AET 2050 - DAW Production

2. Physics of Sound

Objectives:

1. Define the following terms:
• Waveform
• Amplitude
• Cycle
• Frequency
• Velocity
• Wavelength
• Period
2. Differentiate between a simple and a complex waveform.
3. For a given fundamental frequency, determine a specified overtone, partial, or harmonic.
4. Understand the information conveyed by a frequency spectrum graph.

Waves

The following is a list of terms used to describe sound waves: Waveform (waveshape) - A graphic representation of sound-pressure level over time.

Amplitude (displacement) - The vertical distance above or below the zero line (normal atmospheric pressure) at that particular instant of time. The maximum excursions are referred to as the peak amplitudes.

Amplitude is measured logarithmically using a decibel unit. A doubling of a signal's amplitude gives a 6dB increase. A halving of a signal's amplitude gives a 6dB decrease.

Cycle - One complete pass from one point in a waveform to the other.

Frequency - The rate at which an object repeats a cycle of positive and negative amplitude. The number of cycles that occur in one second is measured in hertz (Hz). One kilohertz (kHz) is equivalent to 1,000 hertz (or 1,000 cycles per second).

Velocity - The speed at which a wave travels through a medium. At 70 degrees Fahrenheit, the speed of sound waves in air is approximately 1130 feet per second. This speed changes with different temperatures and mediums. (distance/velocity = time) As sound travels, high frequencies are more prominently attenuated than low frequencies.

Wavelength - The distance covered by one cycle. (wavelength = velocity/frequency.. for example: 1130/30 = 37.66 feet)

Period The time it takes to complete one cycle. (1/frequency = period)

Consider a continuous sine wave: It is periodic, or repeating.

It is simple, or contains only one frequency.

Consider a continuous square wave: It is periodic, or repeating.

It is complex, in that it is composed of multiple frequencies.

French physicist Jean-Baptiste Fourrier (1768-1830) discovered that any complex wave can be decomposed into a fundamental sine wave and a set of harmonic sine waves. Harmonics are integer multiples of a given frequency. The 1st harmonic is the fundamental, and the others are overtones or partials.

 1st partial or harmonic (the fundamental) 100 Hz 2nd partial or harmonic (1st overtone) 200 Hz 3rd partial or harmonic (2nd overtone) 300 Hz 4th partial or harmonic (3rd overtone) 400 Hz 5th partial or harmonic (4th overtone) 500 Hz 6th partial or harmonic (5th overtone) 600 Hz 7th partial or harmonic (6th overtone) 700 Hz 8th partial or harmonic (7th overtone) 800 Hz

The harmonic series for a 100 Hz tone

In the case of the square wave, there is a fundamental frequency and a series of odd harmonics. The amplitude of each harmonic is inversely proportional to the fundamental by a factor equal to its harmonic number.

### 1st partial or harmonic (the fundamental) 100 Hz 3rd partial or harmonic (2nd overtone) 300 Hz 1/3 the amplitude 5th partial or harmonic (4th overtone) 500 Hz 1/5 the amplitude 7th partial or harmonic (6th overtone) 700 Hz 1/7 the amplitude 9th partial or harmonic (7th overtone) 900 Hz 1/9 the amplitude

The harmonic series for a 100 Hz square wave

Any wave with a sharp edge (a fast rise or fall time) will contain a number of upper harmonics and possess a very high frequency content.

Consider a noise wave (representative of true audio): It is aperiodic - it does not have a repeating pattern.

It is also complex, made up of a series of frequencies combined together.

Representing waves in different domains

The previous figures show sound waves in the time domain - how the wave behaves over time. Often, it is better to analyze a sound signal in the frequency domain. A frequency spectrum shows the the frequency content of a given period of a signal.

Fourrier's work establishing the relationship between time and frequency allows us to transform a wave from the time domain to the frequency domain. Looking at sound this way will display the frequency spectrum of a given wave.      The spectrum defines the frequencies included in a given period of a wave.

filters

A filter is used to limit the frequency of a signal:

High-Pass Low-pass Band-pass Consider a low-pass filter applied to an impulse:

A frequency spectrum: The filter has a cutoff frequency, fc (in the diagram, fs/2)

The output will cross zero at 2fc (or fs in the diagram)

This will become more apparant when discussing sampling.

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