PHYSICS 231 Lecture 35: interference

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PHYSICS 231Lecture 35 interference

• Remco Zegers
• Question hours Thursday 1200-1300
  1715-1815
• Helproom

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example
A pendulum with a length of 4 m and a swinging
mass of 1 kg oscillates with an maximum angle of
10o. What is the gravitational force parallel to
the string, perpendicular to the string, the
total gravitational force and the centripetal
force when the mass passes through
the equilibrium position and when it reaches its
maximum amplitude?
equilibrium maximum ampl.
gravitation // to string 1gcos(00)9.8N 1gcos(100)9.65N
gravitation perpendicular 1gsin(00)0N 1gsin(100)1.7N
total gravitational 9.8N 9.8N (vectors!!)
centripetal 0.3N (mv2/L) 0 N
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describing a traveling wave
? wavelength distance between two maxima.
While the wave has traveled one wavelength,
each point on the rope has made one period of
oscillation.
v?x/?t?/T ?f
On a string v?(F/?)
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Interference
Two traveling waves pass through each other
without affecting each other. The resulting
displacement is the superposition of the two
individual waves.
example two pulses on a string that meet
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Interference II
constructive interference
destructive interference
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Interference III
demo interference


constructive interference waves in phase
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Interference IV
If the two interfering waves always have the same
vertical displacement at any point along
the waves, but are of opposite sign standing
waves
Two interfering waves can at times
constructively interfere and at times
destructively interfere
later more!!!
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Interference holds for any wave type
The pulses can be sine-waves, rectangular
waves or triangular waves
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Interference in spherical waves
maximum of wave
minimum of wave
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Interference of water waves
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Example
two speakers separated by 0.7m produce a sound
with frequency 690 Hz (from the same sound
system). A person starts walking from one of
the speakers perpendicular to the line
connecting the speakers. After what distance
does he reach the first maximum? And the first
minimum? vsound343 m/s
0.7m
direction of walking person
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Reflection of waves.
Frope on wall -Fwall on rope
demo rope on wall
FIXED END pulse inversion
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Connecting ropes
If a pulse travels from a heavy rope to a light
rope (?lightlt ?heavy) the boundary is nearly
free. The pulse is partially reflected (not
inverted) and partially transmitted.
If a pulse travels from a light rope to a heavy
rope (?lightlt ?heavy) the boundary is nearly
fixed. The pulse is partially reflected
(inverted) and partially transmitted.
before
before
Ain
Ain
AR
AR
AT
AT
after
ARltAin ATltAin
after
ARltAin ATgtAin
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Sound longitudinal waves
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The speed of sound
Depends on the how easy the material is
compressed (elastic property) and how much the
material resists acceleration (inertial
property) v?(elastic property/inertial
property) v?(B/?) B bulk modulus ?
density The velocity also depends
on temperature. In air v331?(T/273 K) so
v343 m/s at room temperature
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Quick quiz

• The speed of sound in air is affected in changes
  in
• (more than one possible)
• wavelength
• frequency
• temperature
• amplitude
• none of the above

answer c)