Amplitude (A, a)
This is the maximum displacement of a particle from its equilibrium position. (It is also equal to the maximum displacement of the source that produces the wave).
The energy that a wave transports per unit time across unit area of the medium through which it is travelling is called the intensity (I). From our knowledge of SHM we know that the energy of the oscillating system is proportional to the square of the amplitude (equation 4.12). Hence for a wave of amplitude A, we have that
Period (T)
This is the time that it takes a particle to make one complete oscillation. (It is also equal to the time for the source of the wave to make one complete oscillation).
Frequency (f)
This is the number of oscillations made per second by a particle. (It is also equal to the number of oscillations made per second by the source of the wave). The SI unit of frequency is the hertz-Hz. Clearly then, f = 1__
T
Wavelength (λ)
This is the distance along the medium between two successive particles that have the same displacement
Wave speed (v, c)
This is the speed with which energy is carried in the medium by the wave. A very important fact is that wave
speed depends only on the nature and properties of the medium.
You can demonstrate this by sending pulses along different types of rubber tubes or by sending pulses along a slinky in which you alter the distance between successive turns by stretching it.
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(In some circumstances the wave speed is a function of wavelength, a phenomenon known as dispersion)
Figure 427 shows how the different terms and definitions associated with waves relate to both transverse and longitudinal waves. From these diagrams, we also see that the wavelength of a transverse wave is equal to the distance between successive crests and also between successive troughs. For a longitudinal wave the wavelength is equal to the distance between successive points of maximum compression and also between successive points of maximum rarefaction. di sp la ce m ent of eq ui libr iu m p os it io
n equilibrium positionof tube
amplitude, A wavelength crest crest
trough trough amplitude wavelength
distance along tube
di sp la ce m ent of pa rt ic le period, T time compression rarefaction maximum compression wavelength tube from TRANSVERSE TRANSVERSE AND LONGITUDINAL LONGITUDINAL period, T
Figure 427 How the definitions apply
4.4.7 Draw and explain displacement-time and
displacement-position graphs for transverse
and for longitudinal waves
4.4.8 Derive and apply the relationship between wave speed, wavelength and frequency
4.4.9 State that all electromagnetic waves travel with the same speed in free space and recall the orders of magnitude of the wavelengths of the principal radiations in the electromagnetic spectrum.
© IBO 2007
4.4.7 DISPLACEMENT-TIMEAND
DISPLACEMENT-POSITIONGRAPHS
4.4.8 THE
RELATIONSHIPBETWEEN
WAVESPEED, WAVELENGTH
ANDFREQUENCY
Figure 428 shows an instantaneous snapshot of a medium through which a wave is travelling. A particle of the medium is labelled ‘P’. d is p la c eme n t o f me d iu m
distance along medium P At time t = 0
Figure 428 Instantaneous snapshot of displacement of medium
If we take another photograph half a period later then the particle ‘P’ will be in the position shown in Figure 429.
di sp la ce m e n t of m edi um
distance along medium At time t T
2
---
=
P
Figure 429 Particle ‘P’ half a period later
In this time the wave will have moved forward a distance of half a wavelength
λ
2
--- .
We have therefore that the speed v of the wave
= distance_______time = __
T , but f = 1__T,
Hence we have
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Example
Water waves of wavelength 5.0 cm are travelling with a speed of 1.0 ms–1.
Calculate the frequency of the source producing the waves?
The waves travel into deeper water where their speed is now 2.0 m s–1. Calculate the new wavelength λ
new of the
waves.
Solution
Using v = fλ we have that 1.0 = f × .05 and so f = 20 Hz.
In the deeper water using v = f λ we now have that 2.0 = 20 × λ
new
and so λ
new = 10 cm.
4.4.9 ELECTROMAGNETIC
WAVES
We mentioned above that light is a transverse wave but in fact light is just one example of a most important class of waves known as electromagnetic waves. They are called electromagnetic waves (em waves) because they
actually consist of an electric field and a magnetic field oscillating at right angles to each other. Their existence was first predicted by Clerk Maxwell in 1864 and verified some 20 years later by Heinrich Hertz (hence Hz for the unit of frequency). This was one of the great unifications in Physics.
Before Maxwell’s prediction, Optics (light) was studied independently of Electricity and Magnetism. After the verification of his prediction, there was just the study of Electromagnetism. Maxwell’s theory also predicted that all em waves would have the same speed in free space (vacuum) of very nearly 3 × 108 m s–1. This prediction
had great implications for the development of Physics as will be seen in Topics D.1 and H.1.
The source of all em waves is essentially the accelerated motion of electric charge. If the charge is oscillating then the frequency with which the charge oscillates determines the frequency of the em wave. The so-called spectrum of em waves is vast. Suppose in a thought experiment, we were to have a charged metal sphere and were able to set it oscillating at different frequencies. When vibrating with a frequency of 103 Hz, the oscillating charged
sphere would be a source of long wave radio signals, at 109 Hz a source of television signals, at 1015 Hz a source
of visible light and at 1018 Hz, it would emit X-rays. Of
course this is just a thought experiment and we should identify the actual sources of the different regions of the em spectrum. These are shown in Figure 430.
Our thought experiment might be somewhat absurd, but it does emphasise the point that the origin of all em waves is the accelerated motion of electric charge.
103 106
Radio waves
104 108 1010 1012 1014 1016 1018
106 104 102 100 10–2 10–4 10–6 10–8 10–10
f / Hz
Source Electrons moving in conductors Hot Objects Microwaves Infra-red Ultra- violet Gas discharge X-rays γ-rays Electrons striking targets Radioactive decay V isible (v er y hot objec ts) λ / m
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4.5.1 Describe the reflection and transmission of waves at a boundary between two media.
4.5.2 State and apply Snell’s law.
© IBO 2007