Chapter 12 Flashcards
What is the principle of superposition
When two waves meet at a point snd superpose, the resultant displacement at that point is equal to the vector addition of the displacements of bith wages
As a result this can be bigger , smaller or nothing compsred to what waves where like eitre
What happens when two waves continuously superose, what is this called
They suppose pose and produce a resultant wave with a dispalcemtnequalmtonthe sum of vector displacement, known as an INTERFERENCE PATTERN
Where they meet in phase, then maximum posit be displacements and negatives one meet each other, creating a displacement with maximum amplitude, this is CONSTRUCTIVE INTERFERENCE
Where they meet in ANTIPHASE, the maximum displacement of one peak meets with the minimum displacement of wnother trough, so the vector sum of these leaves zero amplitude (or less) this is destructive interfernece
How do interference and superposition cause waves that have different intensities
As intensity proprtional to amplitude sqaured, if suporospiton causes an increase in amplitude, intensity will increase or decreases too, causing it be brighter, louder stringer sound if constructive and dimmer weaker quieter if desrcifiobe
If a plotufe 0 then quiet too
What does coherence mean
Having CONSTANT PHASE DIFFERENCE , which means must have the SAME FREQUENCY
How to produce a CONSTANT INTERFERENCE PATTERN
A constant interference pattern means the same pattern being seen.
This only happens if incoming waves are COHERENT and have the same phase difference each time, whatever it may be. This way only one pattern is seen
If they keep changing phase difference due to change of frequencies (like raindrops)
There will be an interference pattern but it’d just one that keeps on changing
So needs to be coherent = frequency same = phaendifferncethe same
What happen if wave like light in general superpose (knowing that they aren’t coherent)
Fact that filament lamps emit a range of reauenices meam that they are never cohener, and always produce unstable interference pattern
This cannot be resolved and detected, we just see this as CONSTANT LIGHT
What is miminima and maxima in interference patterns (constant ones)
Minima is ooijte if minimum amplitude, meaning points where the waves meet in antiphase and destcutirive interferenfe
Maxima is points of maximum amplitude, so points where waves meet in phase and so constructive intefrenece
What is PLD
Path length difference for a point where two cohenernt waves (remember this means constant phase difference not they are in phase) is just the difference in distances from the source of the waves to thst point
However if this difference is an INTEGER multiple of the wavelentgh of the waves, then it meets here in PHASE, so it will constructively interfere to produce a MAXIMA
And if it is a half integer multiple wavelentgh of then it meets in NAITPHADE and so will destructively interfere producing a minima amplitudem
Again for pld phsse thing what had to be of the wave
S must be cohenerent to produce stable interferenfe , otherwise no point finthry keep changing phsse
How do the orders of inter fence go
Where they meet equidistant from each other, the path lens difference is 0, so there is 0 phase difference (which is meetining in phase), thus it’d the 0 Oder CENTRAL Maxima
Then going up and own it goes in half wavelentgh PLD meaning minima maxima minima maxima
Goes like
0 1st minima 1sr maxima 2nd minima 2nd maxima
And I’m bith direcutoms
If it’s a 2nd order minima, it means 1.5 wavelentgh difference = PLD
again it meets in phase antiphase phase antiphase etv
How can you use microphone to find out the wavelentgh of a sound wave produced by speakers
What hwppejsnirnthe frequency of thr sound were halved
If the speakers are connected to the same generator then the two waves they produce will be cohenerent, as a result a stable interference pattern will be seen
Thus use microphone to find areas of minima and a,dims, measure the PLD HERE AND YOU CAN THENUSE ORDER FORUMSL TO WORK OUT THE WVAKENTGH! And dna work out frequency if you know speed of sound is 330
If the frequency of sound is halved then wavelentgh is doubled. As a result the waves suporsoption would be more spread out, and to reach the same orders, you need double the PLD now !
How to Hecke if so,etching I’d palne poslrised
Use a filter through a single place where a wave (that has been du proposed) comes out from
Rotate it @80, if it drops in intensity like expected it’d polarided, if intensity kinda constant then not polarised
To find wavelentgh First recognise where 0 order 1st order maxima etc are then measure lengths. Do sporptiste claudskruojs to find wavelentgh and average these out!
What did the young double split experiment move to show?
That light waves have properties as a WAVE rather than a particle which Newton thought it to be
What was the experiment and what did it show
Experiment was
1st to show an interference pattern you need a source of coherent waves . As a result, he used a filter against a random light source ti only give waves of one frequency, thus cohenernt
He then used a single split to diffract it, such that it could ILLUMINATE THE TWO DPLITS AFTER
the two splits after then diffract sperwtely , creating basically two source of waves that as they came from the same point source (which is coherent) are also coherent
These could then superpose and create interference patterns as they are cohener, and if they are waves
The fact that they did produce interference patterns show that light has properties like a wave, as it can create interferenfe patterns of minima and maxima dimilsr to the orders, which depend on PLD etc.
