Progressive waves: Transfer energy from one place to another Stationary waves: Store energy without transferring Mechanical waves: Produced by vibrating objects, which cause particles to oscillate about fixed points. They need a medium to propagate.Electromagnetic waves: Electric and magnetic fields oscillate at right angles to each other. They don't need a medium to propagate.Transverse waves: Oscillations are perpendicular to the direction of propagation/direction of energy transfer. Longitudinal waves(e.g. sound): Oscillations are parallel to the direction of propagation/direction of energy transfer. Contain compressions (particles closer) and rarefactions (particles further apart).Displacement (): Distance from the mean position. Amplitude ( or

): Maximum displacement from the mean position. Period (): Time taken for a particle to undergo one complete oscillation. Frequency (): number of complete oscillations per unit time Unit: Hertz (Hz). Wavelength (): Distance between two successive oscillationswhich are in phase. Wave speed (): Distance travelled by wave energy per unit time. A displacement vs. distance graph: A displacement vs. time graph: Basic equations:

You can use a cathode ray oscilloscope (CRO) to measure the frequency of sound. To do this, you connect a microphone to the input of a CRO. The sound waves are converted to a varying voltage, which has the same frequency as that of sound. The frequency with which the voltage varies is the frequency of sound.BasicsWaves18 June 2015 06:01Summaries Page 1Phase difference of 0oor 360o(0 or 2 rad): In phase. Phase difference of 180o( rad): Completely out of phase/in antiphase. Consist of an oscillating electric field and a magnetic field. Electric and Magnetic fields oscillate at right angles. The direction of propagation is at right angles to both electric field and magnetic field oscillations.They are transverse waves. They don't require a medium to propagate through. In vacuum, they travel at "the speed of light", 3108m s-1. They can be polarised. Properties of Electromagnetic Waves The electromagnetic spectrum: Electromagnetic WavesSummaries Page 2Intensity: Energy transmitted per unit time per unit area at right angles to the wave velocity (units: W m-2).

If a point source radiates power , at a distanceaway, the intensityof the radiation is given by:

Intensity of a wave is directly proportional to the square of the wave's amplitude:

Note:

and

. So

. The amplitude of a wave is inversley proportional to the distance travelled. Intensity(Plane) Polarised waves: have all oscillations in one plane. Only transverse waves can be polarised. Sunlight is unpolarised. Radio waves and microwaves are typically polarised.Seeing light through two polaroids: Polarisation (American English: Polarization)Summaries Page 3Maximum intensity is observed when transmission axes are parallel ( = 0oin this diagram). Asis increased, the intensity gradually drops. When= 90o(transmission axes perpendicular), no light comes through analyzer. As the second polaroid ("analyzer") is rotated, Superposition of Waves: When two or more waves of the same type meet, the resultant displacement is equal to the vector sum of displacements due to each wave.SuperpositionCoherent sources: have the same frequency, and at a given point they maintain a constant phase difference. Monochromatic light: consists of light of a single wavelength (same frequency, or same colour). Interference: occurs when waves from two coherent sources superpose. Path difference: difference in the distances from each source (slit) to a point.Two-slit InterferenceSummaries Page 4Path difference: difference in the distances from each source (slit) to a point.Setup for Young's double-slit experiment: Single slit: to select a small portion of light from the lampensures light is coherent. Not needed when the lamp is laser.You get a pattern of bright and dark fringes, equally spaced. Bright bands: constructive interference: Path difference = , with = 0, 1, 2, Dark bands: destructive interference: Path difference =

, with = 0, 1, 2, : separation between two adjacent bright fringes and : slit separation. Fringes observed when . Typically,~ 0.1 mm and~ 2 m . The quantities are related by:

Diffraction: is the spreading of a wave as it passes through a gap or around an obstacle, into regions where it would not have travelled otherwise (the region it would not have travelled into otherwise is called the geometric shadow).Wavefront: a line joining points which are all in the same phase. Wavelength is larger Gap is narrow Diffraction is larger when: DiffractionSummaries Page 5When the gap size is similar to the wavelength, diffraction is greater. Diffraction gratings are an example of multi-slit Interference. Diffraction gratings have a large number of small gaps. Light passes through each of these gaps, diffracts, and interferes.Maxima produced by diffraction gratings are sharper and brighter compared to ones in the two-slit interference experiment. = "order".= 1: first orfer maximum, etc.= distance between two slits. The quantities are related by:

Number of slits per unit length =

. If white light is shone on the grating rather than light, the zeroth order maximum would be white, but subsequent maxima will show the white light separated into component colours, with blue closer to the central maximum. This happens because blue has smalland so itsis small.Multi-slit Interference (Diffraction Gratings)Stationary Waves (Standing Waves)Summaries Page 6Stationary waves are formed when two waves of the same type, having the same amplitude and frequency travelling in opposite directions superpose (e.g. when a string with fixed ends is pluckedthe incident wave superposes with the reflected wave to form a stationary wave).Nodes: Points on a stationary wave which show no displacement. Antinodes: Points on a stationary wave which show maximum displacement. All points between two successive nodes ("in one loop") are in phase. All points in one loop are in antiphase with points in adjacent loops. The distance between two successive nodes or two successive antinodes is half a wavelength. When forced to oscillate, stationary waves are formed only at certain resonant frequencies. Fundamental frequency (

): is the smallest frequency at which a stationary waves can be formed. The appearance of a stationary wave at different times during its cycle of oscillation (N: node, A: antinode): "Fixed ends" form nodes. "Open ends" form antinodes. Different types of stationary waves: A node forms at each end. (In these diagrams, fundamental frequency =

.= length): String fixed at Both Ends (e.g. guitar string)Stationary Waves (Standing Waves)Summaries Page 7Pipe Closed at One EndPipe Open at Both Ends (e.g. flutes)Summaries Page 8Sound waves are longitudinal so actual vibrations are parallel to the length. The wavelength of a sound wave can be measured using the setup below (a resonance tube dipped in water) Length of air column in the resonance tube: .= end correction. Whenever a stationary wave is set up, a loud sound is heard. The tube is fully immersed in water, and slowly brought up. The shortest length

to produce the loud sound and the next shoortest length

is measured. Then

.The wavelength of microwaves can be measured with the following setup: The metal plate reflects the microwaves emitted by the transmitter and sets up a stationary wave. There is a Summaries Page 9The metal plate reflects the microwaves emitted by the transmitter and sets up a stationary wave. There is a node at the metal plate.Detector is moved between metal plate and transmitter. The signal is observed. Distance between two maximum signals = distance between two minimum signals = . Note: Further away from the metal plate, the reflected waves have spread out more. I.e. its intensity, and hence its amplitude, is less. So the reflected wave cannot completely cancel out the incident wave, and so the minimum reading won't go all the way down to 0.Summaries Page 10