physics of music (physics 198) dr. anatoli frishman frishman@iastate.edu web page:...
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Physics of Music(PHYSICS 198)
Dr. Anatoli Frishmanfrishman@iastate.edu
Web Page: http://course.physastro.iastate.edu/phys198/
Introduction•Music and physics – what is in common?
•What is physics?•A science•A basic science•The most basic science•Discovered by several generations of scientists
•Physics and measurements•Relationship between experiments and theory•Mathematics - language of science
•Music and sound•Sound
•An auditory sensation in ear•Disturbance in a medium that can cause this sensation
•Sound waves•Transverse and longitudinal waves•Waves in different media•Speed of waves and speed of particles of the media 2
Sound
Acoustic waves in the range of frequencies: 20Hz -20,000Hz
Sound waves:• can travel in any solid, liquid or gas•in liquids and gases sound waves are longitudinal ONLY!• longitudinal and transversal sound waves could propagate in in solids
Sound in air is a longitudinal wave that contains regions of low and high pressure
Vibrating tuning fork
These pressure variations are usually small – a “loud” sound changes the pressure by 2.0x10-5 atm
Pressure sensor
3
We need physics to understand properties of sound:•How it propagates?•How it reflects?•Interaction (interference) between sound waves created by different sources•What is pitch?•What is loudness?•What is timbre?•And many other interesting questions
More questions about music:•Relations between different scales•Tone and half tone •Octave
4
Course structureI.Background in the fundamentals of physics sufficient to understand basic ideas in sound and musical acousticsII.Hearing, loudness pitch and timbre, combination tones, musical scales and temperamentIII.How musical instruments produce soundIV.Physics of auditoriums
Course organization•Lectures•Laboratory•Homework•Exams
Brief mathematics review
5
MECHANICS
KINEMATICSKinematics is the study of motion, without the investigation of the cause for the motion
1. Motion
•Motion of what? Material point (An object with an irrelevant dimension for the purposes of a particular problem)•Development of models
Example: linear movement v. rotation•Motion is relative to the object of reference
Examples: the motion of an airplane passenger relative to the air plane, or the motion of an air plane passenger relative to the ground.
6
x
mxxx 1012 21
21
xx
ttsttt 212
sms
mv /5
2
10
Example 1:
mssmtvx 102/5
12
12
tvxx
tvxx
tvxxttt 1221 ,0 if
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2. One dimensional (1D) uniform motion(Motion along a straight line with a constant speed)
Velocity:
t
xv
Displacement:
t – time
x – position
... then ... if 2121 xxtt ...2
2
1
1
t
x
t
xv
Uniform - motion with a constant ratio:
For uniform motion, velocity (v) is the displacement of an object over
the time passed.
mmmxxx 4610121
mx
mx
mx
st
st
st
14
10
6
7
5
3
3
2
1
3
2
1
Example 2:
mmmxxx 41014232
sssttt 257232
sssttt 235121
sms
m
t
x
t
xv /2
2
4
2
2
1
1
?v
Given:
8
3. Velocity of 1D uniform motion geometric interpretation
x
t1t 2t 3t 4t
1t
2t
1x
2x
t
xv
tant
x
tvx
00 ttvxx
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Velocity is equal to the slope of the graph (rise over run): distance over time.
Question: The graph of position versus time for a car is given above. The velocity of the car is positive or negative?
4. Average speed and velocity
t
x x
tt
xv
• speed is the distance covered over time passed
• velocity is the displacement of an object over time passed
• velocity has a direction, while speed does not
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A B
Example 1
Given:1x
Formula used:
t
xv
Solution:
?v
mi/hv
mi/hv
xxx
xAB
60
40
mi502
mi100
2
1
21
48mi/h 12/25
100
h 12
25h
6
5h
4
5
h 6
5
60mi/h
50mi h;
4
5
40mi/h
50mi
21
2
22
1
11
h
mi
t
xv
ttt
v
xt
v
xt
2x
Answer:
/h48miv 11
Example 2
Given:
?
60
40
1
2
1
21
v
km/hv
km/hv
httFormula used:
t
xv
Solution:
km/h50h2
km100
h2
100kmkm60km40xx
km60x km40
21
21
t
xv
t
x
x
Answer:
km/h50v
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5. Instantaneous velocity (Velocity at a given point)
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A
B
t
x
x
t
C
t
xv
t
0
lim
Question: The graph of position versus time for a car is given above. The velocity of the car is positive or negative? Is it increasing or decreasing?
Instantaneous velocity is equal to the slope of the line tangent to the graph.(When Δt becomes smaller and smaller, point B becomes closer and closerto the point A, and, eventually, line AB coincides with tangent line AC.)
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