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Fundamentals of Sound

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.

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

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

Harmonic Motion

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

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

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

Types of Reflection

There are two types of reflection that can occur1. Fixed end reflection – wave reflected at opposite

polarity

2. Free end reflection – wave reflected at same polarity

Polarity – up/down orientation of a wave

Reflection/Refraction

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 interference1. 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

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:

l = (2/n)L

Where is wavelength value, L is the length and n could equal 1, 2, 3, 4…

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

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 180o out of phase, what is the result?

Phase

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