Chapter 12

Question 1

Principle of superposition of waves

Answer 1

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

Question 2

Superposition vs interference?

Answer 2

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

Question 3

What does it mean if two waves are coherent ?

How to achieve constsnt phase difference?

Answer 3

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

Question 4

How ti think of superposition and deduce where waves are in phase/ not based on path travelled

Answer 4

If same frequency, then path lenght difference / wavelength = phase

Based on the wavelengths = phase or not

Question 5

Okay so if it’s not coherent? Now how will superposition look like

Answer 5

It won’t be possible to determine where they meet in ohsde / anti so they just become (visible light) that just consntslth emitted

Question 6

How do the orders go on a superposition scale

Answer 6

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

Question 7

Now how ti described supermodel interference and minima maxima

Answer 7

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

Question 8

What was young double slit edleiemnt used ti prove?

Answer 8

Was used to disprove newton idea that light behaved like a stream of tint larticle

Question 9

Explain the double slit experiment

Answer 9

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&raquo_space;»>a , formula made as ax/d = lambda

Question 10

EQUATUIN

Answer 10

Ax / d

Where a is slit separation, d is distance between slitd and screen, and x is the distance from successive fringes

Question 11

Laser

SO WHY DO WE NORMALLY NEED A SINGLE SLIT BUT FOR LASER we don’t

Answer 11

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)

Question 12

What conditions are needed for a stationary wave to form?

Answer 12

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

Question 13

How is a stationary wave often made

Answer 13

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

Question 14

Energy transfer stationary wave vs progressive?

Answer 14

As the two waves are travelling OPPSITE each other there is NO NET TRANSFER

But in progressive wave there is

Question 15

Wvalenetht stationary wave

Answer 15

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

Question 16

Phase difference?

Answer 16

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

Question 17

Amplitude

Answer 17

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

Question 18

Summary 9

Answer 18

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

Question 19

What are harmonics?

Answer 19

These are stationary waves produced on strings or air etc of SPECIFIC FREWUENCIES

Question 20

Can any harmonic be produced Ona given string?

Answer 20

NO, based on the mass tension and lenght of the strings, only some frequencies csn produce harmonics

Question 21

What’s the LOWEST frewuency harmonic called

Answer 21

It’s called the fundamental node of vibration

Question 22

For a strewing what are the possible frewuencies a multiple of the fundamental?

Answer 22

Yeah 2nd 3rd 4th all multiples of the fundamental

(Obviously when the frequency increases as speed constsnt the wavelength decreases in proration)

Question 23

What about one closed one open

VERY IMPORTSNT

Answer 23

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

Question 24

How to find the fundamental frewuency at any time based on graph

Answer 24

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

Question 25

If they say why is the sand collected

Answer 25

Just have to imagine if it’s a node the reason is probably because of 0 amplitude at nodes, one mark DONT STRESS

Question 26

HOW TO TRACE WAVES IN TIME AGAIN?

Answer 26

You must go BACK the wave to find where it all end up FORWARD IN TIME!!,!,

Question 27

For open on both side?

Answer 27

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 !

Question 28

Where will a close end be?

Answer 28

Whoever the STAIONARY wave STARTS FROM

So if if pluck, node there, if speaker plays, node there etc

Question 29

How to find speed or sound in clsss

Answer 29

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!

Question 30

What’s add happenign

Answer 30

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

Question 31

How to make stationary waves with sound

Answer 31

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

Question 32

Why is a node formed at close end?

And at open?

Answer 32

Air at that end CANT MOVE !!!
Open too because maximum amplitude of the tube can be reached there, and this is ANTINODE

Question 33

What happens in general with sound used to create waves

So two speakers

Answer 33

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