Physics 2111
Unit 24
Today’s Concepts:
A) Sound waves
B) Interference
C) Intensity and Intensity Level
D) Doppler Effect
E) Beats
Sound Waves
Sound is longitudinal wave
- media oscillates back and forth in the
direction of travel of the wave
direction of travel
direction of oscillations
x
So what the heck am I plotting when I show a sound wave like this?
Pressure or maybe longitudinal displacement
Sound Waves – Unit 24 – Slide 2
Interference
Recall that if I have two waves that a half
of wave length out of phase, I get
destructive interference
l/2
No sound - silence
Sound Waves – Unit 24 – Slide 3
How do I get them out of phase like that?
Start in phase and travel different distance to
receiver
L1
L1
L2
L1-L2 = DL
L2
DL = l *1, 2, 3, 4... constructive
DL = l *1/2, 3/2, 5/2... destructive
Sound Waves – Unit 24 – Slide 4
Phase Angle
Shift sometimes written in terms of “phase angle”
y(x,t) = sin(kx - wt + f)
f = 2p*Dx/l
Constructive
Shifted by m*2p
just some integer (0, 1, 2, 3, 4……)
(In terms radians. In terms of distance is m*l or in terms of degrees is m*360o)
Destructive
Difference in phase (m+1/2)*2p
(In terms radians. In terms of distance is (m+1/2)*l)
Sound Waves – Unit 24 – Slide 5
Example 24.1 (Two Speakers)
3.2m
2.4m
A 214 Hz tone is emitted from
two stereo speakers, 3.2
meters apart. Alex stands 2.4
meters in front the right
speaker. The speed of sound
in the sounding air is
343m/sec. Does he hear a
loud or a soft tone?
Sound Waves – Unit 24 – Slide 6
Example 24.2 (Two Different Speakers)
2m
3.45m
A varying tone is emitted from two
stereo speakers, 2m meters
apart. Augie stands 3.45 meters
in front the right speaker. The
speed of sound in the sounding
air is 343m/sec. What are the first
three frequencies above 300Hz
for which he hears completely
constructive interference?
Completely destructive
interference?
Sound Waves – Unit 24 – Slide 7
Question: Interference
A tone of varying frequency is emitted
from two stereo speakers, 2.4 meters
apart. Our hero stands 15 meters in
front the right speaker.
2.4m
15m
If the tone starts at 2000Hz and
increases what is the first frequency for
which he will hear the loudest sound?
Sound Waves – Unit 24 – Slide 8
Intensity
Recall
Power = Energy/Time
Intensity = Power/Area
= Energy/Time*Area
α Amplitude2*w2
Related to how loud it sounds
Sound Waves – Unit 24 – Slide 9
Example 24.3 (Intensity)
A ringing bells put out 20 Joules of
sound energy every second. The
sound goes uniformly in all
directions.
What is the intensity of this sound
2m away from the bell?
What is the intensity 4m away?
Sound Waves – Unit 24 – Slide 10
Intensity Level
Doubling intensity does not double the “loudness”
of the sound to you.
Human “loudness scale” approximated by
Intensity Level, b
b = 10db log (I/Io)
Io = 10-12 Watt/m2
Recall:
•
10n
= y  n = log(y)
• log(1) = 0
• log(10) = 1
lowest threshold of hearing
Small changes in value of Intensity Level
 BIG changes in power output
• log(100) = 2
Sound Waves – Unit 24 – Slide 11
Mechanics Lecture
Intensity Level
Sound Waves – Unit 24 – Slide 12
Resonance Patterns/Harmonics
Recall resonance for string instrument
Note the
frequency
pattern:
1,2,3,4,5…
where
and
f = m*2L/2
These happen
because the
wave reflects from
a node. (We can’t
change the
position.)
Sound Waves – Unit 24 – Slide 13
Sound Waves
Sound is longitudinal wave
- media oscillates back and forth in the
direction of travel of the wave
direction of travel
direction of oscillations
x
So what the heck am I plotting when I show a sound wave like this?
Pressure or maybe longitudinal displacement
Sound Waves – Unit 24 – Slide 14
Open Ended Wind Instruments
Sound wave will reflect off either
end of a enclosed pipe…
where
and
even if
it’s open.
l/4
Air is completely free to move at
open end.  motion anti-node
Sound Waves – Unit 24 – Slide 15
Open Ended Wind Instruments
DEMO
where
l/4
and
These happen because
the wave reflects from a
anti-node. (We can’t
change the pressure.)
Sound Waves – Unit 24 – Slide 16
where
Recall
diagram
from lab.
Sound Waves – Unit 24 – Slide 17
where
and
Note the
frequency
pattern:
1,3,5,7,9…
Even
harmonics
are missing
Sound Waves – Unit 24 – Slide 18
Mechanics Lecture
Example 24.4 Resonance in Tube
You have a tube that is 15cm long
with one end up and one end closed
(like in lab). What tuning fork you
could hold over the open end so that
it would resonant at it fundamental
frequency?
Sound Waves – Unit 24 – Slide 19
Doppler Effect
Image a speaker put out a uniform tone in all
directions.
Distance between waves
peaks is v*T = l
Now image
the speaker
moves
forward as it
puts out
sound
Distance between
waves peaks is
v*T – vs*T = l’
Sound Waves – Unit 24 – Slide 20
Doppler Effect (moving observer)
What if the observer moves?
Observer now “runs into” more
waves per second than before.
Hear higher frequency.
fo = fs +vo/l
= fs (1+vo/fsl)
= fs (1+vo/v)
Combine the two
equations
(1 +/- vo/vsound)
s (1 -/+ vs/vsound)
fo = f
Sound Waves – Unit 24 – Slide 21
Example 24.3 (police car)
A police car is moving to the left at 34m/sec while its
siren is emitting a 600Hz tone.
What tone would you hear if you were parked along
side the road?
What tone would you hear if the police car were parked
and you were moving towards the police car at
34m/sec?
What if you are both moving at 34m/sec?
Sound Waves – Unit 24 – Slide 22
Beats
What would happen if we added two sound waves with
slightly different frequencies….
A*cos(k1x-w1t) and A*cos(k2x-w2t)
where
Recall:
cos(a) + cos(b) = 2cos((a+b)/2)*cos((a-b)/2)
Sound Waves – Unit 24 – Slide 23
Beats
So we’d wind up with something that looked
like…….
A cos(w1t ) + A cos(w2t )  2 A cos(wLt )cos(wH t )
where wL 
1
(w1 - w2 )
2
cos(wLt)
and wH 
1
(w1 + w2 )
2
cos(wHt)
Sound Waves – Unit 24 – Slide 24