1. Physics of Music (PHYSICS 198)
Dr. Anatoli Frishman
Web Page:

2. 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

3. 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
Pressure sensor
Vibrating tuning fork
These pressure variations are usually small – a “loud” sound changes the pressure by 2.0x10-5 atm

4. 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

5. Course structure
Background in the fundamentals of physics sufficient to understand basic ideas in sound and musical acoustics
Hearing, loudness pitch and timbre, combination tones, musical scales and temperament
How musical instruments produce sound
Physics of auditoriums
Course organization
Lectures
Laboratory
Homework
Exams
Brief mathematics review

6. MECHANICS KINEMATICS 1. Motion Motion of what? Material point
Kinematics 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.

7. 2. One dimensional (1D) uniform motion
(Motion along a straight line with a constant speed)
Example 1:
t – time
x – position x
Velocity:
Displacement:

8. Uniform - motion with a constant ratio:
Example 2:
Given:
Uniform - motion with a constant ratio:
For uniform motion, velocity (v) is the displacement of an object over the time passed.

9. 3. Velocity of 1D uniform motion geometric interpretationx t
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?

10. 4. Average speed and velocity
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 x t

11. Example 1
Given: A B
Formula used:
Solution:
Answer:

12. Example 2
Given:
Formula used:
Solution:
Answer:

13. x 5. Instantaneous velocity (Velocity at a given point) C B A t
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 closer
to the point A, and, eventually, line AB coincides with tangent line AC.)
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?