Chapter 22B: Acoustics
A PowerPoint Presentation by
Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
© 2007
Objectives: After completing this
module, you should be able to:
• Compute intensity and intensity
levels of sounds and correlate
with the distance to a source.
• Apply the Doppler effect to
predict apparent changes in
frequency due to relative
velocities of a source and a
listener.
Acoustics Defined
Acoustics
Acoustics isis the
the branch
branch of
of science
science that
that deals
deals with
with
the
the physiological
physiological aspects
aspects of
of sound.
sound. For For example,
example, in
in
aa theater
theater or
or room,
room, anan engineer
engineer isis concerned
concerned with
with
how
how clearly
clearly sounds
sounds can
can be
be heard
heard oror transmitted.
transmitted.
Audible Sound Waves
Sometimes it is useful to narrow the classification
of sound to those that are audible (those that can
be heard). The following definitions are used:
• Audible sound: Frequencies from 20 to 20,000 Hz.
• Infrasonic: Frequencies below the audible range.
• Ultrasonic: Frequencies above the audible range.
Comparison of Sensory Effects
With Physical Measurements
Sensory effects Physical property
Loudness Intensity
Pitch Frequency
Quality Waveform
Physical properties are measurable and repeatable.
Sound Intensity (Loudness)
Sound
Sound intensity
intensity isis the
the power
power transferred
transferred
by
by aa sound
sound wave
wave perper unit
unit area
area normal
normal to
to
the
the direction
direction of
of wave
wave propagation.
propagation.
P
I
A
Units: W/m2
Isotropic Source of Sound
An isotropic source
propagates sound in
ever-increasing spherical
waves as shown. The
Intensity I is given by:
P P
I
A 4 r 2
Intensity
Intensity II decreases
decreases with
with the
the square
square of
of the
the
distance
distance rr from
from the
the isotropic
isotropic sound
sound source.
source.
Comparison of Sound Intensities
The
The inverse
inverse square
square relationship
relationship means
means aa sound
sound that
that isis
twice
twice as as far
far away
away isis one-fourth
one-fourth as as intense,
intense, and
and one
one
that
that isis three
three times
times as
as far
far away
away isis one-ninth
one-ninth as
as intense.
intense.
I1
P P
I1 I2
r1 4 r12 4 r22
r2 P 4 r12 I1 4 r22 I 2
I2
Ir I r
11
2
2 2
2
Constant Power P
Example 1: A horn blows with constant power. A
child 8 m away hears a sound of intensity 0.600
W/m2. What is the intensity heard by his mother
20 m away? What is the power of the source?
Given: I1 = 0.60 W/m2; r1 = 8 m, r2 = 20 m
2
Ir 2
r1
Ir I r
1 1
2
2 2
2
or I2 I1
1 1
2
r 2 r2
2
8m
I 2 0.60 W/m 2
II22 == 0.096 W/m
0.096 W/m
22
20 m
Example 1: (Cont.) What is the power of the
source? Assume isotropic propagation.
Given: I1 = 0.60 W/m2; r1 = 8 m
I2 = 0.0960 W/m2 ; r2 = 20 m
P
I1 or P 4 r 2
I 4 (8 m) 2
(0.600 W/m 2
)
4 r12 1 1
PP == 7.54
7.54 W
W
The same result is found from: P 4 r I 2
2 2
Range of Intensities
The hearing threshold is the standard minimum of
intensity for audible sound. Its value I0 is:
Hearing threshold: I0 = 1 x 10-12 W/m2
The pain threshold is the maximum intensity Ip that
the average ear can record without feeling or pain.
Pain threshold: Ip = 1 W/m2
Intensity Level (Decibels)
Due to the wide range of sound intensities (from
1 x 10-12 W/m2 to 1 W/m2) a logarithmic scale is
defined as the intensity level in decibels:
I
Intensity level 10 log decibels (dB)
I0
where is the intensity level of a sound
whose intensity is I and I0 = 1 x 10-12 W/m2.
Example 2: Find the intensity level of a
sound whose intensity is 1 x 10-7 W/m2.
I 1 x 10-7 W/m 2
10 log 10 log
I0 1 x 10-12 W/m 2
10 log10 (10)(5)
5
Intensity
Intensity level:
level:
== 50
50 dBdB
Intensity Levels of Common Sounds.
