3.3.1 progressive + stationary waves

define amplitude

a wave’s maximum displacement from its equilibrium position

define frequency

number of cycles of vibration of a particle/waves passing a point per second

define wavelength

the distance between successive peaks/troughs

or distance from a point on a wave to the same point on the next wave

what is a period

time taken for one full oscillation

or time for one complete wave to pass a fixed point

what is phase

the position of a certain point on a wave cycle.

it can be measured in radians, degrees or fractions of a cycle

what is a cycle

one complete cycle is from maximum displacement to the next maximum displacement

what is a progressive wave

a progressive wave transfers energy from one point to another without transferring matter. It is made up of particles of a medium oscillating

equation for speed

c = fλ

speed (m/s) = frequency (Hz) x wavelength (m)

equation for frequency

f = 1/T

frequency (Hz) = 1/time period (s)

converting degrees into radians and vice versa

transverse waves: define and give examples

• oscillations are perpendicular to the direction of energy transfer

• all EM waves are transverse and travel at 3 × 10^8 m/s in a vacuum

• e.g. EM, seismic (S) waves, guitar string

longitudinal waves: define and give example

• oscillations are parallel to the direction of energy transfer

• made up of compressions and rarefactions + can’t travel in a vacuum

• can be shown on a slinky spring

• e.g. sound + ultrasound, seismic (P) waves

define polarisation

polarisation is the filtering of waves to only oscillations in one plane by putting a filter on it

explain polarisation as evidence for the nature of transverse waves

• a polarised wave oscillates in only one plane

• polarisation can only occur if a waves’ oscillations are perpendicular to its direction of travel

• longitudinal waves cannot be polarised because they oscillate parallel to the direction of travel

investigating light intensity with two polarisers

If an unpolarised light source is placed in front of two identical polarising filters, A and B:

if they have the same transmission axis (filters are parallel) the maximum intensity of light is transmitted → filter A will polarise light in a certain axis → all polarised light from Filter A will pass through Filter B unaffected

as one of the filters is rotated, the light intensity observed reduces periodically

when they are perpendicular, the minimum intensity of light is transmitted → filter A will polarise the light in a certain axis and none of the polarised light will pass through filter B

applications of polarisers

polaroid glasses/sunglasses/windscreens - reduces glare by polarising the light

camera - to reduce glare, enables photographers to take photos of objects underwater

radio + microwave signals - receiving signals at full strength

how polaroid lenses work

• contain polarising filter with transmission axes that are vertically oriented

• do not allow horizontally polarised light to pass through

• when light is reflected from a reflective surface, it undergoes partial plane polarisation

• therefore polaroid lenses (in sunglasses etc) reduce the glare of any reflective surface as the partially polarised light will be eliminated by the polarising filter

how polarisation for signal transmission work

broadcasting towers always send either vertically or horizontally polarised signals.

receiving aerials must be positioned accordingly, in the same plane, in order to receive the signal at full strength

define stationary waves

stationary waves are formed from the superposition of two identical (coherent) progressive waves travelling in opposite directions.

• energy is stored (not transferred)

• have variable amplitude

4 conditions for a stationary wave to form

1. same frequency

2. similar amplitude

3. constant phase relationship

4. travelling in opposite directions

types of interference

constructive interference → occurs when two waves have displacement in the same direction

destructive interference → occurs when one wave has positive displacement and the other has negative. total destructive interference occurs if the two waves have equal but opposite displacements.

what are nodes and antinodes

a node is formed when the wave superposes to create a point of minimum displacement.

an antinode is formed when the wave superposes to create a point of maximum displacement.

the distance between adjacent nodes (or antinodes) is half a wavelength

formula for first harmonic

L = length of string

T = tension

μ = mass per unit length

what is the first harmonic

the lowest frequency at which a stationary wave forms is the first harmonic. this forms a stationary wave with two nodes and one antinode.

how is a stationary wave formed in a pipe?

1. waves travel to the boundaries and are reflected off

2. the two waves travelling in opposite directions superpose to create a stationary wave

3. closed end is a node and open end is an antinode

4. node = no displacement/amplitude and waves destructively interfere, antinode = maximum displacement and constructive interference

difference between stationary and progressive waves