Wave and Wave Phenomena

8/13/2019 Wave and Wave Phenomena

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Wave and wave phenomena


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Learning outcome

Determine frequency of sound from CRO


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Determining frequency of sound

A microphone converts _____ into electrical_________.

This voltage when fed into a Cathode Ray

Oscilloscope (C.R.O) will produce a waveformon the CRO monitor display

The amplitude can be found from the vertical

grids (Y-sensitivity) while the ______ can bedetermined from the horizontal grids (timebase)


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Determining frequency of sound


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Wave phenomena

Interference

- 2 light waves

- 2 sound waves

Diffraction

- single slit (qualitative)

- multiple slits (calculation)

Formation of standing or stationary waves


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Learning outcome

Use principle of superposition to determine

displacement of resultant wave at a point of

interference

State conditions for interference

Describe how interference pattern looks like

State conditions for clear interference pattern

Calculate fringe spacing


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interference

Waves interfere with each other when

their amplitude or energy is changed

To determine the amplitude of the resultant,

we need to use the principle of superposition


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P.O.S

Principle of superposition

States that when 2 or more waves overlap, theresultant displacement is equal to the sum of

the individual displacements at that point.


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Whats the resultant amplitude?


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Constructive interference

When crest of one wave meets crest from

another,

The resultant is a maximum amplitude.

Maximum energy


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Destructive interference

When crest from one wave meets a trough

from another, the resultant amplitude is

minimum or zero. Minimum energy


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3 conditions for interference to happen

This can only happen if

A) the waves meet

B) the waves are the same type C) both waves are polarised in the same plane

or non-polarised


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Interference of two light waves


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A series of bright and dark fringes are seen on

the screen in front of the slits


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Can you explain the formation of

a) bright fringes

b) dark fringes ?

- bright fringes formed due to constructiveinterference of two waves. The two waves are inphase with each other

- dark fringes formed due to destructiveinterference. The two waves are in antiphase(180o)


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Fringe spacing

The distance between the successive bright

fringes can be calculated from the formula

X = D/s where wavelength

Ddistance of screen

sslit separation


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example

The slit separations is 0.5 mm. the wavelength

of red light is 680 nm. The distance of screen

is 1.0 m. calculate the fringe spacing (width)

Ans: 1.4 mm


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example

The distance between 7 bright fringes apart is 12 mm. Calculate thewavelength of the light used.

Ans: 670 nm

12 mm


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Path difference


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Waves from slit 1 and slit 2 travel the same

distance to point O.

The waves are in phase with each other at the

slits 1 and 2. They will still be in phase with

each other at point O. Hence, a ________

interference occurs. ________ amplitude.

Bright fringe formed.


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At point P, the waves from slit 1 will havetraveled further than waves from slit 2.

Suppose the wave from slit 2 traveled one

wavelength more than wave from slit 1, thewaves arriving there will be in phase with eachother.

From the triangles, /s = x / D

Therefore x = D/s


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If the path difference is 2, then there will be

another bright fringe formed further away.

Hence, a series of bright fringes are formed at

equal interval if path difference = , 2, 3.

In between the bright fringes, there are points

where the path difference = , 1

____ fringe will be formed. Why?


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example

c) Mark with an X on the photograph the fringe or fringes

where light from one slit has traveled a distance of twowavelengths further than the light from the other slit.


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Interference pattern

Refers to the series of alternate maxima and

minima.

Conditions for clear pattern to be observed.

The waves from the sources must be

i) coherence

Ii) have comparable amplitude


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Coherence source

- the waves from these sources have

the same frequency and

constant phase difference


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If one wave is 10 Hz and another is 15 Hz, noclear pattern observed when they overlap

If both are 10 Hz and they have a constant

phase difference (example 90 o) throughoutthe experiment, a clear pattern can beobserved.

If the phase difference changed, say to 60 oor20 o as time goes by, then no clear pattern canbe observed.


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The waves need not to be in phase or

antiphase. As long as the phase difference is

constant, then the waves are said to be

coherent.

This ensures that the positions of the bright

fringes (maxima) and dark fringes (minima)

are fixed on the screen.


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Comparable amplitude

If one source is more intense than the other,the amplitudes would not be comparable.Therefore, when destructive interference

occurs, the waves do not cancel each othercompletely.

The contrast between the bright and darkfringes would not be obvious in the eyes ofthe viewer.


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Daily examples of interference:

Rainbow in the sky after rainfall

Rainbow in water spray from garden hose

Rainbow from CD reflection

Alternating loud and soft sound across field

when two loud speakers face the field


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diffraction

Refers to the spreading or bending of waves

when passing through a gap or round an

obstacle.

The smaller the gap, the greater the

diffraction

If the gap is too big, no diffraction will happen


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Daily examples of diffraction of waves

Water surface waves bend around pillars

Sound bends around wall corner into next

corridor

Light bend around the moon during eclipse ofthe sun

i l li diff i d d bl li


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Single slit diffraction and double slit

interference Waves from a single slit

spread out and arrive atdouble slits

Waves from each of thesetwo slits spread out again

and overlap in the regionbeyond.

If separation of the 2 slitsreduces, more area ofoverlapping. Hence more

fringes seen. Each fringe will be dimmer

compared to the previous


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Diffraction grating

Consists of multiple slits formed on surface of

a glass coated with opaque layer.

Each slits diffracts light falling upon it. The

diffracted light waves interfere in the region

beyond and form a pattern.

Pattern observed using a moving telescope


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The pattern consists of very sharp bright lines

separated quite apart from each other.

The bright lines are formed due to

constructive interference

The one at the center is known as zero order

On the right and left are the 1storder and

followed by 2ndand 3rdorder.


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The formula

d sin= m where dslits separation

angle made with

original direction

morder

wavelength


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Stationary waves

Stationary waves can occur for any waves

from light, sound, water surface to string

waves.

Formed when two waves of same speed,

frequency and comparable amplitude travel in

the opposite direction and meet.


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http://www.phys.unsw.edu.au/jw/strings.html

The frequency of the waves and the boundarywhere the waves are confined must be such

that there is a multiple of half wavelengths

formed between them
http://www.phys.unsw.edu.au/jw/strings.htmlhttp://www.phys.unsw.edu.au/jw/strings.htmlhttp://www.phys.unsw.edu.au/jw/strings.html


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Stationary waves are characterised by alternatingnodes and antinodes.

Nodespoints of zero amplitude (d.i.) Antinodespoints of max amplitude (c.i.)

Distance between two successive nodes is


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Stationary waves on string


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Stationary sound wave


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Standing a e in one


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Standing wave in both

open ended pipe

Standing wave in one

close end and one

open ended pipe


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summary

Able to define interference

Use principle of superposition to determine

resultant amplitude

State conditions for interference and for clear

interference pattern

Calculate fringe spacing

Describe change to pattern when , D and s is

changed


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Define diffraction

Draw diffraction of waves when passing gap

Calculate the wavelength from diffraction

pattern of a diffraction grating


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Describe how a stationary wave is formed.

Calculate wavelength from a series of nodes

and antinodes

Calculate fundamental frequency and

harmonics.

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Wave and Wave Phenomena