# Acoustic Theory and Synthesis

Topics: Square wave, Acoustics, Sound Pages: 5 (1146 words) Published: August 21, 2013
Acoustic Theory and Synthesis

Frequency:

Frequency means the number of cycles per second and depending on the amount of cycles per second determines how high or low pitched the sound is and the time that it takes to complete one cycle is called the period. Frequency is measured in Hertz (Hz). And An average human is able to hear sounds between 20Hz and 20,000Hz.

As the cycles per second increases, the smaller the wavelengths become, therefore there is a higher frequency which will cause the pitch of the sound to increase or get higher. If there is frequency of say 20KHz then it is going to be a much higher pitch than a 20Hz because there is a lot more cycles per second.

Fundamentals:

A fundamental is the lowest frequency of vibration for any oscillator and this is known as (f) this is also the 1st harmonic. The next lowest frequency the oscillator will vibrate at is exactly double the frequency of the fundamental. Known as (2f) and the 2nd harmonic. The next lowest is called (3f) and this carries on.

Harmonics:

A harmonic is a frequency that an object called a “Harmonic Oscillator” will naturally vibrate at. The harmonics will occur periodically to the fundamental frequency at equally spaced (by width) points The resultant frequency is all of the frequencies put together and is what we see when we see a sound frequency.

There are two types of harmonics, odd and even.

Even harmonics are ones that sound pleasing nice to the ear. Even harmonics are those that have an even multiple of the fundamental frequency so if the fundamental frequency was 440Hz then the next harmonic would be at 880Hz and this is even.

Harmonic Points
Harmonic Points
Odd harmonics are the odd multiples of the fundamental and these don’t sound as nice and have a harsher sound. If the fundamental was 440Hz then the first odd harmonic would be 970Hz. !!!

Harmonic Frequencies on a graph
Harmonic Frequencies on a graph

Waveforms: There are four main waveform types.

Sine: A sine wave only has a fundamental and no harmonics so the sound it creates is a very simple, plain sounding sound so therefore sounds pleasing and nice to listen to. An Example of a sine wave can be found on track 1 of my logic session which is with my assessment.

Triangle: A triangle waveform contains only odd harmonics which decrease in amplitude quite rapidly. An Example of a triangle wave can be found on track 2 of my logic session which is with my assessment.

Sawtooth: The sawtooth waveform is made up of both odd and even harmonics. Sawtooth have more of a brass and string instrument sound.
An Example of a sawtooth wave can be found on track 3 of my logic session which is with my assessment.

Square: The square waveform only contains odd harmonics so sounds not very nice by itself and sounds quite crunchy where as a triangle wave is just odd but they decrease amplitude a lot faster than square waves. These sound like plucked instrument or some low wind instruments. An Example of a square wave can be found on track 4 of my logic session which is with my assessment.

!!
Amplitude:

The amplitude is the distance above and below the centerline of a waveform and the bigger the distance between the center line and the wave then the higher the amplitude is (the louder it sounds).

Amplitude.
Amplitude.

Attack, Decay, Sustain, Release. These are called envelopes and are used to edit and manipulate the frequency over the occurring time and this can massively change the outcome of the sound.

time
time
release
release
Attack

Attack

Sustain

Sustain

Decay

Decay

Attack: The attack is how long it take for the sound to build up when the initial start of it is played. An acoustic sounding instrument with a fast attack is say a snare drum. An Example of a fast and slow attack can be found on track 5 and 6 of my logic session which is with my assessment.

Decay:...