# Acoustics - in the beginning

Acoustics - the study of sound. The information about acoustics here is a resource for people who wish to use some of this knowledge and apply it to simple 'at home' or 'in the village' recording techniques. This information can be used with recording programs which are available for computers, such as the open source recording application 'Audacity'. Experimentation with programs (such as Audacity) and knowledge of basic acoustic principles can help people make the most of introductory recording concepts with out any prior experience. The marriage of available recording applications, learning networks and community based radio, can help develop a foundation for music at the level of participation, feedback, and demonstration.

While this information can be found elsewhere on the web, it is presented here in an order which represents the content of several consecutive lessons.

Acoustics: Beginning Notes [[A Room Resonance ]]= 3 main waves.

Width, height, and length.

Formants, or dominant frequencies can be worked out by finding room dimensions.

F= c/2d

c = 340ms-1 (the speed of sound) d = the distance between walls

[[The Harmonic Series: ]]To transpose a frequency by an interval, you must multiply it or divide it by some number. Eg. Transposition up one octave by multiplying the base frequency by 2

[[Modes of Vibration: ]]Because no vibration can occur at a node only certain frequencies are available in enclosed spaces. -only integer multiples of the fundamental frequency are possible.

Traveling and Standing Waves Traveling wave – with no reflective surfaces, waves propogate freely in the medium. Standing wave – when the medium has reflective surfaces “standing” waves are created in any enclose medium with reflective surfaces.

Nodes and Antinodes In standing waves we get areas of maximum displacement and areas of no displacement node = no displacement antinode = maximum point of displacement

Amplitude: Max displacement of particles / density from equilibrium relates to sound intensity not always loudness.

Frequency: Larger frequencies = higher pitches

Phase Shift: Horizontal offset makes a difference when adding sounds together. ie. where the wave starts on the vertical (y ) axis.

In time domain representation with time on x and amplitude on y loud speakers are driven with this representation in mind.

The purest tone to the human ear is the sinusoidal curve.

Y = Asin(wt+B) A = Amplitude w = angular frequency = 2π f t = time B = phase constant

[[Simple Harmonic Motion : properties ]] equations for,

Pitch vs Noise

SHM figures of pitch as smooth longitudinal waves

Noise rendered as a chaotic jagged image.

[[Resonance / Filtering ]] Single resonant frequency (fR)

f= fR is loudest resonance

Resonance cannot create new frequencies that do not exist in the principal vibration. 

Resonance curve, height and width of curve determines how strongly defined the resonance is.

Note: Sound representation as time domain information or frequency domain information.

FDR= Sonogram/spectrum

TDR= Waveforms

Over tones, create a sense of timbre. Inharmonic tones, are when overtones do not conform to harmony.

[[Timbral indicators: ]] Vibrato: Oscilation of pitch and Amplitude. Tremelo: rapid rearticulation of note Timbral modifications: mutes, sulpont, sultasto.

Timbre is the sound of the tone that is other than perfect pitch.

The Harmonic series in equal temperament

f (n12) = 2f n12 =2 n = 12√2 = 1.05946

semitones above fundamental = 1.50946 (number of tones above fundamental)

Speed of sound in String V= √T/ml

T = tension m = mass l = length

The wave equation:

[[ c (meters/second) ]] (Hz) f l (wavelength in meters)

waves are transverse or longitudinal T/V = displacement at 90o to wave motion L/T = displacement at 180o to wave motion

Sound waves are periodic or aperiodic. P + Ap = additive +stochastic

Intervals Notes Frequency Ratio Semitones 8ve c-c 1:2 12 per5th c-g 2:3 7 per4th c-f 3:4 5 Ma3rd c-e 4:5 4 m3rd e-g 5:6 4 Ma6th c-a 3:5 9 m6th e-c 5:8 8 dampening: the sound of a musical instrument in the air, and the sound in the wood

Sound at lower frequency will penetrate deeper into materials than ultrasound

Condenser mics for are good for faster sounds but are more sensitive

A dynamic mic would would be good over a tom drum for example, but a combination of condensers and dynamic would be better for the overall kit.

If only one type of mic is available a studio compressor can be used to reduce the exceeding threshold by a ratio. For example if a ratio of 5:1 is set, an input signal exceeding the threshold by 5dB will be output with a level of only 1dB over the threshold.

A compressor is a device for automatically controlling the level of an audio signal. More specifically, a compressor 'turns down' the audio when the level exceeds a threshold set by the user. The amount by which the gain is turned down depends on the ratio of the compressor.

Once the signal falls back below the threshold level, the gain returns to normal. It's exactly the same as manually turning the level down with a fader whenever it gets too loud, but it's much faster to respond than any human and it's totally automatic.

[[Sound Module: ]] Introduction to Sound:

How sound travels (forms, transmits, is received) How sounds combine Musical instruments Simple pitches – complex acoustics

A Basic Maths and Physics Refresher: About Waves and their properties, and sound transmission as simple harmonic motion.

ab = a.b Reciprocal of x=1/x d (distance) v(speed) t(time) Scientific units: d = (m)eters t = s(econds) v = meters per second (m/s) Frequency = Hz 1/s

Waves Particles excited, propagate a disturbance = Primary Vibration

There are two types of waves: Transverse waves (displacement at 90º to wave motion) Longitudinal waves (displacement parallel to wave motion)

Sound Waves Periodic vs Aperiodic

Periodic waves repeat at regular intervals = pitch =>

Aperiodic waves are without pattern = noise =>

Most real world sounds have pitch and noise components.

[[Simple Harmonic Motion ]]Covers the well defined properties of: period (s), frequency (Hz), wavelength (m), and speed (m/s), amplitude.

Period = 1 complete wave cycle measured in (s) the reciprocal of p= 1/f

Frequency = reciprocal of period measured in Hz (x times per s) convert (f) from other time bases by dividing by No. of (s)

Note: 20Hz : Lowest audible to a human 24Hz : Lowest audible on piano 50Hz : Mains hum 440Hz : Concert A 4000Hz: Highest note on piano 20000Hz: Highest note audible to a human

Wavelength = distance in (m) of 1 complete wave cycle

Speed = speed of sound is dependent on properties of medium: temperature, density, elasticity.

The Wave Equation:

c (speed (m/s))

  (frequency) f   m (wavelength)


Pitch Equation for Simple Harmonic Motion and properties of SHM Travelling waves vs Standing waves Nodes and anti nodes the harmonic series

Pitch vs Noise: For us to hear pitch, a component of a sound's waveform must repeat at a frequency within our hearing range.

Spectrum // white noise => pitch (pure sinusoidal)

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