Waves class notes

Def: equilibrium position

The undisturbed position

def: longitudinal

Oscillations are parallel to the direction of energy transfer

def: transverse

Oscillations are perpendicular to the direction of energy transfer

def: compression

Region where the particle spacing is small, pressure is high

Def: rarefaction

region where particle spacing is large, pressure is low

Phase difference:

Φ = x/λ x 360

(Φ = phase diff, x= distance)

def: displacement:

distance from the equilibrium position in a given direction

def: amplitude

maximum displacement from equilibrium position

def: wavelength

Distance between adjacent identical points on the wave

def: period

time for one complete oscillation (peak to peak)

def: frequency

Number of oscillations per unit time

Def: phase difference

how out of sync the oscillations are in radian

π means…

anti-phase

Wave equation =

speed= frequency x wavelength

v = fλ

c = fλ

period =

1/ frequency

Reflection:

the angle of incidence is equal to the angle of reflection.

called the law of reflection

reflection hack

FAST

Faster

Away

Slower

Towards

FAST explained

• of the wave speeds up, it moves away fro the normal and vice versa

• electromagnetic waves speed up in ‘lighter, thinner’ material, whereas sound waves slow down in ‘lighter, thinner’ media

Determine how refraction changes speed and wavelength

• if speed increases, wavelength increases

• if speed decreases, wavelength decreases

• v = fλ becomes v ∝ λ (frequency is fixed)

Water: refraction

• deeper the water, the faster the ripples

• deeper the water the longer the wavelength

plane waves can be made by..

bobbing a ruler up and down a ripple tank

when they reflect off a surface their frequency and wavelength remain unchanged

when circular waves reflect off surfaces..

their wavelength and frequency remain the same

diffraction:

spreading out of waves as they pass through a gap

polarised waves

waves that oscillate in a single direction perpendicular to a gap

Diffraction effect:

• effect is very pronounced when the size of the gap roughly matches the wavelength of the waves

• (narrow gap= large diffraction effect)

polarization effect:

• when waves oscillate in the same direction perpendicular to the direction of energy transfer

• only transverse waves can be produced

example: light is partially polarized hen it reflects off a surface, light can be partially polarized b the same chemicals

intensity:

the power passing through a surface per unit area

intensity equation

Intensity = power/ area

I= P/A OR I= P/π r² (for a point source emitting uniformly in all directions)

Relationship between intensity and amplitude

• as intensity decreases, so does the amplitude according to:

• Intensity ∝ (Amplitude)²

• less energy a wave carries, the less amplitude it has

Refractive Index

The ratio of the speed of light in a vacuum to the speed of light in that material

Material and refractive index (n)

• vacuum - 1.0

• air- 1.0 (over 1)

• water - 1.33

• Crown glass - 1.52

• Diamond - 2.42

refractive index equation

n = c/v

(if n = 2 then speed is the same as the speed of light#0

the greater the refractive index…

the more light entering the material is refracted to the normal

refraction law / snell’s law

n1Sinθ2 = n2Sinθ2

critical angle equation

n = 1/SinC or C = 1/n

Young’s double slit: Source

• Source must be coherent (waves in a fixed phase difference)

• In reality, the waves are often in phase and have equal wavelength (monochromatic)

• Source is a laser

• Distance from the slits to the source to the screen is ‘large’ compared to the separation of the slits

Young’s double slits: measurements

• slit separation: vernier caliper

• Slit to screen distance- ruler

• fringe spacing - graticule

Young’s double slit: pattern

• the pattern is an interference pattern

• the pattern is made of interference fringes

• the fringes are a pattern of light and dark alternating lines

  • the light lines are called maxima

  • the dark lines are called minima

• The pattern in symmetrical fringes have equal spacing, maxima have equal intensity/ brightness

Young’s double slit: explanation

Bright spots/ maxima

• constructive interference

• path difference is an integer number of wavelengths - nλ

• phase difference = 0, perfectly in phase

Young’s double slit: explanation

Dark spots/ minima

• destructive interference

• path difference is an odd number of half wavelengths - (n + 1/2) λ

• phase difference is π radian or 180 degrees

Young’s double slit

Equation

• λ = ax / D

• wavelength =slit separation x fringe spacing / distance from slits to screen

Young’s double slit

Typical questions: if we cover the slit

if we cover the slit, there is no interference pattern.

Young’s double slit

Typical questions: If the slits move closer

If the slits move closer, x (fringe spacing) increases as a (slit separation) is inversely proportional to x.

(a ∝ 1/x for fixed λ, D)

Young’s double slit

Typical questions: red vs. blue laser

Red vs blue laser: λ ∝ x for fixed a, D

Red has a greater fringe spacing (x) and a greater wavelength

Young’s double slit

Typical questions: white light used

white light used- rainbow appears in maxima

central maximum = white, left: ROYGBIV, right: VIBGYOR

Stationary waves: definition

• stationary waves store energy whereas a progressive wave transfers energy

• A progressive wave has fixed amplitude at all points, whereas a stationary wave has a pattern of nodes and anti nodes

Making stationary waves

• when 2 progressive waves travelling in opposite directions interfere (superpose), a standing wave is formed

  (if the waves have equal frequency and near equal amplitude)

• String - original wave + reflection from a fixed point

What a stationary wave looks like

Node - no displacement, at 0 energy

(Node - Anti node- Node) repeated

Node= point of 0/ minimum displacement

Anti-node= point of maximum displacement

Stationary waves: quantities

• wavelength: one wavelength is two loops (1 = 2 loops)

• Frequency: same frequency for all points except nodes

• Amplitude: varies along the wave (opposite to a progressive wave)

• phase:

  • if 2 points are separated by an even number of nodes they are in phase (i.e. phase difference 0 degrees, or 0 radian).

  • If 2 points are separated by an odd number of nodes they are in anti-phase (i.e. phase difference 180 degrees or π radians)

Stationary waves: diagrams

1st harmonic= NAN, f0. 2L (for wavelength)

2nd harmonic= NANAN, 2F0, L (for wavelength)

3rd harmonic= NANANAN, 3F0, 2L/3

4th harmonic = NANANANAN, 4f0, L/2

5th harmonic= NANANANANAN, 5f0, 2L/ 5

Pipes: open at both ends

diagram

1st harmonic= ANA

2nd harmonic= ANANA

3rd harmonic= ANANANA

(node= quiet, anti-node= loud)

Half-open pipes: diagrams

1st harmonic= NA, ¼ λ, f0

3nd harmonic= NANA, 3/4λ, 3F0

5rd harmonic= NANANA, 5/4λ, 5fo

Half open pipes, explanation

• the air at the closed end cannot move, and must form a node

• at the open end, the oscillations of the air are at their greatest amplitude - must be an anti-node