Waves - Interference of Waves

diffraction

the bending and spreading of a wave when it passes through an opening or around an obstacle

ex. water waves bending around a breakwall

What affects the amount of diffraction?

• wl

• freq

• opening size (w)

wl must be >= to the

slit width FOR THE DIFFRAC TO BE NOTICEABLE and to be MAXIMIZED

as wl increases, diffrFOR

increases

as w increases, diffr

decreases

longer wl must

bend around more

FM radio

short wavelength, higher frequency

AM radio

long wavelength, low frequency → bends around hills better than FM waves

as freq increases, diffr

decreases

Why can you hear a person standing behind a tree but you cannot see him/her?

Sound waves are able to diffract around the tree due to their long wavelength but light has a very short wavelength due to high frequency and cannot diffract to make a person visible.

Constructive Interference (CI)

larger amplitude (antinode)

• waves are in phase (same λ), Ex: crest + crest

Destructive Interference (DI)

smaller amplitude (node)

• waves are out of phase (λ differs) , Ex: crest + trough

interference of waves → tapping two spots in a dish of water

see notes

Two Point Source Pattern

• A pair of identical point sources that are in phase produce a symmetrical pattern of constructive interference areas and nodal lines. → see diagram in notes

To perform suitable calculations for two pt source patterns, the sources must

have the same f and v, thus same λ

two pt source interference pattern math

see notes

the eqn with PnS1 and PnS2 is only for

large wls and close dists

the eqn with sintheta is for

when you are asked to calc the angle between the nth nodal line and the bisector OR the angle b/w A and S2

• for when the PATH lines are basically || due to the large dist b/w the pt and the sources

the formula without the ang is for

small wavelengths and small dists between sources (see notes)

Xn =

dist from bisec to nodal pt (the bisec stretches far in front)

L =

distance from centre of sources to nodal point

Pn

point on nth nodal line

d =

distance between 2 sources

θn

angle between d and AS2 NOTE: θn is the angle to the nth nodal line AND the angle between the bisector and the path from the center to the pt

the formula w sintheta is also good for

1. calcing the max # of nodal lines (set the angle to 90)

2. location of antinodes

“180 deg” means

out of phase (one wave is flipped by 180 deg) so instead of being crest to crest they are crest to trough

path len diffs are always

• at least half a wl

• never a whole number

• mults of half a wl

for these calcs, source 1 and 2 must be

in phase

• if one dispels a crest, the other must dispel a crest at the same time

nodal lines are counted from

in to out

(see notes)

Xn =

dist from the nth nodal line pt to the bisector (shortest dist to connect to the bisector)

ex. X3 woul dbe from the 3rd nodal line

as the freq of vibration of sources increases,

wl decreases and the nodal lines come closer together and the # of nodal lines increase