Wave Behaviour and the EM Spectrum

What Is a 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 — it is the disturbance that moves, not the material. This is why you can feel a sound wave in your chest even though no air travels from the speaker to you; instead, the air molecules pass the vibration along like a row of falling dominoes.

All waves fall into one of two categories. In transverse waves, the vibrations are perpendicular to the direction of energy transfer — the wave forms crests and troughs. Examples include light, water surface ripples and all electromagnetic waves. In longitudinal waves, the vibrations are parallel to the direction of energy transfer. Instead of crests and troughs, longitudinal waves have compressions (regions where particles are pressed together) and rarefactions (regions where particles spread apart). Sound is the main longitudinal wave at GCSE.

Wave Properties

All waves share four measurable properties:

• Amplitude — the maximum displacement from rest position, measured in metres. A larger amplitude means more energy. For sound, greater amplitude means a louder sound; for light, it means brighter light.
• Wavelength (\(\lambda\)) — the distance from one crest (or compression) to the next. 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 higher pitch.
• Period (\(T\)) — the time for one complete wave to pass a point. Period and frequency are reciprocals: \(T = \frac{1}{f}\).

The Wave Speed Equation

The relationship between wave speed, frequency and wavelength is one of the most important equations in physics:

$$v = f \times \lambda$$

Where \(v\) is wave speed in m/s, \(f\) is frequency in Hz, and \(\lambda\) is wavelength in m. This equation applies to all waves — whether a ripple on a pond or a gamma ray from a radioactive source. You can rearrange it to find frequency (\(f = \frac{v}{\lambda}\)) or wavelength (\(\lambda = \frac{v}{f}\)).

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). Speed, frequency and wavelength are unchanged.
• Refraction — a wave changes speed when passing from one medium to another (e.g. light entering glass from air). If it hits the boundary at an angle, it also changes direction. A wave bends towards the normal when it slows down (entering a denser medium). Frequency stays the same; wavelength and speed change.
• Diffraction — a wave spreads out as it passes through a gap or around an obstacle. The spreading is greatest when the gap size is similar to the wavelength. This is why sound diffracts around a doorway (sound wavelengths are comparable to door sizes) but light does not (visible light wavelengths are millions of times shorter than a doorway).

The Electromagnetic Spectrum

All electromagnetic waves are transverse waves that travel at the same speed in a vacuum: approximately \(3 \times 10^8\) m/s (the speed of light). They are arranged on the electromagnetic spectrum in order of increasing frequency (and decreasing wavelength):

Radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays

As frequency increases, wavelength decreases (since \(v = f\lambda\) and \(v\) is constant). Higher-frequency (shorter-wavelength) EM radiation generally carries more energy per photon and tends to be more ionising — which is why UV, X-rays and gamma rays are more hazardous to living tissue than radio waves or infrared.