It is important to realise that, for both types of mechanical wave, the particles that make up the material through which the wave is travelling do not move along – they only oscillate about a fixed point. It is energy that is transmitted by the wave. Each particle vibrates; as it does so, it pushes its neighbour, transferring energy to it. Then that particle pushes its neighbour, which pushes its neighbour. In this way, energy is transmitted from one particle to the next, to the next and so on down the line.

Intensity

The term intensity has a very precise meaning in physics. The intensity of a wave is defined as the rate of energy transmitted (power) per unit area at right angles to the wave velocity.

${\mathop{\rm int}} ensity = \frac{{power}}{{area}}$

Intensity is measured in watts per square metre ($W\,{m^{ - 2}}$). For example, when the Sun is directly overhead, the intensity of its radiation is about $1.0\,kW\,{m^{ - 2}}$ (1 kilowatt per square metre). This means that energy arrives at the rate of about $1 kW$ ($1000\,J\,{s^{ - 1}}$) on each square metre of the surface of the Earth. At the top of the atmosphere, the intensity of sunlight is greater, about $1.4\,kW\,{m^{ - 2}}$.

Intensity and amplitude

- The intensity of a wave generally decreases as it travels along. There are two reasons for this:
- The wave may ‘spread out’ (as in the example of light spreading out from a lamp in Question 4).
The wave may be absorbed or scattered (as when light passes through the Earth’s atmosphere).
As a wave spreads out, its amplitude decreases. This suggests that the intensity I of a wave is related to its amplitude A.
In fact, intensity I is directly proportional to the square of the amplitude A:

${\mathop{\rm int}} ensity\, \propto \,amplitud{e^2}$ or $I\, \propto \,{A^2}$

The relationship also implies that, for a particular wave:

$\frac{{{\mathop{\rm int}} ensity}}{{amplitud{e^2}}} = constant$

So, if one wave has twice the amplitude of another, it has four times the intensity. This means that the wave is transmitting four times the power per unit area at right angles to the wave velocity.