Waves

Waves

1. The Nature of Waves

   • INTENSITY is the rate of flow of energy per unit area at right angles to the direction of travel of the wave and measured in W/m2
     • Intensity is proportional to the square of the amplitude of the wave
   • wave speed = wavelength x frequency
   • Frequency = 1/period

2. Longitudinal and Transverse Waves

   • In transverse waves the vibration is at right angles to the direction of travel. All EM waves are transverse, along with ripples on water and waves on ropes
   • In longitudinal waves the vibrations are along the direction of travel, for example sound.
   • A polarised wave only oscillates in one direction. Polarisation can only happen for transverse waves. The fact you can diffract light is proof that it's a transverse wave.
     • If you direct a beam of unpolarised light at a reflective surface then view it through a polarising filter, the intensity of light leaving the filter changes with the orientation of the filter. This is because light is partially polarised when reflected
     • The amplitude of the transmitted wave is the component of the incident wave in the direction of the new plane of polarisation. A = Acos0
     • The intensity of the transmitted light is proportional to the amplitude squared - this is Malus' law. I = Icos20

3. Superposition and Coherence

   • The principle of superposition says that when two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
   • Two points on a wave are in phase if they are both at the same point in the wave cycle
   • In order to get clear interference patterns, the two or more sources must be coherent. Two sources are coherent if they have the same wavelength and frequency and a fixed phase difference between them
   • Constructive interference occurs when the path difference is a whole number
   • Destructive interference occurs when the path difference is an odd number of half wavelengths

4. Stationary waves

   • A standing wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions
   • Nodes are where the amplitude of the vibration is zero, antinodes are points of maximum amplitude
   • Finding the speed of sound in a resonance tube: Place a hollow plastic tube into a measuring cylinder of water, tap a tuning fork of known frequency and hold it above the tube. The sound wave is reflected and forms a node at the water surface. Move the tube up and down until you find the shortest distance that the sound resonates at, which will be a quarter of the wavelength.

5. Two source interference

   • Young's double slit experiment: A single laser is shone through two slits (laser light is coherent and monochromatic) The slits have to be narrower than the wavelength of the laser so that it diffracts. You get a pattern of light and dark fringes depending on whether constructive or destructive interference is taking place
     • To see interference patterns with microwaves, you can replace the laser with two microwave transmitter cones, and replace the screen with a microwave receiver probe. If you move the probe along a straight path you get an alternating pattern of strong and weak signals
     • Fringe spacing = distance from slits to screen x wavelength/ spacing between slits

6. Diffraction Grating

   • Interference patterns get sharper when you diffract through more slits
     • When monochromatic light is passed through a grating with hundreds of slits per mm, the interference pattern is really sharp because there are so many beams reinforcing the pattern for more accurate measurements
   • dsin0 = nλ
     • If λ is bigger, sin0 is bigger, and so 0 is bigger. This means that the larger the wavelength, the more the pattern will spread out
     • If d is bigger, sin0 is smaller. This means that the coarser the grating, the less the pattern will spread out
     • Values of sin0 greater than 1 are impossible