In studying this topic you need to think carefully about and be able to interpret each of the figures shown.


A wave describes a mechanism of how energy is transferred from one place to another without any matter being transferred. It is the disturbance that is propagated only. Waves travel with well-defined speeds determined by the properties through which they travel.


A disturbance on a string (e.g. guitar string) propagates along the string. Figure (1) shows an animation of a pulse travelling along a string.




                 Fig. (1)   Animation of a pulse along a string.


As the pulse propagates, the string moves up or down but the energy in the form of the kinetic energy and potential energy is transferred as shown in figure (2).




                  Fig. (2)   Animation of the transfer of energy (K.E. + P.E.)  along a string.



Important parameters describing a wave are its amplitude A, its wavelength l, period T, frequency f and speed of propagation v. The period and frequency are the reciprocals of each other


The speed of propagation through a given medium is constant and depends upon its wavelength and frequency (or period).



Figure (3) shows an animation of a sinusoidal wave travelling along a string. Study the animation carefully and before you look at the answers below, determine the amplitude, wavelength, period, frequency and speed of the wave.



                  Fig. (3)   Animation of a sinusoidal wave travelling along a string.


Notice that it is the shape of the disturbances that advances while parts of the string move up and down, each segment of the strings executing simple harmonic motion.


From the animation:

     amplitude      A = 6.0 m

     wavelength   l = 25.0 m

     period           T = 20.0 s2

     frequency     f =  0.050 Hz

     speed           v = 1.25 m.s-1


A disturbance on water produces water waves. Figure (4) shows a water wave propagating from the left to the right then the wave travels into shallower water and is slowed down which produces a change in direction of propagation. This phenomenon is called refraction.



           Fig. (4)   Animation of water waves entering shallow water. The frequency does not

              change but the speed and wavelength are reduced. This type of bending of the waves

              is known as refraction.





·        Transverse wave.

·        An electromagnetic waves is propagated by the oscillations of the electric and magnetic fields. A changing electric field produces a changing magnetic field and a changing magnetic field produces a changing electric field. Thus, an electromagnetic wave is self propagating and does not need a medium to travel through.

·        Can travel through vacuum, speed is c = 3.0 x 108 m.s-1

·        When electromagnetic waves are emitted or absorbed by an atom, done so in quanta of energy:

             E = h f



             Fig. (5)   An electromagnetic wave.



             Fig. (6)   The electromagnetic spectrum




A progressive electromagnetic wave is a self-supporting, energy-carrying disturbance that travels free of its source. The light from the Sun travels through space (no medium) for only 8.3 minutes before arriving at Earth. Each form of electromagnetic radiation (radiowaves, microwaves, infrared, light, ultraviolet, x-rays and g rays) is a web of oscillating electric and magnetic fields inducing one another. A fluctuating electric field (electric charges experience forces) creates a magnetic field (moving charges experience forces) perpendicular too itself, surrounding and extending beyond it. That magnetic field sweeping off to a point further in space is varying there, and so generates a perpendicular electric fields that spreads out. Nothing is actually displaced in space like a water wave where the water oscillates up and down and side-ways.


All electromagnetic waves propagate in vacuum at exactly the speed of light


               c = 2.997 924 85 m.s-1


This is a tremendous speed, light travels 1 m in only 3.3×10-10 s.


"There are only two fundamental mechanisms for transporting energy and momentum: a streaming of particles and a flowing of waves. And even these two seemingly opposite conceptions are subtly intertwined – there are no waves without particles and no particles without waves … " from Hecht.


The particles associated with electromagnetic waves are called photons. The energy of a single photon is


     (3)            E = h f


          E          energy of photon (J)   electron volt    1 eV = 1.6×10-19 J   

          f          frequency of electromagnetic wave (Hz)

          h = 6.62606876×10-34 J.s         Planck's constant (J.s)



For each picture below write a sentence describing the application shown.



            Fig. (7)   Applications of electromagnetic waves.





The images below show the interference effects when two waves pass through each other. At some points the waves reinforce each other (constructive interference) and at other points cancel each other (destructive) interference.


                      Fig. (8)   Interference of two travelling waves.

       (a) constructive  (b) destructive  (c) partial

                Fig. 9   Two dimensional animation of two point interference.



Light behaving as a wave

When light passes through very narrow apertures and falls on a screen, a diffraction / interference pattern consisting of a band of bright and dark regions is observed. The brightness (intensity) of light detected on the screen is proportional to the square of the amplitude of the wave. For a plane wave incident upon an aperture, we observe Fraunhoffer diffraction when the screen distance is much larger than the width of the apertures.

               Fig. 10.     Fraunhoffer diffraction from a double slit.



Particles behaving as waves

Waves are a mechanism for transferring energy via some kind of vibration without any matter being transferred. One characteristic of waves but not of particles, is that, diffraction / interference is observed as shown in figures (10) when a wave passes through an aperture. However, in experimental arrangements analogous to the two slit interference for light, when a beam of electrons is incident upon a biprism (mimics two slits for light as the electrons can travel in two paths around a filament) and are detected upon a screen, an interference pattern is observed. When a few electrons hit the screen, no notice pattern is discerned as shown in figure (11).

              Fig. 11.   Pattern formed by 2000 electrons on passing through the equivalent of a double slit.         


However, for much longer exposures involving 80000 plus electrons, a very distinctive two slit diffraction pattern is clearly observed as shown in figure (12).


          Fig. 12. Pattern formed by 80000 electrons on passing through the  equivalent of a double slit.

            As more and more electrons hit the screen a two slit interference pattern develops.


The electrons are individual particles when they strike a single point on the detection screen, but the distribution of the points on the screen gives an interference pattern which can only be attributed to a wave phenomenon. Hence, we can only conclude that electrons have this dual nature – they behave as particles or as waves. We can’t predict where a single electron will arrive on the screen. We only know the probability of where an electron will strike. This behaviour is typical of the quantum world and is a good example of the interplay between indeterminism and determinism.  


So particles exhibit wave characteristics, but we also find that light which we normally think of as a wave has particle like properties. The particle nature of electromagnetic waves is observed in the photoelectric effect – when light of a sufficient frequency strikes a metal surface, electrons are emitted from the surface. To account for the emission of the electrons from the surface, the light is modelled as a stream of particles called photons. The energy of each photon is E = h f.


PARTICLES – particle and wave properties

WAVES – wave and particle properties



Emission & Absorption of electromagnetic radiation by atoms & molecules

The emission and absorption of light (transfer of energy & momentum) takes place in a particle manner. All forms of electromagnetic radiation interact with matter in the process of emission and absorption. The radiation propagates in a wavelike fashion but in an interaction the radiation behaves as a concentration of energy (photons) moving at the speed of light. Each photon carries very little energy. However, even an ordinary torch beam is a torrent of ~1017 photons.s-1. When we “see” light what we observe by eye or on film is the average energy per unit area per time arriving at some surface.










Video clip Japan 2011 tsunami