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taupeselectionMechanics

Nov 14, 2013 (3 years and 9 months ago)

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Chapter 15

Properties of Sound

Properties of Sound Waves


Sound is
a
compression

wave in
any material medium oscillating
within the frequency range of
20
Hz to 20 kHz.


Sound waves are
longitudinal

and can propagate as a sphere in
an elastic medium such as air.

Properties of Sound Waves


Amplitude determines loudness


Frequency determines pitch



**Most sounds you hear are multi
-
frequency
combinations superimposed to create complex wave
patters**

Categories of Sound Waves


Audible

waves


Lay within the normal range of hearing of the
human ear


Normally between 20 Hz to 20,000 Hz


Infrasonic

waves


Frequencies are below the audible range


Earthquakes are an example


Ultrasonic

waves


Frequencies are above the audible range


Dog whistles are an example

Measuring Sound

Intensity


The rate of transfer of energy is the
acoustic power.


A person speaking at a normal conversational level emits
power at about 10
-
5

J/s and shouts at about 1
mJ
/s.


The
Intensity

(I) of a wave is defined as the average
power divided by the perpendicular area across which
it is transported.









Intensity has units of W/m
2
.


As a spherical wave expands outward, its area (4
p
R
2
) increases,
the intensity diminishes
inversely with the square of the
radius



Inverse Square Law

A
P
I
av

Loudness


Loudness depends on the frequency, duration, and
intensity of the sound.


We judge the relative loudness of a sound not by
the difference in intensity between it and some
reference but by their
ratio
.


Multiplying
any intensity by 10 will generally be
perceived as approximately doubling it in
loudness; 10
-
8

W/m
2

sounds twice as loud as 10
-
9

W/m
2



the ear responds logarithmically.

Sound
-
Level


The sound
-
level (or
intensity
-
level)
of an acoustic wave is defined
as
the number of factors of 10 that its intensity is above the
threshold of hearing: I
0

= 1.0 X 10
-
12

W/m
2
.


The unit of sound intensity
-
level is called the
bel
.


A decibel (abbreviated dB) is 1/10 of a
bel

and is
unitless
.


By definition, the
logarithm

to the base 10 of any number
X
equals the power to which 10 must be raised to equal X


In other words, if
X =
10
Y
, then the log
10

X = Y.


1000 = 10
3

and so log
10

1000 = 3.

Sound
-
Level


The
in
tensity
-
level

b

in dB of any sound is







For example, a sound wave with an
intensity of 10
-
6

W/m
2

has an
intensity
-
level of





Increasing the intensity by a factor of 10 changes the sound
-
level
by 1
bel

or 10 dB
.

0
10
10
I
I
log

b
dB
m
W
m
W
60
6
10
10
10
10
10
10
6
10
2
12
2
6
10






)
(
log
/
/
log
b
Frequency Response Curves


Bottom curve is the threshold
of hearing


Threshold of hearing is
strongly dependent on
frequency


Easiest frequency to hear is
about 3300 Hz


When the sound is loud (top
curve, threshold of pain) all
frequencies can be heard
equally well

Example 1


A faint sound with an intensity of 10
-
9
W/m
2

is
measured by a sound
-
level meter

what will be the
reading in dB?

Example 2


Two public address systems are being compared, and
one is perceived to be 32 times louder than the other.
What will be the
difference

in sound levels between
the two when measured by a dB
-
meter?


Given: a factor of 32 in loudness


Find: ∆
b

Example 2


Solution: Sound level problem. Given a change in
loudness


note that a doubling in loudness is
approximately the same as multiplying the intensity by
10


by equation 11.11 this would be about a change of 10
dB.


Since 32 = 2
5



the loudness is doubled five times. So
the difference in sound levels (∆
b
) is 5 times the 10 dB.



b

= 5(10 dB) = 50 dB

Sound Waves

Sound Waves

Sound behaves like any other wave, having:



Frequency



20Hz


20,000Hz (audible)



Wavelength



relatively long, in the
centimeter to meter range measured between
successive areas of high or low pressure



Velocity



which remains constant in any
given medium (343 m/s in air: 660 mi/hr),
therefore wavelength and frequency trade off

Velocity of Sound


v = 330m/s; 660 miles/hour in “typical conditions”



v increases with increasing temperature and pressure



v increases in s lighter medium (hydrogen as opposed



to air)


v increases sharply as sound passes into liquids and
again in solids (about double each time).

Example 3


By international agreement, most orchestras tune to a
frequency of 440 Hz, which is called A440 (the A note
above middle C). Given that the speed of sound in air
at room temperature is 343.9 m/s, what is the
wavelength of A440?


Given:
f

= 440 Hz and
v

= 343.9 m/s


Find:
l

Example 3


Solution:
f
,
v
, and
l

are related.

m
Hz
s
m
f
782
0
440
9
343
.
/
.
v



l
Doppler Effect


A Doppler effect is experienced whenever there is
relative motion between a source of waves and an
observer.


When the source and the observer are moving toward
each other, the observer hears a higher frequency


When the source and the observer are moving away
from each other, the observer hears a lower frequency

Doppler Effect, cont.


