1. AS Physics

2. Waves Progressive waves (travelling waves) transfer energy from one place to another. There are two types of waves …. Transverse waves have oscillations perpendicular to the direction of travel of the wave Longitudinal waves have oscillations parallel to the direction of travel of the wave Frequency is the number of waves or oscillations per second Wavelength is the distance between the same point on two successive waves

3. Sound Waves Sound waves are longitudinal waves consisting of compressions and rarefactions. Sound waves are in fact pressure waves.

4. Longitudinal Waves Applet http://www.cbu.edu/~jvarrian/applets/waves1/lontra_ g.htm http://www.cbu.edu/~jvarrian/applets/waves1/lontra_ g.htm http://www.ngsir.netfirms.com/englishhtm/Lwave.ht m http://www.ngsir.netfirms.com/englishhtm/Lwave.ht m http://www.mta.ca/faculty/science/physics/suren/Lwa ve/Lwave01.html http://www.mta.ca/faculty/science/physics/suren/Lwa ve/Lwave01.html

5. Electromagnetic Waves There are seven electromagnetic waves…. Radio, micro, IR, light, UV, x-rays and gamma rays All of these can travel through a vacuum and travel at the speed of light These waves are transverse and are made of vibrating electric and magnetic fields.

6. Transverse Waves Applet http://surendranath.tripod.com/Applets/Waves/Twav e01/Twave01Applet.html http://surendranath.tripod.com/Applets/Waves/Twav e01/Twave01Applet.html http://www.ngsir.netfirms.com/englishhtm/TwaveA.h tm http://www.ngsir.netfirms.com/englishhtm/TwaveA.h tm http://www.cbu.edu/~jvarrian/applets/waves1/lontra_ g.htm http://www.cbu.edu/~jvarrian/applets/waves1/lontra_ g.htm

7. The Wave Equation Speed = frequency x wavelength c = f x λ Frequency = 1/ time period f = 1/T Speed or velocity (m/s) Frequency in Hertz (Hz) Wavelength (m) Time period in seconds (s)

8. Answers to past paper questions Question 2 a. Longitudinal: sound, ultrasound or seismic p-waves Transverse: any electromagnetic wave, seismic s-waves bi. Frequency is the number of waves/vibrations/oscillations per second/unit time bii Period is the time taken for 1 complete cycle / wave / vibration / oscillation ci Amplitude = 4 x 10 -5 m

9. Answers to past paper questions Question 2 cii Particle at A moves 4 x 10 -5 m in one direction parallel to the direction of the wave and then returns to its original equilibrium position before moving 4 x 10 -5 m in the opposite direction (three marks for.... idea that the particle is vibrating or moves in one direction and then the opposite direction.... the movement of the particle is in the same direction as the direction of the wave because the wave is longitudinal in nature..... inclusion of magnitude of the distance moved)

10. Answers to past paper questions Question 2 ciii Similarity – same amplitude/frequency/period or both move longitudinally Difference – particles at A and B are out of phase or have a phase difference of 180 degrees or π radians. iv Wavelength – 0.8m v Frequency = c/λ = 340/0.8 = 425 Hz (three marks from stating the equation, showing working and the final answer)

11. Answers to past paper questions Question 4 aiamplitude = 3.8 cm aiidisplacement = -3.4 cm (one mark for negative sign) aiiiperiod = 2.66 ms aivfrequency = 1 / T = 1 / 2.66 x 10 -3 = 376 Hz (student lose one mark if they have not taken into account the idea that the time period was in milliseconds!) bwavelength = c/f = 3 x 10 8 / 376 = 0.798 m (one mark for working out and one mark for final answer)

12. Polarisation Experiment Describe the apparatus used. What is true about the microwaves leaving the microwave transmitter? What is true about the microwave receiver? What did you observe to happen to the strength of the microwaves received, as the receiver was rotated through 360 °? Was the effect any different when the transmitter was rotated? What affect did the metal grille have on the strength of the microwaves detected?

13. Polarisation Summary Waves are polarised if the vibrations stay in one plane. Waves are unpolarised if they vibrate in many planes. Only transverse waves can be polarised.

14. Refraction Refractive index = Speed of light in a vacuum Speed of light in a substance n = c / c s Dense materials, that slow down light significantly, have larger refractive indexes. Refractive index does not have a unit. The refractive index of air or a vacuum is 1.

15. Refraction Light undergoes total internal reflection when moving from a dense to a less material at an angle of incidence greater than the critical angle. Sin θ c = n 2 / n 1 Note material 1 is always denser and material 2 less dense hence n 2 is always smaller.

16. Optical Fibres Optical fibres transmit light by total internal reflection. Some have a core and a cladding. The cladding has a lower refractive index than the core. In the absence of cladding, light could pass from one optical fibre into another, if the two were in optical contact and the fibre surface was scratched or contain moisture. Multipath dispersion causes the light signal to become ‘smeared’.

17. Optical Fibres Past Paper Question 3 ai cladding has a lower refractive index aii Angle of incidence must be greater than the critical angle at the boundary between the core and the cladding b Multipath dispersion occurs when different rays of light travel different distances because they take different routes through the fibre. The different rays hence arrives at the end of the fibre at different times and this produces a spread out signal which is lower in quality.

