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PHYSICS 231
Lecture 35: interference & sound
Remco Zegers
Question hours:Monday 9:15-10:15
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?
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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 interference5
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demo: interference
Interference III



+
+
=
=

constructive interference
waves in phase
destructive interference
waves ½ out of phase 6
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Interference IV
Two interfering waves can
at times constructively
interfere and at times
destructively interfere
If the two interfering
waves always have the
same vertical displacement
at any point along the
waves, but are of opposite
sign: standing waves
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 r =r
1
2
minimum of wave
r1
r2
positive constructive interference
negative constructive interference
destructive interference
if r2-r1=n then constructive interference occurs
if r2-r1=(n+½) the destructive interference occurs 9
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Interference of water waves
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Example
0.7m
direction of
walking person
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?
vsound=343 m/s
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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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FREE END:
no inversion
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Connecting ropes
If a pulse travels from
a light rope to a heavy rope
(light< heavy) the boundary is
nearly fixed. The pulse is
partially reflected (inverted)
and partially transmitted.
Ain
before
AR
|AR|<|Ain|
|AT|<|Ain|
If a pulse travels from
a heavy rope to a light rope
(light< heavy) the boundary is
nearly free. The pulse is
partially reflected (not
inverted) and partially
transmitted.
before
Ain
AR
AT
AT
after
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|AR|<|Ain|
|AT|>|Ain|
after
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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:
v=331(T/273 K)
so v=343 m/s at room temperature
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Quick question
The speed of sound in air is affected in changes in:
(more than one possible)
a) wavelength
b) frequency
c) temperature
d) amplitude
e) none of the above
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Intensity
Intensity: rate of energy flow through an area
Power (P) J/s
A (m2)
I=P/A (J/m2s=W/m2)
example: If you buy a speaker, it gives power output
in Watts. However, even if you put a powerful
speaker in a large room, the intensity of the
sound can be small.
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Intensity
Faintest sound we
can hear: I~1x10-12 W/m2
(1000 Hz)
Loudest sound we can
stand: I~1 W/m2
(1000 Hz)
Factor of 1012? Loudness works logarithmic…
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decibel level 
=10log(I/I0)
y=log10x
log(ab)
log(a/b)
log(an)
I0=10-12 W/m2
inverse of x=10y
=log(a)+log(b)
=log(a)-log(b)
=nlog(a)
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(y=ln(x) x=ey)
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decibels
=10log(I/I0)
I0=10-12 W/m2
An increase of 10 dB:
intensity of the sound is
multiplied by a factor of 10.
2-1=10
10=10log(I2/I0)-10log(I1/I0)
10=10log(I2/I1)
1=log(I2/I1)
10=I2/I1
I2=10I1
Next quiz!
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Frequency vs intensity
1000 Hz
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example
A machine produces sound with a level of 80dB. How
many machines can you add before exceeding 100dB?
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