# Waveform

## Waveform of sound

Audio: waveform (0:02)

waveform plays the sound of a sine wave. The waveform figure shows its shape.

A waveform provides visual information about the shape of a sound.

A waveform is a graph in two dimensions. The vertical dimension shows the amplitude of the sound, a measure of how loud or soft it is. The horizontal dimension represents time and shows how amplitude fluctuates over time.

Waveforms come in all shapes and sizes. A sine wave has a smooth shape, other types of waveform have a different shape.

This chapter looks at the components of a waveform - frequency, amplitude and phase - and why the sine wave is so unique and important.

## Frequency

Audio: frequency (0:02)

frequency plays a sound with 100Hz frequency. The frequency figure shows a portion of the waveform. The shaded area represents one cycle of the wave and lasts for 10ms. 1 millisecond (ms) is one thousandth of a second.

Frequency is a measure of how often something recurs. In music, frequency is a measure of how often a sound wave recurs.

Frequency is measured in Hertz (Hz). One Hertz (1Hz) represents a frequency of one cycle per second.

Wavelength is the period it takes for a wave to repeat itself.

Wavelength is inversely proportional to frequency. A sound wave with a frequency of 100Hz repeats itself 100 times a second. Its wavelength is 1/100 seconds, or 10 milliseconds.

The relationship between frequency and wavelength can easily be demonstrated by playing an open string on a guitar or other stringed instrument, and then fretting it. A fretted string is shorter than an open string. The shorter wavelength of the fretted string makes its frequency higher than that of the open string.

## Amplitude

Audio: amplitude (0:02)

amplitude plays a sound with a frequency of 250Hz. The amplitude figure shows a portion of its waveform. Starting at zero, silence, the shaded area shows amplitude rising to its peak value, 0.89dBFS, one millisecond later. The amplitude table lists amplitude values in decibels and on a scale from 0 to 1.

Amplitude is a measure of loudness or volume.

Amplitude is measured in decibels (dB).

decibels full scale (dBFS) is used to measure amplitude in digital audio. Peak amplitude is always zero decibels full scale (0dBFS). There are two commonly used dBFS scales. The first, shown in the left-hand column of the amplitude table, is 0dBFS=0. In this scale amplitude values are negative below the peak. The second, shown in the right-hand column, is 0dBFS=1. In this scale amplitude values are positive and range between zero (silence) and 1 (peak).

All the music in the guide has a peak amplitude of -1dB on the 0dBFS=0 scale, 0.89 on the 0dBFS=1 scale.

Amplitude and power are both measured in decibels. They are related but distinct measures of loudness. Power is proportional to the square of amplitude. Doubling the amplitude of a sound, for example, makes the sound four times more powerful.

It is easy to get confused between power and amplitude. To (over)simplify, amplitude is an indirect measure of loudness, power is a direct measure. Power is usually what is being referred to when a sound is described as loud or soft. To confuse matters further, the term, gain is often used in music, although it is an ambiguous word, sometimes it means amplitude, other times it means power.

## Phase

Audio: phase (0:03)

phase plays three sounds in succession and the phase figure shows their respective waveforms. A sine wave with a frequency of 220Hz is the first sound, shown in the top waveform. A sine wave with a frequency of 228Hz is the second sound, shown in the middle waveform. The third sound, shown in the bottom waveform, plays both sine waves together. It shows the two sound waves interacting to produce a beating effect eight times every second (228Hz-220Hz=8Hz).

Phase is the fraction of a wave cycle which has elapsed relative to its start.

Beating is a physical phenomenon caused by the phase differences between two sounds.

Phase is measured in degrees of a circle. A periodic wave cycles through 360 degrees of phase. At the start the phase is zero degrees. At 90 degrees phase, the wave is one-quarter of the way through its cycle, at 180 degrees phase, half-way through, at 270 degrees phase, three quarters of the way through, and at 360 degrees the cycle is complete.

Phase can be ignored for much of the time. Most people are unable to perceive differences in the phase of a single sound.

Phase becomes important when two or more sounds are mixed (added) together. Mixing two sounds together causes the two sound waves to interact with each other. Sometimes the phases of both sounds interact to increase the total amplitude, other times the phases cancel each other out resulting in silence. phase illustrates this effect because the difference between the frequency of the two sounds is 8Hz and this causes the two sounds to beat eight times a second.

Phase really comes into its own in sound effects such as phasing.

## Sine wave

Audio: sine wave (0:02)

sine wave plays a 220Hz sine wave. The sine wave figure shows a close up of its waveform.

A sine wave is a sound with a single frequency.

It has three remarkable properties:

1. It contains a single frequency. A sine wave is the simplest sound there is. There is nothing simpler.
2. It is an artificial sound. A single sine wave does not exist in nature, a curious fact, but true. Whistling is about the closest you will come to a sine wave in real life. The only way to generate a single sine wave is to use a computer.
3. All sound consists of sine waves. This amazingly simple fact was discovered in the early nineteenth century by Joseph Fourier. Every sound that you hear consists of sine waves. Every sound can be broken down into its constituent sine waves. Any sound can be reconstructed by adding sine waves back together. Digital audio is based on breaking down and building up sine waves.

A sine wave has a thin quality to it and an artificial sound because it contains a single frequency. Some people find prolonged exposure to a single sine wave unnerving.