20 dB Leaves or 65 dB
whisper
Normal
conversation
Subway 140-
100 dB 160 dB
Jet engines
Hearing threshold: 0 dB Pain threshold: 120 dB
Comparison of Two Sounds
Often two sounds are compared by intensity
levels. But remember, intensity levels are
logarithmic. A sound that is 100 times as
intense as another is only 20 dB larger!
Source
20 dB, 1 x 10-10 W/m2
A
IB = 100 IA
Source
B 40 dB, 1 x 10-8 W/m2
Difference in Intensity Levels
Consider two sounds of intensity levels 1 and 2
I1 I2
1 10 log ; 2 10 log
I0 I0
I2 I1 I2 I1
2 1 10 log 10 log 10 log log
I0 I0 I0 I0
I2 / I0 I2
2 1 10 log 2 1 10 log
I1 / I 0 I1
Example 3: How much more intense is
a 60 dB sound than a 30 dB sound?
I2
2 1 10 log
I1
I2 I2
60 dB 30 dB 10 log and log 3
I1 I1
Recall definition: log10 N x 10 N
x
means
I2 I2
log 3; 103 ; I2 = 1000 I1
I1 I1
Interference and Beats
f
+
f’
f f’
=
Beat
Beat frequency
frequency == f’f’ -- ff
The Doppler Effect
The Doppler effect refers to the apparent change in
frequency of a sound when there is relative motion
of the source and listener.
v Sound source moving with vs
f
Left person
hears lower f
due to longer
Right person
hears a higher f
due to shorter Apparent f0 is affected by motion.
General Formula for Doppler Effect
V v0
f0 f s Definition of terms:
V vs
f0 = observed frequency
Speeds are fs = frequency of source
reckoned as
positive for V = velocity of sound
approach and v0 = velocity of observer
negative for
recession vs = velocity of source
Example 4: A boy on a bicycle moves north at
10 m/s. Following the boy is a truck traveling
north at 30 m/s. The truck’s horn blows at a
frequency of 500 Hz. What is the apparent
frequency heard by the boy? Assume sound
travels at 340 m/s.
30 m/s fs = 500 Hz 10 m/s
V = 340 m/s
The truck is approaching; the boy is fleeing. Thus:
vvss == +30
+30 m/s
m/s vv00 == -10
-10 m/s
m/s
Example 4 (Cont.): Apply Doppler equation.
vs = 30 m/s fs = 500 Hz v0 = -10 m/s
V = 340 m/s
V v0 340 m/s (10 m/s)
f0 f s 500 Hz
V vs 340 m/s - (30 m/s)
330 m/s
f 0 500 Hz ff00 == 532
532 Hz
Hz
310 m/s)
Summary of Acoustics
Acoustics
Acoustics isis the
the branch
branch of
of science
science that
that deals
deals with
with
the
the physiological
physiological aspects
aspects of
of sound.
sound. For
For example,
example, in
in
aa theater
theater or
or room,
room, anan engineer
engineer isis concerned
concerned withwith
how
how clearly
clearly sounds
sounds can
can be
be heard
heard or
or transmitted.
transmitted.
Audible sound: Frequencies from 20 to 20,000 Hz.
Infrasonic: Frequencies below the audible range.
Ultrasonic: Frequencies above the audible range.
Summary (Continued)
Measurable physical properties that determine
the sensory effects of individual sounds
Sensory effects Physical property
Loudness Intensity
Pitch Frequency
Quality Waveform
Summary (Cont.)
Sound
Sound intensity
intensity isis the
the power
power transferred
transferred
by
by aa sound
sound wave
wave perper unit
unit area
area normal
normal to
to
the
the direction
direction of
of wave
wave propagation.
propagation.
P
I
A
Units: W/m2
Summary (Cont.)
The
The inverse
inverse square
square relationship
relationship means
means aa sound
sound that
that isis
twice
twice as as far
far away
away isis one-fourth
one-fourth as as intense,
intense, and
and one
one
that
that isis three
three times
times as
as far
far away
away isis one-ninth
one-ninth as
as intense.
intense.
P P
I Ir I r
2 2
A 4 r 2
11 2 2
Summary of Formulas:
P I I2
I 10 log 2 1 10 log
A I0 I1
Hearing
Hearing threshold: 10-12
threshold: II00 == 11 xx 10 W/m22
-12 W/m
Pain threshold: I = 1 W/m 22
Pain threshold: Ipp = 1 W/m
V v0
= ff
vv = Beat
Beat freq.
freq. == f’f’ -- ff f0 f s
V vs
CONCLUSION: Chapter 22B
Acoustics
