2
G
N

• Position x vs. time t
• Definition of period T
• Definition of amplitude A

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)

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 =
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

overpressure
Closed tubes
(closed on one end)
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/m 2

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)
I
0 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/m 2 and as high as 1 W/m 2 .
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
C
3
C
3
- C
4
- E
4
Interval unison semitone
Frequency ratio
1/1
16/15 whole tone (major second) 9/8 minor third 6/5 major third 5/4
4/3 perfect fourth augmented fourth perfect fifth minor sixth
45/32
3/2
8/5 major sixth minor seventh major seventh octave octave+major third 5/2
5/3
16/9 (or 7/4)
15/8
2/1

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 5 th
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 f
1
-f
2
= beat frequency
Average frequency “heard” =
(f
1
+f
2
)/2

Modes
• Ionian – Major Scale
• Dorian – 2 nd of Major Scale
• Phrygian – 3 rd of Major Scale
• Lydian – 4 th of Major Scale
• Mixolydian – 5 th of Major Scale
• Aolian – 6 th of Major Scale (Minor)
• Locrian – 7 th of Major Scale

Non-Western Scales

Fourier Synthesis
Demo- PhET (Physics,Fourier)

String Instruments

epiglottis
The Vocal Tract

“had”
Vocal Formants

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 m 3 , A in m 2
T= 0.16 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= S
1 a
1
+s
2 a
2
+S
3 a
3
+…

Basic Analog Electronics
Ohm’s Law
Links: Bob Holtzworth part 1 slides 1-
11,12,16

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

We can write the number 752 as
2x10 0 + 5x10 1 + 7x10 2
Similarly
We could use the base 2 , e.g.
3 = 1x2 0 + 1x2 1 , which we represent as
11.
Hence
01 is 2
These are 2bi nary digi t (bit) numbers.

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 x Resolution x
Number of
Channels x
Time in
Seconds
/
Bits
/
Byte =
File Size
(in Bytes)
44,100 x 16 x 2 x 60 / 8 = 10,584,000
MP3 compression at 128 kbps compresses this by a factor of 11

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.

More on CDs
Link: “how Edison got his groove back”
750 Mbytes
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: