chapter 12

Question 1

what is the principle of superposition

Answer 1

when two waves meet the Toal displacement at any given point in time is the VECTOR sum of the two individuals displacements

displacement is a vector, so add them up

Question 2

what happens when two waves superpose
what called

what constructive and deconstructive

Answer 2

they produce a resultant wave that is equal to the sum of the individual displacements of the two waves , called interference

constructive: if two waves are in PHASE, then this is the maximum positive displacement and waves reinforce = constructive

destructive : if waves meet in anti phase then will add to form the minimum displacement as max and min cancel out

Question 3

how does interference lead to different intensities (like brighter light, stronger sound)

Answer 3

I is proprotional a ^2

constructive and deconstructive lead to increased amplitudes

intensity proportional to amplitude squared so if you increase amplitude you increase intensity…

• if amplitude deconstructive to 0, intensities 0 too

Question 4

how to produce a CONSTANT interference pattern

Answer 4

interference produces patterns, however these may be changing

for an interference pattern to remain constant the waves in question being superposed must be COHERENT

Question 5

what does being coherent mean(2)

Answer 5

• having constant phase difference

- having the same frequency

Question 6

what happens if waves like light superpose not coherent

Answer 6

it would not be possible to resolve and detected when the phase difference is changing,

as a result the changing intensities produced would be just “CONSTANT LIGHT”

Question 7

what is PLD and how relates to phase

Answer 7

2 waves travelling and say one has traveled more distance than other, PLD is distance of length difference between both paths

• ir wave Is coherent (same WL) fraction of wl = phase difference

Question 8

when is PLD gives constructive and when deconstructive

Answer 8

integers of WL will always be in phase

0.5n of WL will always be anti phase= deconstructive and antiphrases and minimum

Question 9

how are the orders go

Answer 9

at centre no PLD so phase difference 0

• at 1st order maxima OLD = 1 WL so PD is 2 pi
• 1st order minimum is 1/2 WL= pi so antiphase

goes up and down In half

Question 10

what was the young double slit experiment used to show

Answer 10

to show light has properties as a wave

Question 11

how was double slit experiment done

what doe monochromatic mean

Answer 11

1) used a filter from a piece of light to make it MONOCHROMATIC ( of one WAVELENGTH)
2) then passed it through a small slit to make it diffract
3) then passed through a double slit to diffract again- essentially producing two COHERENT WAVES
4) these waves could then superpose with each other and show an interference pattern of constructive and deconstructive as it is coherent

Question 12

what equation links wavelength to different features of experiment

WHEN DOES THIS EQUATION HOLD ONLY

Answer 12

wl +ax/d

where a is slit separation , x is fringe separation BETWEEN TWO MAXIMA and d is distance between source and screen.

ONLY HOLDS WHEN D is»»»»A, as this means distance here of s to p is equal to wavelength

Question 13

again when does this equation only hold (2)

Answer 13

• coherent waves

- D is&raquo_space;»»>a

Question 14

What conditions needed for stationary wave ti form

Answer 14

Two progressive waves of SAMW FREQUENCY

- and OPPOSITE DIRECTION meet snd superpose

Question 15

How is a stationary wave produced snd looked like (antonode) and node

Answer 15

As same feequency when meet in ohase will superpose constuctively and make ANTINODE (high points) , when suPerpose decostructively it will superpose to make nodes (lowest amplitude )

Question 16

What about wavelentgh between two antinodes or nodes
What about frequency!

Phase difference between nodes / sntinodes?

Answer 16

This will be half the wavlengh of the orignal wave

Frequency stays the same

2) begween nodes and between antinodes particles always in phase but from either side if a node / antinidenantiohase (one goes up, other goes down), one reaches max positbe the other reaches max negstive

Question 17

Energy trnadfer?

Answer 17

As bith waved fome frok opposite directions there is NO NET ENERGY TRANSFER, UNLIKE PROGRESSIVE WAVES which transfer energy

Question 18

How the progresisve vs stationsry wave main differenced (4)

Answer 18

1) no net energy transfer vs energy transfer
2) all points in progressive keep changing phase difference , only certain points in stationwry in phase while others in antiphase
3) distance between nodes in stationsry is half orignal wavelentgh compared to points of two peaks
4) amp,itude : all parts of wave in progressive wave has same amolitude, wheras maximum amolitude occurs at antinode and minimum at node, where displadment always “

Question 19

Intro to harmonics, can all frequnceis cause stationary waves?

Answer 19

No in agiven shstem like string with ine end free, only certain frequenceis wikk produce superposition and stationary waves, these are haemonicd

Question 20

What is the first and fundamental frequency of a harmonic , f 0? Of a system?

Answer 20

This id the lowest frequency sound that can be produced, f0

Question 21

How are harmonics made in strings (theory behind it)

Answer 21

A pluck hapoens on a system a progressive wave travles along the end of the strungs then is reflected to FORM TWO PROGRESSIVE WAVES.