These are called fringes
It was this way using maths he was able to calculate the wavelentgh of many different spectrums of light
What does monochromatic mean
He used a filter on a source of light to produce light of a single wavelentgh (and thus frequenc7j. This was MONOCHOMSTIC LIGJT
so again to do the double split
1) need monochromatic source of light
2) slit need to be small enough tissue diffract and illuminate the other elite
Which also need to be small enough to diffract again
What is the wuation then that he found out and what condition does this only hold for
That wavelentgh =ax /d
Where a is thr slit separation
X is the fringe separation between two ADJACENT MAXIMA OF MINIMA FRINGES
And D is the distance between the slits and the fringes
Only holds true as long as the slit separation is much much bigger than the Distamce D
So that small angle approving,action can be used
And again when does this equation only hold
When D is»_space;»> then a
And that the waves cohrern t(which they are if bith fame form monochromatic cpoitm dource
If you have a laser, why don’t yiu need a filter
Laser is already monochromatic and in phase, so you don’t need filter, and since guaranteed all the light from laser is monochromatic don’t need single slit either
Need singl slit before be a use waves that escape the filter may not be I. Lande and mah reach the double slit. It’s just to make sure
Why when measuring fringe separation should you messire distance between as many as you can
Uncertainty decrease by far over a long distance, the. Just divide by how many you wanted
= much better and remember this could be a way to reduce uncertainty
What is a stwitonawry wabe
This is when two progressive waves that are COHERENT (thus stable interference) SUPERPOSE And trailing in oppsite directions
This means where they meet in phase they will constructively interfere producing maxima displacement of amplitudes and where they meet at antiphase destructively interfere, where amplitudes cancel out and is always 0
Thus you get a standing wave
What are the conditions needed to produce a stationary wave (2) importsnt
Progressives waves which are COHERENT
But travelling in oppsite directions!
So what is it again
Where in phase constructive interfere produce an ANTINODE , where they meet antiplahse destructive interference and so always 0 amplitude = NODE
remember has ti be cohener fand oppsite directions
Nodes vs antibodies
AntiNodes highest smllitude highest intensities but nodes lowest intensity
How are stations ray waves often forked
A wave of constant frequency is emitted and hits a boundary, such that it reflects 180° so thst is has a phase difference of pi radians with the first one. These two waves are both cohenernt tho and so will suporpose and as one travllingother direction, will form a stationary wave
What is the distance between two ADJACENT NODES or ANTINIDES
FREQUENCY?
Equal to HALF THE WAVELENEGTH OF THE ORIGJNAL WAVE
The frequency is the SAME (has to be or reflected wave isn’t cohener)
What about phase difference
BETWEEN POINTS IN BETWEEN ADJACENT NODES (points if 0 displacement) everything is IN PHASE
- all the particles in these reach max displacement at the same time, however the amplitudes aren’t the same, with the maximum amplitude being reached at thr ani node
on points either side if a node, points are ANTIPHASE, one goes up and down
Also what about transfer of energy
THERE IS NO NET ENERGY TRANSFER BY A STATIONARY WAVE unlike a progressive wave
Make sure not to use maxima and minima ideas on stwtiinarynwaves, these are just nodes and antinodes
Okay so what are differences with progressive wave
Wavelentgh =
- progressive wave the wavlentgh is between two pojnts which are in phase with each other on adjacent Waves
- stationary waves the distance between adjacent nodes or antinides are = to half the wvakentgh (makes sense its lit half a wavelentgh )
Phase difference
- in s atauonary wave the Phase changes as cycle progessed
- only point in between stationary waves are in phase, on either side of a node = antiphase
Energy transfer
- progressive waves transfer energy without transferring matter
- stationary waves = no net transfer of energy (oppsite directions )
Frequency
Stationary waves and progressive waves frequency is constant
Amplitude
- all parts of wave in progressive wave has same amplitude , whereas maxim amplitude occurs at antinides and minus at node
4 main difference drains
Energy
Phase
Amplitufel
Wavelentgh
- no net transfer vs transfer
- wavelentgh min distance between two adjacent pointd in phase of two adjacent waves , distance endtween two nodes adjacent = to 1/2 length of originakw avkentgh of wave
- phase difference changes constantly between points on progressive as it vycles, all loitns between two adjacent waves in phase and on either side antiphase
- amplitude. Eysenck all points in progressive same, but ststainary maximum at antinides and min at node!
How to make stationary waves with microwaves and find the Abel eg the if it?
Use a Transmitter that transmits one wave that is cohenernt, snd let this reflec toff a boundary.
It will reflect off at 180° so that it is in oppsite direction now
Now you have two progressive waves of same frequency thst are in oppsite directions, and where they meet in phase and antiphase they will suporoseto create nodes and antinodes
Using a microwave receiver, move it across the path until you find two nodes (area of no intensity)
Thus you can find out the distance. Esten two adjacent nodes and know the abelenthj
IMPORTSNT FEATURE
WHEN THESE WAVES GO FUETHER ALSRT WHAT HALLEND TO THEIR SMLLITUFES
Their amplitudes change, thus the cancellation is non perfect and the effect of superposition is less distinct
Thus on concert furthe you go from speakers that try to superpose, the energy of waves decreases so amplitudes change and SUPERPOSTION STULL HAPPENS BUT INTERFERENCE PATRERN NOT AS CLEAR CUT!
