Sampling resolution 4.5
When sound is represented digitally the amplitude of the sound wave is taken at different points in time and recorded as a number. How often a sample is taken defines the sampling rate. What number is used to record the amplitude of each sample defines the sampling resolution. In 8-bit recording, for example, each sample is represented by an 8-bit number. Eight bits can only represent 256 numbers (2 to the power of 8) and so only 256 different amplitudes can be written. This makes for a very small dynamic range of a sound recording. A 16-bit recording uses 16 bits for each sample. 16 bits can represent 65,536 different numbers and amplitudes, which makes for a much better dynamic range.
The sampling resolution is the representation (or size of the numbers) used to write samples in digital sound recording.
The sampling resolutions used regularly in current digital music practice are: 8-bit, 16-bit, 24-bit, and 32-bit. 8-bit digital sound uses only positive (unsigned) integer numbers by convention, but not always. 16-bit and 24-bit digital sound usually uses positive and negative (signed) integer numbers. 32-bit sound is rare and usually uses signed floating point numbers between -1 and 1. 16 bits are used in contemporary CD audio.
The selection of the 16-bit sampling resolution used in CD audio was not chosen at random. 16 bits can properly represent dynamic ranges of about 90 dB, which is basically the maximum dynamic range of human hearing.
The advantages and disadvantages of larger and smaller sampling resolutions are obvious. Larger sampling resolutions allow for larger dynamic ranges, but require more recording space.
Frequency, wavelength, amplitude and wave speed
You need to know about these quantities used in waves – what they mean, the symbols used for them and the units used to measure them.
The amplitude, a, of a wave is the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough. Be careful with this quantity – the centre line is not always given in a diagram. Amplitude is measured in metres (m). The greater the amplitude of a wave then the more energy it is carrying.
The wavelength, λ, of a wave is the distance from any point on one wave to the same point on the next wave along. (The symbol is a Greek letter, ‘lambda’.) To avoid confusion, it is best to measure wavelength from the top of a crest to the top of the next crest, or from the bottom of a trough to the bottom of the next trough. Wavelength is also measured in metres (m) – it is a length after all.
The frequency, f, of a wave is the number of waves passing a point in a certain time. We normally use a time of one second, so this gives frequency the unit hertz (Hz), since one hertz is equal to one wave per second.
Don’t get confused with this quantity frequency. It is not a distance travelled by waves, nor is it a speed, although it is linked to both of these quantities. For water waves and sound waves the unit hertz is usually good enough but radio and TV waves have such a high frequency that the kilohertz (kHz) or even the megahertz (MHz) are better units.
- 1 kHz = 1,000 Hz
- 1 MHz = 1,000,000 Hz
The speed (or sometimes you might see it called velocity) of a wave, v, is how far the wave travels in a certain time.
Wave speed is measured in metres per second (m/s).
All the electromagnetic waves travel at 300,000,000 metres per second (3 x 108 m/s). Sound travels at about 340 metres per second.