wave and wave phenomena
TRANSCRIPT
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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.