Chapter 12 Flashcards
Principle of superposition of waves
When two waves meet the total displacement of thr new wave at any time is the VECTOR ADDTIOM OF THE displacements of the two original waves that made it
Superposition vs interference?
When two waves meet each other in space and superpose they produce INTERFERENCE
If they meet in phase they produce constructive interference and if anti phase destructive interference
As COMPLETLEY anti phase means new amplitude 0, and amplitude prop to intensity, new intensity 0, no sound no light
The resultant wave is the interference pattern due to the superposition of the first two waves
What does it mean if two waves are coherent ?
How to achieve constsnt phase difference?
It mean they have CONSTANT PHASE DIFFERENCE
This means they will produce a constant interference pattern
In order to be coherent it means that the waves must have the SAME FREQUENCY , otherwise the phase will keep changing
How ti think of superposition and deduce where waves are in phase/ not based on path travelled
If same frequency, then path lenght difference / wavelength = phase
Based on the wavelengths = phase or not
Okay so if it’s not coherent? Now how will superposition look like
It won’t be possible to determine where they meet in ohsde / anti so they just become (visible light) that just consntslth emitted
How do the orders go on a superposition scale
0th order when PLD the same
Then 1st order minima and 1st order maxima , 2nd order minima maxima on both oppsite sides
So you’ll hear quiet loud quiet loud etc
Now how ti described supermodel interference and minima maxima
Supeorsotion lesds to interference, when in phase, constructive and anti destructive. When COMPLETLEY in ohsde they superpose to produce a maxima and COMPLETLEY out of ohsde superpose to produce a minima
What was young double slit edleiemnt used ti prove?
Was used to disprove newton idea that light behaved like a stream of tint larticle
Explain the double slit experiment
1) the light source used was MONOCHRAMTIC (so one wavelength only)
2) then it was ran through a single slit . The reason for this is such that the light arriving at the double slit is properly ILLUMINATED (think about it, not true that it would spread out to find the slitd , so single slit is used first
Light then arrived at double slit and diffracted agsin . Coming from one source, this was coherent light, and being diffracted again meant that was two sources of coherent light
3) they were then allowed to interfere. Where they met in phase they supepreosed to form constructive interference and vice Verca. This produced a pattern of white and dark fringed
4) based on trig calculations, and the assumption that D is»_space;»>a , formula made as ax/d = lambda
EQUATUIN
Ax / d
Where a is slit separation, d is distance between slitd and screen, and x is the distance from successive fringes
Laser
SO WHY DO WE NORMALLY NEED A SINGLE SLIT BUT FOR LASER we don’t
Is already monochramtic snd in phase
Single slit is needed to GUARANTEE light arriving at double slitd are coherent ( as not guaranteed light coming from orignal source arrived in phase ), and therefore light coming OUT of the double slit is in phase top
Also to ILLUMINATE THE TWO SLITD
TWO RESSOSNS
However a laser doesn’t need because already monochromatic snd I’m phase! (So no single slit there)
What conditions are needed for a stationary wave to form?
Two progressive waves with the SAME FREQUENCY but travelling in OPPSITE DIRECTIONS ARE SUPPERPOSED
Where they meet in phase they superpose to for, an ANTINODE, where they meet in antiphase they superpose to form destructive interference in the form of a NODE
There is 0 intensity and amplitude at nodes and max at ANTINODE
How is a stationary wave often made
Progressive wave travels along a string or something snd hits the bindsur, and is reflected in other way but liras out of ohsde.
As a result now have two coherent sources of progressive waves that travel OPPSITE each other, and so after supoerpose ti on they will produce a STATIONARY WAVE
Energy transfer stationary wave vs progressive?
As the two waves are travelling OPPSITE each other there is NO NET TRANSFER
But in progressive wave there is
Wvalenetht stationary wave
Wavelength in general is the HORIZONTAL DISTAMCE between two points COMPLELTELY IN OHASE WITH EACH OTHER in a progressive wave
But in stationary wave the distance between two nodes (draw out) is equal to HALF THE WAVELENGNT OF THE ORIGNAL WAGEEEE
Phase difference?
