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

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

MECHANICS KINEMATICS 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. 6

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

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

3. Velocity of 1D uniform motion geometric interpretation x t 9 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 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 10

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

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

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