1.  Fundamentals of Sound

2. What is sound?  Sound is the result of vibrating air molecules. Molecules can be in 2 states of motion. What are they? 1. Compression – when the molecules are tightly packed together, resulting in audible sound 2. Rarefaction – when the molecules ricochet away from one another and are less densely packed, resulting in no sound.

3. Sound Waves  Sound is made up of waves.  There are two types of waves, longitudinal and transverse  Longitudinal waves – waves that move horizontally to their propagation; sound waves are an example  Longitudinal waves are measured according to the horizontal aspect of the wave, such as how the wave moves/changes over a period of time  Transverse waves – waves that move perpendicular to their propagation; water waves  Transverse waves are measured according to the vertical aspect of the wave, such as the height of the peak from its source of propagation

4. Harmonic Motion  The motion of sound waves is referred to as simple harmonic motion and are the result of a vibrating system in action.  Physical oscillators are not an example of a vibrating system, but the speakers used to diffuse their sound are an example of a vibrating system  As a vibrating system vibrates, tension is created, resulting in what is called displacement (distance from equilibrium)  Restoring force returns the system to equilibrium  Greater displacement requires greater restoring force

5. Harmonic Motion

6. Hooke’s Law  Illustrates the relationship between force (F), tension (K) and displacement (y) F = -Ky  The inverse of the product of the initial tension of the system and the amount of displacement

7. Properties of Waves  Sound waves have 5 properties. They are: 1. Wavelength – distance between corresponding points, represented as Lambda ( ) 2. Frequency – number of times a wavelength repeats itself in a given period of time; measured in cycles per second or Hertz (Hz) 3. Amplitude – Measures the change in sound pressure level and is an objective measure of the loudness/softness of a sound 4. Wave shape/waveform – structure of a wave, corresponds to the timbre of a sound; 4 types (sine, triangle, sawtooth, square/pulse) 5. Phase – position of a wave at a point in time

8. Reflection/Refraction  Reflection and refraction refers to how a wave behaves when it comes in contact with a physical object  Depends on the wavelength of the wave and the dimension of the object it comes into contact with  Reflection = sound bounces off the object at the same angle at which it struck the object  Wavelength < Object’s surface dimensions  Refraction = sound bends around the object  Wavelength > Object’s surface dimension

9. Types of Reflection  There are two types of reflection that can occur 1. Fixed end reflection – wave reflected at opposite polarity 2. Free end reflection – wave reflected at same polarity  Polarity – up/down orientation of a wave

10. Reflection/Refraction

11. Combining Waves  When two waves come into contact with each other they can react in various ways.  Superposition – two waves meet and combine, but then separate with their original characteristics intact  Combination of waves also causes one of two types of interference 1. Constructive interference – waves of similar polarity combine and create a wave with greater amplitude 2. Destructive interference – waves of opposite polarity combine and cancel each other out

12. Standing Waves  A standing wave is a wave that does not appear to propagate at all, but oscillates in one position  Created by patterns of wavelengths that are integer subdivisions of the sounding object (1/2, 1/3, 1/4, etc.)  String harmonics are an example of standing waves  The following equation determines where standing waves will be produced in a string secured at both ends: = (2/n)L Where is wavelength value, L is the length and n could equal 1, 2, 3, 4…

13. Standing Waves  Nodes – point that remains motionless and results in zero amplitude  Antinodes – points that remain motionless but result in maximum amplitude (points at which standing waves occur)  Frequencies that produce standing waves are called resonant frequencies or characteristic frequencies  Initial wavelength is called the fundamental  Integer multiples of the fundamental are called harmonics

14. Phase  Mentioned earlier as the position of a wave’s peak and trough at a given point in time  Phase is typically only considered when working with multiple waves  2 waves with simultaneous 0-crossing points are said to be “in phase”  Resulting in what kind of interference?  2 waves without corresponding 0-crossing points are said to be “out of phase”  If they are 180 o out of phase, what is the result?

15. Phase

16. Speed and Velocity  We have talked about velocity as it relates to MIDI, but now we will discuss it as a property of sound  Speed of sound in air is 1000 feet/second  Speed of sound increases slightly in higher temperatures  Air particle velocity – speed at which individual molecules oscillate  Velocity increases as amplitude and/or frequency increases