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.
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Properties of Sound Waves Amplitude determines loudness
Frequency determines pitch **Most sounds you hear are
multi-frequency combinations superimposed to create complex wave
patters**
Slide 5
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
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Measuring Sound
Slide 7
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 R 2 ) increases,
the intensity diminishes inversely with the square of the radius
Inverse Square Law
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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.
Slide 9
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.
Slide 10
Sound-Level The intensity-level 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.
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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
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Example 1 A faint sound with an intensity of 10 -9 W/m 2 is
measured by a sound-level meterwhat will be the reading in dB?
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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:
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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 ( ) is 5 times the 10
dB. = 5(10 dB) = 50 dB
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Sound Waves
Slide 16
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
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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).
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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:
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Example 3 Solution: f, v, and are related.
Slide 20
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
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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
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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)
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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)
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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 When
source is stationary
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Case 1 Equation, General When moving toward a moving source v
s, the observed frequency is When moving away from a moving source,
the observers frequency is When source is not stationary
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Overall CONSIDER A LINE FROM THE OBSERVER TO THE SOURCE THIS IS
THE POSITIVE DIRECTION V O AND V S ARE ASSIGNED + OR -
ACCORDINGLY
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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
Slide 28
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
Slide 29
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
Slide 30
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.
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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
Slide 32
Tube Closed at One End
Slide 33
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, =
0.52m) the pipe needs to be 0.26m long to create the
fundamental.
Slide 34
Tube Open at Both Ends
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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.
Slide 36
Reverberation
Slide 37
Fouriers Theorem Any complex wave pattern can be represented by
the addition of multiple, single-frequency waves called component
frequencies.
Slide 38
Frequency Spectrum
Slide 39
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
Slide 40
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
Slide 41
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**
Slide 42
Scales A series of frequencies occurring at set intervals
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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
Slide 44
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: