stationary and progressive waves

Polarisation

• un polarised: oscillations exist in more than a single plane

• plane polarised - oscillations restricted to a single plane only

• plane of polarisation of em wave defined as the plane in which electric field oscillates

• only transverse waves can be polarised - evidence for nature of transverse waves

• plane and direction of propagation coplanar

polarising filters

• only transmits component of light with oscillations parallel to a certain direction, according to alignment of its molecules - rest absorbed - intensity of transmitted light less than intensity of incident light

• if unpolarised light is passed through two polaroid filters, the transmitted intensity gradually changes as one polaroid is rotated relative to another one - as it approaches 90 , the component of the light from first filter that can be transmitted by second filter reduces

• filters crossed when transmitted intensity is at a minimum - polarised light from first filter cannot pass through second filter as the alignment of the molecules is perpendicular to the alignment of the first

applications of polarisation

• polaroid material - absorbs component of incident light that is perp to that which filter transmits

• alignment of aerials must be in same plane as radio wave oscillations for reception and transmission. rotate aerials in vertical plane - if signal on receiver at maximum, transmitter emits vertically plane polarised waves (same with horizontal)

• sunglasses - reduces intensity of reflected light from surface of water or glass which is polarised - reduce glare

progressive wave

• transfers energy from one point to another

• without causing permanent displacement of medium

• all particles vibrate at same frequency

• amplitude is the same for all particles

em waves

• travel at c in a vacuum

transverse and longitudinal

• transverse - oscillations perpendicular to direction of energy propagation

• longitudinal - oscillations parallel to the direction of energy propagation

formation of stationary waves

• disturbance in material

• a progressive wave travels until it reaches a fixed boundary (or 2 boundaries)

• it reflects off the boundary (or boundaries)

• the two progressive waves of same frequency travelling in opposite directions superpose / interfere

• fixed boundaries cannot move so are nodes

• in some positions the waves always interfere destructively to give zero amplitude / zero vibration / nodes

• in some positions the waves always interfere constructively to produce positions of maximum amplitude / vibration / antinodes

features of stationary waves

• all particles except for those at the nodes vibrate at the same frequency / same time period

• the amplitude varies with position from 0 at the nodes to a maximum at the antinodes

• phase difference between two particles $m\pi$ where m is the number of nodes between the two particles - if the particles are look like / are corresponding to each other bt on opposite sides of a node, they will have similar / same amplitudes

• two progressive waves it consists off are polarised in the same plane

• the two progressive waves that form stationary wave have a constant phase difference and same frequency

• the oscillations at two adjacent antinodes are in antiphase

• energy is a maximum at nodes ( increases with amplitude)

stationary wave harmonics

• first harmonic: $\lambda=2L$

• second harmonic $\lambda=L$

• third harmonic $\lambda=\frac23L$

• each harmonic frequency is an integer multiple of the first harmonic frequency

microwave stationary waves

• microwaves from a transmitter are directed normally at a metal plate

• reflected at wall (fixed boundary), and travels back towards transmitter in opposite direction to incident waves

• reflected waves and incident waves from the transmitter superpose and form a stationary wave

• detector is moved along the line between the transmitter and the metal plate

• detector signal found at zero / a minimum at equally spaced positions along the line

• detector signal at maximum at equally spaced positions along the line

• the positions of no signal / 0 amplitude / 0 displacement are nodes, positions of maximum signal / amplitude are antinodes - these are at fixed positions

• turntable to rotate food that positions of antinodes and nodes in food can change continuously

stationary waves sound in pipe

• nodes occur at closed end/ fixed ends

• antinodes occur at open / not fixed ends

• resonant frequencies occur when these conditions are satisfied

wave speed of stationary wave on string

$$v=\sqrt{\frac{T}{\mu}}$$

where T is tension and mu is mass per unit length