Page 194 - Physics Coursebook 2015 (A level)

Cambridge International AS Level Physics
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However, this is rather difficult to draw, so you will often see a longitudinal wave represented as if it were a sine wave. The displacement referred to in the graph is the displacement of the particles in the wave.
We can compare the compressions and rarefactions (or expansions) of the longitudinal wave with the peaks and troughs of the transverse wave.
Phase and phase difference
Wave energy
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 (i.e. power) per unit area at right angles to the wave velocity.
intensity = power cross-sectional 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 1.37 kW m−2.
QUESTION
4 A 100 W lamp emits electromagnetic radiation in all directions. Assuming the lamp to be a point source, calculate the intensity of the radiation:
a at a distance of 1.0 m from the lamp
b at a distance of 2.0 m from the lamp.
Hint: Think of the area of a sphere at each of the two radii.
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 light bulb 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 is proportional to the square of the amplitude:
All points along a wave have the same pattern of vibration. However, different points do not necessarily vibrate in step with one another. As one point on a wave vibrates, the point next to it vibrates slightly out-of-step with it. We say that they vibrate out of phase with each other – there is a phase difference between them. This is the amount by which one oscillation leads or lags behind another.
Phase difference is measured in degrees. As you can see from Figure 13.9, two points A and B, with a separation of one whole wavelength λ, vibrate in phase with each other. The phase difference between these two points is 360°. (You can also say it is 0°.) The phase difference between any other two points between A and B can have any value between 0° and 360°. A complete cycle of the wave is thought of as 360°. In Chapter 14 we will see what it means to say that two waves are ‘in phase’ or ‘out of phase’ with one another.
C
AB
0
D
Points A and B are vibrating; they have a phase difference of 360° or 0°. They are ‘in phase’
Points C and D have a phase difference of 90°.
Figure 13.9 Different points along a wave have different phases.
QUESTION
3 Using axes of displacement and distance, sketch two waves A and B such that A has twice the wavelength and half the amplitude of B.
Distance
intensity ∝ amplitude2 (I ∝ A2)
Displacement