chapter 12 Flashcards
what is the principle of superposition
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
what happens when two waves superpose
what called
what constructive and deconstructive
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
how does interference lead to different intensities (like brighter light, stronger sound)
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
how to produce a CONSTANT interference pattern
interference produces patterns, however these may be changing
for an interference pattern to remain constant the waves in question being superposed must be COHERENT
what does being coherent mean(2)
- having constant phase difference
- having the same frequency
what happens if waves like light superpose not coherent
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”
what is PLD and how relates to phase
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
when is PLD gives constructive and when deconstructive
integers of WL will always be in phase
0.5n of WL will always be anti phase= deconstructive and antiphrases and minimum
how are the orders go
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
what was the young double slit experiment used to show
to show light has properties as a wave
how was double slit experiment done
what doe monochromatic mean
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
what equation links wavelength to different features of experiment
WHEN DOES THIS EQUATION HOLD ONLY
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
again when does this equation only hold (2)
- coherent waves
- D is»_space;»»>a
What conditions needed for stationary wave ti form
Two progressive waves of SAMW FREQUENCY
- and OPPOSITE DIRECTION meet snd superpose
How is a stationary wave produced snd looked like (antonode) and node
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 )
What about wavelentgh between two antinodes or nodes
What about frequency!
Phase difference between nodes / sntinodes?
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
Energy trnadfer?
As bith waved fome frok opposite directions there is NO NET ENERGY TRANSFER, UNLIKE PROGRESSIVE WAVES which transfer energy
How the progresisve vs stationsry wave main differenced (4)
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 “
Intro to harmonics, can all frequnceis cause stationary waves?
No in agiven shstem like string with ine end free, only certain frequenceis wikk produce superposition and stationary waves, these are haemonicd
What is the first and fundamental frequency of a harmonic , f 0? Of a system?
This id the lowest frequency sound that can be produced, f0
How are harmonics made in strings (theory behind it)
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
How can you calukate wavlength of harmonic made in terms of Length of syring for TWO FIXED ENDS
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
What are fundamental frequencies of each other , like 2f0 of f0
What about wavelnegth
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
How to see different hwrmonics in a classroom
- 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!
What determines a harmonic and so what do you see change in practicals
- 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
For string tied in both ends how do you oniw how many times the fundamental feequency is?
In terms of loops or antinodes
How do harmonics contribute to wave energies and thus internsoty
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
What is a sationary wave
A wave that has still motion
- and transfers no energy
How can stationary waves be produced with sound?
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
What will thus determine the feequency of standing waves in coloumns?
- open or close
- density if air and temperature too
Where is a node and where is an antinode
If open end = antinode
If closed = node like before
What is different about multiples of harmonics now at one end and one closed
Why is it like this
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
How to work out the harmonics for one closed one open
Fundamental
After thwt
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
What about bith ends open?
How to draw them?
Dundamental and after
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
How to do experiment for one open one closed?
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
How to find stationary waves in class for sound
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
WHY SHOULD FIRST SLIT BE NARROW
= - wider diffraction
- ensures s1 and s2 are iluminated
What happens when two loudspeakers connected from same source ?
But key point, why is this effect less noticeable the further we go?
- 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 )