Can all frequencies of waves produce harmonics? What even are harmonics
Harmonics are different garaitonsof stationary waves that are produced on a system like a string with snd opend end, two closed ends etc
But on a given system , with like tension mass length etc, only CERTAIN FREQUECNOES CAN PRODUCE CERTAINS HARMONICS!
What is the funamdetal frewuency f0 for a system
This is the minimum frewuency of a stationary wave that can be produced on a wave , but the. The string can form other harmonics that will be multiples of this frewuency
How are harmonics even made in strings (theory)
Say you have two closed ends, then these will both act as NODES
When a pluck happens in the middle, this created a wave that travles to the ends of the nodes and reflects, creating two waves of same frequency travelling in oppiste directions
As a result these can then superpose and if at the correct frequencies etc can produce stationary waves and harmonics
Met condition of two progressive aves oppsite directions and coherence,t!
How to find wavelentgh and frewuency of a harmonic made in terms of length of thr string for two fixed end
- the minimum is two nodes one antinide, and we know the distance between two nodes is 1/2 the wvakentgh
So the L = 1/2 WL, and WL = 2 L of the string
Now we know that wave speed for waves here is constant , so f = s /2L
And now as you orogress you see that you can get whole integer multiple of the fundamental frewuency !
Add up all the nodes so you know how long the wvakentgh is in terms of the length of the strong
Here the second fundamental frequency ey I’d?
The first by 2, by 3 , by 4, but this only true so far for two closed ends
How to seemdifferent harmonics in a classroom
- attach a signal generator to a vibration generator
- and use the signal generator to generate vibrations of a specific freqeucny
- based on the length mass tension of the string only s specific freqeucny will,produce the first fundamental harmonic, which then integer multiple of this frequency can produce more and more (for this system)
You did this wrong, what do you do
So count do number if 1/2WL
So 6/2WL= L
Then WL = 1/3L
That’s what you need to have done got whole a wing !
How do harmonics change energies of the aeves
Where superpose and a,plotufe increase means increase in intensity and energy
Somlaouder sound and auiter too
What is a stationary wave
A wave that hsd still motion and transfers no net energy!
How can stationary waves be proeiuce using sound aswell
1) either by blowing over the top creates a standing wave inside (ofc right frewuency etc must be used)
2) or by vibrstinf the air inside the tube at frequencies related to the length fi tube, done using a pitch forkm
Tube closed at one end
Means that one end is a node and open is antinode, this is the minimum frewuency so fundamental frewuency
As a result this as a 1/4 wavlength this distance is = to L, so the wavlentgh = 4 times the length
And f= s/ 4L
For second you can put snother one on, mwanignlkentgh= 3;4 wL and Wl = 4/3L
And f= 3S/4L
As you can see the second mode of vibration is 3 times the fundamental frequency
As a result it is not possible to produce 2F0,Mathe second modemis JEVER POSSOBLE because each time you have to add and extra 1/4
As a result the only modes possoble are in odd multiples of 1/4 the fundamental
What else steermines the frewuency of the harmonics in a tube
The length
- density and temperature of air
Open vs closedm
With both ends open?
This means a node in the middle and atleast two antinides at both ends.
This is two aueters so minimum is a 1/2wl = L, so Wl = 2L, f= S/2L
Then second is S/L which is twice
Third is 3/2 Wl = al, Wl = 2/3m 3S/2L = f
Which is three times
And so on
Thus can you have 2F0 3F0 In bith open?
Yes it is possible because you increase by 1/2 a wavlentgh Esch time
How to do experiment for one open one closed
Use bith open ended tube , so that one end can be dipped into water to adjust length if the tubes
Now work out with a frequency fork what length of tube is needed to produce a harmonic
And then measure that length and dip in water
And now vibrate and see if you can hear it
Will only be hard at specific harmonics
And others can be heard too if you use the correct inter multiples (odd integer) for the fundamental frequency you just worked outthisnis because you know thr Spee for sound so can workout exactly how long to keep it et
Wha thappejed when two loudspeakers connected from same source
Bith loud speakers will produce waves that are coherent as they are from the same source
These will meet in space and superpose
Where they meet in phase (when PLD is an inter of WL) they will constructively interfere producing a maxima (in amplitude and thus intrnsity) and where they meet in anitphase (wher ePLD is an integer multiplemfon1/2 WL) theory will desconstrucitheky superpose to provide a minima in amplitude and quietest sound isnheard here
As you move from the distance equidistant from them (0morder) , every half wavelentgh apart you will hesr alternating from quiet to loud quiet to loud in bith djrefitoms
However further away you go the effect would be less distinct because the amplitudes begin to change the more you spread out as energy spreads, so less noticeable and effect of superpostion is not fully cancelling
