L 20
Course Review
W= mg,
2
where g=9.8 m/s
In Previous slide
W (=FG) = FN
Simple Harmonic Motion
• Position x vs. time t
• Definition of period T
• Definition of amplitude A
Frequency and Period
f = 1/T or T = 1/f or f T =1
T period, in seconds (s)
f = frequency in Hertz (Hz)
Metric prefixes:
centi- (c), milli- (m), micro- (m)
kilo- (k), mega- (M)
Wave velocity for a
periodic vibration
Let the wavelength be λ
and the frequency of the
vibration be f.
The wave velocity v is just
V=λ/T, or
V= λf
v T /m
More specifically,
 we consider a force acting through a distance.
Work = Force x distance or W = F.d
Units - newtons x meters = joules (J), or
 pounds x feet (foot pounds, ft.lbs)
 BTU = 778 ft.lbs (energy of one wooden kitchen
match)
 Pushing on a wall and wall doesn’t move
(no work done on the wall)
Conversion: 1J= 0.738 ft.lb
Potential Energy
Energy of position or configuration
Other examples - Springs, bow, sling shot,
chemical energy, and gravitational potential
energy
The latter is GPE = mgh (the force required to
lift at constant speed times the distance )
2. POWER
Power = Work/time or P = W/t
Units - J/s =
Watt
W
550 ft.lb/s = 1 hp
1 hp = 746 J/s = 746 W
1 BTU/hr = 0.293 W
100 W bulb =
0.1341 hp
250 hp engine = 186,450 W
Conditions for standing waves
overpressure
L
Closed tubes
(closed on one end)
overpressure
L
Closed end: antinode
open end:node
We define the Sound Intensity I as
the Audio Power crossing a unit
area,
or I = P/A
Units- W/m2
12-2 Intensity of Sound: Decibels
An increase in sound level of 3 dB, which is
a doubling in intensity, is a very small
change in loudness.
In open areas, the
intensity of sound diminishes with distance:
However, in enclosed spaces this is complicated by reflections, and if sound travels through
air the higher frequencies get preferentially absorbed.
12-2 Intensity of Sound: Decibels
The loudness of a sound is much more closely related to the logarithm of the intensity.
Sound level is measured in decibels (dB) and is defined:
(12-1)
I0 is taken to be the threshold of hearing:
12-2 Intensity of Sound: Decibels
The intensity of a wave is the energy transported
per unit time across a unit area.
The human ear can detect sounds with an intensity
as low as 10-12 W/m2 and as high as 1 W/m2.
Perceived loudness, however, is not proportional to
the intensity.
12-3 The Ear and its Response; Loudness
The ear’s sensitivity varies with frequency. These curves translate the intensity into
sound level at different frequencies.
Intervals
12-tone scale (chromatic)
8-tone scale (diatonic)
Note span
C-C
C - C#
C-D
C - D#
C-E
C-F
C - F#
C-G
C - G#
C-A
C - A#
C-B
C3 - C4
C3 - E4
Interval
Frequency ratio
unison
1/1
semitone
16/15
whole tone (major second)
9/8
minor third
6/5
major third
5/4
perfect fourth
4/3
augmented fourth
45/32
perfect fifth
3/2
minor sixth
8/5
major sixth
5/3
minor seventh
16/9 (or 7/4)
major seventh
15/8
octave
2/1
octave+major third
5/2
Pythagorean Scale
Built on 5ths
A pleasant consonance was observed
playing strings whose lengths were
related by the ratio of 3/2 to 1 (demo).
Let’s call the longer string C, and the
shorter G,
and the interval between G and C a 5th
Denote the frequency of C simply by
the name C, etc.
The major triad is the basis for the
just scale, which we now develop
in a way similar to that of the
Pythagorean scale.
We wish to make a chromatic
scale- 12 tones including both
octaves- and we want all the
intervals (ratios of adjacent notes
to all be the same).
Beats
f1-f2 = beat frequency
Average frequency “heard” =
(f1+f2)/2
Modes
•
•
•
•
•
•
•
Ionian – Major Scale
Dorian – 2nd of Major Scale
Phrygian – 3rd of Major Scale
Lydian – 4th of Major Scale
Mixolydian – 5th of Major Scale
Aolian – 6th of Major Scale (Minor)
Locrian – 7th of Major Scale
Non-Western Scales
Resonance
Fourier Synthesis
Demo- PhET (Physics,Fourier)
String Instruments
The Vocal Tract
epiglottis
Vocal Formants
“had”
To calculate T, consider a room with a
hole in one wall of area A.
Call the reverberation time T.
T ˜ volume V, 1/A
T= K V/A
It has been worked out that, for V in ft3 , A
in ft2
T= 0.049 V/A
Let us now replace the open
window area with an absorbing
material of area S and absorption
coefficient a.
Then A= Sa. If there is more than
one type of absorbing material, the
A= S1 a1+s2a2 +S3a3+…
Basic Analog Electronics
Ohm’s Law
Links: Bob Holtzworth part 1 slides 111,12,16
Ohm’s Law
The current (charge per unit time)
flowing through a circuit element is
equal to the potential drop across
this element divided by the
resistance of the element.
I= V/R
Digital Electronics
Introduction to Binary
Numbers
We can write the number 752 as
2x100 + 5x101 + 7x102
Similarly
We could use the base 2, e.g.
3 = 1x20 + 1x21, which we represent as
11.
Hence
01 is 2
These are 2-binary digit (bit) numbers.
Digital Sampling
Calculating Bit-rates (CD quality)
Sampling
Rate
x
Resolution
x
# of
Channels
=
Bit-rate
44,100
x
16
x
2
=
1,411,200
Calculating File Sizes (one minute of CD audio)
Sampling
Rate
44,100
x Resolution x
x
16
x
Number of
Channels
x
Time in
Seconds
/
Bits
/
Byte
2
x
60
/
8
MP3 compression at 128 kbps compresses this by a factor of 11
=
File Size
(in Bytes)
=
10,584,000
More on CDs
750 Mbytes
Link: “how Edison got his groove back”
75 minutes of audio
The elongated bumps that make up the track are each 0.5 microns wide, a
minimum of 0.83 microns, they look something like this:
MP 3 Compression
The most important principle in MP3 compression is the
psychoacustic selection of sound signals to cut away. Those
signals, we are unable to hear are removed. These include
weaker sounds that are present but are not heard because they
are drowned out (masked) by louder instruments/sounds.
Many encoders use the fact that the human ear is most sensitive
to midrange sound frequencies (1 to 4 KHz). Hence sound data
within this range is left unchanged.
An other compression used is to reduce the stereo signal into
mono, when the sound waves are so deep, that the human ear
cannot register the direction. Also the contents of common
information in the two stereo channels is compressed.
The Huffman algorithm reduces the file size by optimizing the
data code for the most often used signals. This is a lossless
compression working within the MP3 system.