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

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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

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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

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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:

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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.)