As these have same frequency and opposite they make a STATIIONARY WAVE

Depending on type of system will cause different wavlengths and possible frequencies

Question 22

How can you calukate wavlength of harmonic made in terms of Length of syring for TWO FIXED ENDS

Answer 22

These two ends become nodes and also anything plucked in the middle a node

• you know the separtion between two nodes is = 1/2 wl
• add up all between nodes and find out what wl equaks
• plug into wavespeed equation to find out frequency this should be the same as orignal wl calculation

Question 23

What are fundamental frequencies of each other , like 2f0 of f0

What about wavelnegth

Answer 23

Just multiples, if frequency of f0 is 10 then frequency at f20 will be 20

And wavlentgh follows proportion, double frequency rhen half wavelentgh too

Question 24

How to see different hwrmonics in a classroom

Answer 24

• attach signal generator to vibration generator
• use signal generator to create different frequencies in vibrations
• when the right frequency is made of a harmonic based on the length, mass and tensiom then a hameonic will be formed.
• if you go up in integer multiples of that harmonic, more will be formed!

Question 25

What determines a harmonic and so what do you see change in practicals

Answer 25

• lentgh, mass and tension dictate the value of the fundamental frequency of harmonic for those conditions and system!
• then it will be integer multipled after that for frequncies and wavkentgh decrease in proportion

Question 26

For string tied in both ends how do you oniw how many times the fundamental feequency is?

Answer 26

In terms of loops or antinodes

Question 27

How do harmonics contribute to wave energies and thus internsoty

Answer 27

When vibrating at harmonic frequency, i guess they superpose to max so amolitude increase = intensity increasee= ENERGY INCREASE,

So high intnsities dhow that energy increases due to harmonics being made

Question 28

What is a sationary wave

Answer 28

A wave that has still motion

- and transfers no energy

Question 29

How can stationary waves be produced with sound?

Answer 29

Here a feflected wave and orignal wave superpose to make stationary waves

Ifnyiu make air inside a column vibrate at frequencies baded on kength or tuge abd if the tubes are open or clsoe you can here a note of partivulwr frequency

Question 30

What will thus determine the feequency of standing waves in coloumns?

Answer 30

• open or close

- density if air and temperature too

Question 31

Where is a node and where is an antinode

Answer 31

If open end = antinode

If closed = node like before

Question 32

What is different about multiples of harmonics now at one end and one closed
Why is it like this

Answer 32

Only odd numbees of dundamnetwl frequency can form, this is due to the way the patttern is made

• THE AIR IN CLOSED END CANT MOVE = node
• AIR AT AIR ARE AT GREATEST AMPLITUDE , WHICH HAPPENS AT AN ANTINODE

Question 33

How to work out the harmonics for one closed one open

Fundamental
After thwt

Answer 33

1) here there is a node at clsoed ant anti at open = 1/4 the wavelentgh and work out
2) next do in terms if antinodes , the “second “ wilk have two antinodes , this im reality is 3 x the first fundamentak frequency so its the THIRD HARMONIC

Basiclaly if they say whats the 5 haemonic, add 1 and divide by 2 = 3 amd draw thwt many antinodes / nodes in this case

Question 34

What about bith ends open?

How to draw them?
Dundamental and after

Answer 34

Both become antinodes

If they say draw first hameonic , draw one node , so do it in nodes
If they say draw second then draw two nodes in middle etc

Question 35

How to do experiment for one open one closed?

Answer 35

Here use tuning fork which fibrestions will cause the air to match the same frequency as it

• then use water to change the lentghnof the apparatus
• at a fixed lentgh if the air inside is virbating wt fundamental feequency sound will be herd
• then other hwmronics can happen too as long as they are odd integes

Question 36

How to find stationary waves in class for sound

Answer 36

Place a speaker opposite a reflective surface

• play a frequency that will generate a sound given the distance and system (work it out
• use microphone to detect nodes and antinodes
• the distance between two successive nodes will be = to 1/2 wavelength of progressive wave

Question 37

WHY SHOULD FIRST SLIT BE NARROW

Answer 37

= - wider diffraction

- ensures s1 and s2 are iluminated

Question 38

What happens when two loudspeakers connected from same source ?

But key point, why is this effect less noticeable the further we go?

Answer 38

• waves from both source will superpose to give a stable interference pattern due to being coherent
• where they meet in phase , (where PLD is lambda n) they constructively superpose to give rise to a maxima (in intensity) so loudest sound heard here
• where they meet in antiphase ( n+ 1/2 lambda) they superpose deconstructively to give minima and quietest sound heard here,
• from middle it goes quiet to loud every constant distance in both planes

HOWEVER
- EFFECT IS LESS NOTICEBALE Further from the speaker because of DIFFERENT AMPLITUDES RECIEVED BY EACH SPEAKER ( due to them spreading out over large distances )