2/16/00
I. Sound
A. Definitions
<Psychological> à what we hear
*<Physical> à a mechanical disturbance
propagated in an elastic medium capable of
exciting the sensation of hearing
B. Sound transmission system
needs:
1. Sound source
- Definition = any object that vibrates to impose
a force on or create a disturbance of the
surrounding environment or medium
- Examples: vocal folds
tuning fork
guitar string
2. Propagation medium
- Definition = a substance capable of
transmitting sound waves
- Examples: air (gas)
water (liquid)
steel rails (solid)
- Necessary physical properties:
- Mass
- Elasticity
- Air is the medium most relevant to this course
- Comprised of ~ 400 billion molecules per
square inch
- normally molecules move in a random
fashion which is called Brownian
motion
3. Receiver
- Definition = anything sensitive to
disturbances in the medium
- The ear is the receiver most relevant to this
course
C. How does sound travel
from the source to a
receiver?
- The vibrating object compresses the air near its
surface
- Condensation (compression) = when air
molecules are compressed closer together
than normal
- At the point of condensation, the density of the
molecules increase and air pressure increases
- The molecules move toward the less dense
region which is farther away from the source.
The density and air pressure in that region now
increase
- The original point of condensation now has
fewer air molecules and less molecule density
and pressure
- Rarefaction = when air molecules are spread
out farther than at rest
- The process repeats itself
- The original regions of condensation and
rarefaction move farther away from the sound
source
- The air molecules move but only over a small
range à they don't move from source
to
receiver à only the disturbance
"wave" moves
- The speed of sound (c)
- Definition = the rate at which the disturbance
wave moves through the medium
- Proportional to the density of the medium
- Water is more dense than air so the speed of
sound in water is higher than in air
- Also dependent on the temperature of the
medium
- In air, c = 330 m/s at 0° C and 343 m/s at
20° C (approx room temperature)
D. How do we describe the
disturbance wave?
- Waveform
- Definition = Plotting a measurement of the
disturbance of air molecules as a function of
time
- Waveforms can be simple:
- a sine wave
- a click
- Normally, waveforms are more complex than
these
- Any waveform can be represented as a set of
sine waves
- This set of sine waves is called a Fourier
series or wave spectrum
- Fourier's Theorem - states that any
waveform can be expressed as a sum of
appropriate sine waves
E. Sine waves (sinusoids)
- Definition = a wave with a distinctive shape
described by a sine function
- Parameters of a sine wave:
1. Frequency (f)
- Definition = The number of times an object
moves/vibrates per second
- Frequency is measured in Hertz (Hz).
Older literature may refer to this as cycles
per second (cps)
- At 500 Hz, the object goes through 500
cycles of vibration in one second
- At 1000 Hz, the object goes through 1000
cycles of vibration in one second
- Period (T)
- Definition = The duration of length of one
cycle
- The reciprocal of frequency
1
T
= ---
f
- A waveform with a higher frequency has
a shorter period and goes through more
cycles in the same amount of time
- Wavelength (l)
- Definition = distance traveled by a sine
wave during
one period
- Related to the frequency of the sine wave
and the speed of sound
- Calculation:
c
l = ---
f
2. Amplitude (A)
- Definition = a measure of how far the
vibrating object moves
- Note:
- We will use the term amplitude as a
summary term to indicate the overall
magnitude of a waveform
- We will use the term instantaneous
amplitude to refer to the vibration at
a particular instant in time.
- For any
vibrating object, there is a single
number that describes its amplitude even
though its displacement is continuously
changing
- Ways to measure amplitude:
- Peak amplitude (APEAK) =
measure the
amplitude at the point of maximum
displacement
- However, waveforms that are essentially
the same can have very different peaks
- Average amplitude (peak to peak)
(AMEAN) = averaging the amplitude
across many different points of the wave
- This is not the best solution – consider the
sine wave:
- Sine waves (and many other waves) have
an average displacement of 0
- Root Mean Square (RMS) amplitude
(ARMS) = an average of many
points in
the wave in which the displacements are
squared so that negative displacements
do not cancel out positive displacements
- order of operations in calculation is
opposite of the name à
- 1st you square the displacement
value
- 2nd you take the average of the
values
- 3rd you take the square root of
the
mean
- Calculation :
- For sine waves, ARMS =
0.707 x APEAK
3. Starting Phase (Q)
- Definition = the point in the cycle when an
object starts to vibrate
- Phase is measured in degrees or radians
- Two sine waves of the same frequency that
start at the same place in the cycle are “in-
phase” while if they start at different places
in the cycle, they are “out-of-phase”
- When a sine wave has zero displacement
and is ready to become positively
displaced, it is at 0°
- When a sine wave reaches its peak positive
amplitude, it is at 90°
- When a sine wave has zero displacement
and is ready to become negatively
displaced, it is at 180°
- When a sine wave reaches its peak negative
amplitude, it is at 270°