frequency and wavelength do not change during reflection.
• Refraction — a wave changes speed when it passes from one medium to another (e.g. from air into glass). If the wave hits the boundary at an angle, it also changes direction. The wave bends towards the normal when it slows down (entering a denser medium) and away from the normal when it speeds up (entering a less dense medium). The frequency stays the same but the wavelength changes.
• Diffraction — a wave spreads out when it passes through a gap or around the edge of an obstacle. The effect is greatest when the gap width is similar to the wavelength of the wave. If the gap is much larger than the wavelength, there is very little diffraction.
In a ripple tank, you can observe reflection, refraction and diffraction of water waves. A vibrating bar creates plane (straight) waves, and a lamp above projects the wave pattern onto a screen below. To measure wave speed: use a strobe light to “freeze” the waves, measure the distance between several wave crests and divide by the number of wavelengths to find \(\lambda\). Count the frequency from the motor speed. Then calculate \(v = f\lambda\).
For sound speed, you can use the echo method: stand a measured distance from a wall, clap and time how long the echo takes to return. The sound travels to the wall and back, so the total distance is twice the distance to the wall. Speed = total distance ÷ time. To improve accuracy, time multiple echoes and divide.
Reflection: angle of incidence = angle of reflection. Refraction: wave changes speed (and may change direction) at a boundary. Diffraction: wave spreads through gaps — most when gap width ≈ wavelength.
Sound waves have wavelengths of roughly 0.1 m to 10 m — similar in size to everyday gaps like doorways and corridors. This means sound diffracts significantly around corners, which is why you can hear someone in the next room even if you cannot see them. Visible light has an extremely short wavelength (about \(400\text{–}700 \text{ nm}\), or \(4 \times 10^{-7}\) to \(7 \times 10^{-7}\) m). Doorways are millions of times wider than light’s wavelength, so light shows almost no diffraction around everyday objects and travels in straight lines.