18. Optical Fibres Past Paper Question 3 ci Material 1 is the core and material 2 is the cladding.... sin θ c = n 2 / n 1 0.98 = sin θ c hence θ c = 78.5 0 cii If the critical angle is large only a small proportion of the light rays are captured by the optical fibre and undergo total internal reflection. These are the light rays that are almost horizontal and hence hitting the boundary at a very large angle of incidence. These light rays are travelling very similar distances down the fibre because they are taking very similar paths through the fibre and this reduces multipath dispersion.

19. Standing Waves A standing or stationary wave is formed when two waves of the same frequency travelling in opposite directions at the same speed, with the same amplitude, undergo superposition. Standing waves contain nodes and antinodes. Nodes are points of zero amplitude and antinodes are points of maximum amplitude. The distance between two nodes is half a wavelength. On either side of a node the vibration is π radians out of phase and between two nodes all particles vibrate in phase.

20. Superposition The principle of superposition states that....‘when two waves meet, the total displacement at a point is equal to the sum of the individual displacements at that point’. When two waves arrive at a point exactly in phase, with a phase difference of 0 or 2π radians, constructive interference or reinforcement occurs to produce a maximum (called an antinode in the case of a stationary wave) When two waves arrive at a point exactly out of phase, with a phase difference of π radians, destructive interference or cancellation occurs to produce a minimum (or node in the case of a stationary wave.)

21. Interference of Light Lasers produce monochromatic coherent light waves. Coherent waves have the same frequency and a constant phase difference. When coherent waves undergo superposition they produce a stable interference pattern. Young’s Double Slit Experiment Coherent laser light diffracts (spreads out) as it passes through each of the double slits. The diffracted light beams overlap. An interference pattern is produced on the screen with bright and dark fringes of equal width.

22. Young’s Double Slit Experiment A bright fringe is produced when two coherent light waves arrive at the screen.......... exactly in phase with a phase difference of 0 or 2π radians constructive interference or reinforcement occurs to produce a maxima A dark fringe is produced when two coherent light waves arrive at the screen.......... exactly out of phase with a phase difference of π radians destructive interference or cancelation occurs to produce a minima

23. Young’s Double Slit Experiment and Path Difference A bright fringe is produced when two coherent light waves arrive at the screen exactly in phase, with a phase difference of 0 or 2π radians and a path difference of a whole number of wavelengths (nλ). Constructive interference or reinforcement occurs to produce a maxima. A dark fringe is produced when two coherent light waves arrive at the screen exactly out of phase, with a phase difference of π radians and a path difference equal to (n + ½) λ. Destructive interference or cancelation occurs to produce a minima.

24. Young’s Double Slit Experiment Fringe spacing (w) is the distance from the start of one bright fringe to the start of the next bright fringe. w = λD / s λ is wavelength (m) D is the distance from the screen to the double slit (m) s is the slit separation (m)

25. Diffraction by a single slit When light passes through a single slit, the light also produces a pattern of bright and dark fringes. This interference pattern is different to that observed in Young’s double slit experiment in two ways..... the central bright fringe is twice the width of all other bright fringes (in Young’s experiment all fringes are the same width) The intensity of the light is less for those bright fringes further from the central maximum (in Young’s experiment all bright fringes have the same intensity)

26. Diffraction Gratings A diffraction grating contains many parallel slits (instead of the two used in Young’s slit experiment) The grating produces bright maxima at discrete points on the screen again due to the principle of superposition. The diffraction grating equation is.... nλ = d sin θ λ is the wavelength of the light (m) d is the grating spacing or the distance from one slit to the next e.g. if a diffraction grating has 300 lines (or slits) per mm d = 0.001 m / 300 = 3.3 x 10 -6 m n is the order number (1, 2, 3 etc) of the maxima angle θ is the angle to each maxima

27. Using the Diffraction Grating Equation Page 207 question 1 Laser light of wavelength 630 nm hits a diffraction grating of 300 lines per mm. Calculate the angle of diffraction of each of the first two orders..... d = 1 mm / 300 = 0.001 m / 300 = 3.3 x 10 -6 m nλ = d sin θ therefore sin θ = nλ/d For the first order....... sin θ = 1 x 630 x 10 -9 / 3.3 x 10 -6 = 0.191 θ = 11.0 0 For the second order....... sin θ = 2 x 630 x 10 -9 / 3.3 x 10 -6 = 0.382 θ = 22.4 0 The number of diffracted orders produced.... For n = 3, sin θ = 3 x 630 x 10 -9 /3.3 x 10 -6 = 0.573, θ = 34.9 0 For n = 5, sin θ = 5 x 630 x 10 -9 /3.3 x 10 -6 = 0.955, θ = 72.6 0 For n = 6, sin θ = 6 x 630 x 10 -9 /3.3 x 10 -6 = 1.15 Therefore five diffracted orders are produced.

28. Deriving the Diffraction Grating Equation If these two light rays are to produce a maxima on the screen, one light ray needs to have travelled a distance = nλ further than the other. The light ray travelling though the top slit will have travelled distance AC further than the other light ray. Angle ABC = θ sin θ = AC / d where d is slit separation AC = d sin θ = n λ d sin θ = n λ

29. Diffraction gratings split or disperse white light into a spectrum in a similar way to a glass prism. Light from stars produce absorption spectra containing dark lines. These dark absorption lines tell astronomers which elements are present in the star and the approximate surface temp of the star.