Although the Doppler Effect is commonly experienced
with sound waves, it is a phenomena common to all
waves


Assumptions:


The air is stationary


All speed measurements are made relative to the
stationary medium

Doppler Effect, Case 1


An observer is moving
toward a stationary
source


Due to his movement,
the observer detects an
additional number of
wave fronts


The frequency heard is
increased

(Observer Toward
Source)

Doppler Effect, Case 1


An observer is moving
away from a stationary
source


The observer detects
fewer wave fronts per
second


The frequency appears
lower

(Observer Away from Source)

Doppler Effect, Case 1


Equation


When moving toward the stationary source
v
s
=0, the observed frequency is





When moving away from the stationary source,
the observed frequency is

v
v
v
O
S
O
f
f


v
v
v
O
S
O
f
f


When source is stationary

Case 1


Equation, General


When moving toward a moving source
v
s
, the
observed frequency is





When moving away from a moving source, the
observer’s frequency is

S
O
S
O
f
f
v
v
v
v



When source is not stationary

S
O
S
O
f
f
v
v
v
v



Overall


CONSIDER A LINE
FROM THE OBSERVER TO THE
SOURCE



THIS IS THE
POSITIVE

DIRECTION



V
O

AND V
S

ARE ASSIGNED + OR
-

ACCORDINGLY

Example 4


An automobile traveling at 20.0 m/s (45 mph) blows a
horn at a constant 600 Hz. Determine the frequency
that will be perceived by a stationary observer both as
the car (a) approaches and (b) recedes. Take the speed
of sound to be 340 m/s.


Given:
v
s

= 20.0 m/s,
v
o

= 0,
v

= 340 m/s, and
f
S

= 600
Hz


Find:
f
o


Example 4


Solution: This is a Doppler effect problem, use
equations 11.23


The source is approaching, use

v
s

in Eq. (11.23)




638 Hz



The source is receding, use +
v
s

in Eq. (11.23)




567 Hz






s
m
s
m
s
m
Hz
f
f
S
S
o
/
.
/
/
v
v
v
0
20
340
340
600





s
m
s
m
s
m
Hz
f
f
S
S
o
/
.
/
/
v
v
v
0
20
340
340
600
Doppler Effect, General Case


Both the source and the observer could be moving






Use
positive

values of
v
o

and
v
s

if the motion is toward


Frequency appears higher


Use
negative

values of
v
o

and
v
s

if the motion is away


Frequency appears lower


ƒ ƒ
o
o s
s
v v
v v
 


 

 
Example 5


A Police care with its siren blaring at 1000Hz is chasing
a truck. The police car is traveling at 20m/s, and the
truck is traveling at 15m/s. What frequency does the
truck driver actually hear as the police car catches up
to him? Assume the speed of sound in air on this
occasion is 330m/s.

Standing Waves in Air Columns


If one end of the air column is closed, a node must
exist at this end since the movement of the air is
restricted


For an “E” note of 660Hz and v = 330m/s the
wavelength is then 0.52m and the pipe needs to be
0.13m to create the fundamental

Tube Closed at One End

Standing Waves in Air Columns


If BOTH ends are open, then antinodes will form at
both ends and the pipe will need to be one half the
wavelength.



For the same “E” note then (660Hz, 330m/s,
λ

=
0.52m) the pipe needs to be 0.26m long to create the
fundamental.

Tube Open at Both Ends

Reverberation



The
multiple
-
echo effect
of reflected sound waves
bouncing off the boundaries in an enclosed space.


When designed correctly, the space
enhances

the
sound.


When designed poorly, the space
muddies

the sound.


Dead spots may be created where
destructive
interference
takes place.

Reverberation

Fourier’s Theorem


Any complex wave pattern can be represented by the
addition of multiple, single
-
frequency waves called
component frequencies.


Frequency Spectrum

Hearing Sound


The outer ear
consists of the ear
canal that
terminates at the
eardrum


Just behind the
eardrum is the
middle ear


The bones in the
middle ear
transmit sounds
to the inner ear

The Ear

Pitch


Pitch is related mainly, although not completely, to
the frequency of the sound


Pitch is not a physical property of the sound


Frequency is the stimulus and pitch is the response


It is a psychological reaction that allows humans to
place the sound on a scale

Timbre


In music, the characteristic sound of any instrument is
referred to as the quality of sound, or the
timbre
,

of
the sound


The quality depends on the mixture of harmonics in
the sound


A flute, a trumpet, a saxophone, or a tuning fork, can
produce the same note (same pitch) at the same
loudness, but have a different
timbre
, which
depends
on the waveform.

**Different instruments have different timbre because
they produce different Fourier spectra**

Scales



A series of frequencies occurring at set intervals

Harmony

Harmony

is a combination of frequencies which
produce a new musical tone.



Consonance



a GOOD combination of frequencies




Dissonance

--

a BAD combination of frequencies




Beats



occur as a pulsating amplitude created by
certain frequency combinations


Beats


Beats

are alternations in loudness, due to
interference


Waves have slightly different frequencies and the
time between constructive and destructive
interference alternates


The
beat frequency

equals the difference in
frequency between the two sources:

2 1
ƒ ƒ ƒ
b
 