Okay so as whole wave moved up and down, ANY POINT BETWEEN A NODE IS PHASE, ON OTHER SIDE OF NODES ANTIPHASE
Progressive wave phase changes across one cycle
Amplitude
All parts of a progressive wave have the same amplitude ( at aLl times each part maintains the SAME AMP,ITUDE)
BUT STAGIKNARY max is achieved at ANTINODE and min at node
Summary 9
1) no energy transfer vs energy transfer
2) wavelength = distance between two parts in complete phase vs distance between 2 nodes is 1/2 wavelength
3) phase difference between node same other side is not, phase difference changed for progressive
4) amp,Ithaca same for all parts of the wave (they all stay the same), max at ANTINODE for stationary
What are harmonics?
These are stationary waves produced on strings or air etc of SPECIFIC FREWUENCIES
Can any harmonic be produced Ona given string?
NO, based on the mass tension and lenght of the strings, only some frequencies csn produce harmonics
What’s the LOWEST frewuency harmonic called
It’s called the fundamental node of vibration
For a strewing what are the possible frewuencies a multiple of the fundamental?
Yeah 2nd 3rd 4th all multiples of the fundamental
(Obviously when the frequency increases as speed constsnt the wavelength decreases in proration)
What about one closed one open
VERY IMPORTSNT
The 2nd fundamental frequency is 3 multiple of the 1st, and the 3rd is 5
It follows a 2n+1 pattern, so the 8th frequency is 17th multiple of the fundamental
The reasons for this is as it’d open there will always be a 1/4 walvelenght extra to account for
As a result the frequencies are all odd multiples of 1/4
How to find the fundamental frewuency at any time based on graph
Look and identity what it is
So like if the f ends up being 11/4 , then we know that is 1a times the f0, so divide the current f y 11! DONT LACK
If they say why is the sand collected
Just have to imagine if it’s a node the reason is probably because of 0 amplitude at nodes, one mark DONT STRESS
HOW TO TRACE WAVES IN TIME AGAIN?
You must go BACK the wave to find where it all end up FORWARD IN TIME!!,!,
For open on both side?
We know that it will be the same as the first dw , theformat I’d the same , 3rd fundamental I’d 3 times the fundamental !
Where will a close end be?
Whoever the STAIONARY wave STARTS FROM
So if if pluck, node there, if speaker plays, node there etc
How to find speed or sound in clsss
Use an OPEN ENDED tube but put it in water, this way you can control the length of the tube
Pitching fork rings it CAUSED THE AIR TO VIBRSGE INSIDE, which can create a stationary wave . When the STAIONARY wave is of same frewuency as the pitivhing fork it will resonance and you will hear it louder
Anyways start with it underwater first and bring it up, pitching as yiu go. . Stop once the FIRST HARMONIC IS FOUND, and measure the distance of the tube
From these calls alone you can find the speed of sound, however better to do this for different pitching forks and work out different distances if tube and plot a groan and find the gradient
Gradient = speed of sound /4!
What’s add happenign
Energy not transfered just resonance happens with pitching fork, and with playing singd it’d the intial strign that makes the note and after it’s just stationary waves
How to make stationary waves with sound
Use pitching fork to make air vibrate at frewuencies and then this can create stationary waves
As the sound wave is being reflected snd so two waves same frequency positbe direction = stationary
Why is a node formed at close end?
And at open?
Air at that end CANT MOVE !!!
Open too because maximum amplitude of the tube can be reached there, and this is ANTINODE
What happens in general with sound used to create waves
So two speakers
They will superpose and form a stable interference elatterm due to both speakers having the same frequency and thus coherent sources
Where they meet in phase superpose and form constructive interference . This will happen when the pLD between speakers is an even integer mueltilke of lambda , and where they meet in antiphase they will supoerpose to form destructive interference, at odd multiples of half lambda
Thud from the centre every ( half lambda?) it will go quite load quite load from both sides
HOWEBER
As this effect continued , it’s less noticeable as the sound waves lose their amplitude due to losing in energy as they spread out. So different a,oltidue waves now superpose and the effect is not as prominent
