The decibel scale

The decibel scale

L = 20 log (p/p0)

 

In acoustics, the decibel (dB) scale is a scale for measuring the relative loudness of two sounds. For example, environmental noise is often measured as follows:

L = 20 log (p/p0)

Where L is the sound pressure level (in dB), p is the sound pressure amplitude, and p0 is a reference amplitude of 20 micropascals (less than one billionth of atmospheric pressure). On this scale, a barely audible sound (p = p0) has a sound pressure level of 0 dB, normal conversation (p = 1,000*p0) is at a level of around 60 dB, and a jet engine at close range (p = 1,000,000*p0) is at a level of around 120 dB.

Similar decibel scales are used in other branches of science and engineering to measure electrical power levels and other signal levels, always with respect to some reference level.

Recording a sound

Recording a sound

To record digital audio, your computer monitors the electrical signal generated by a microphone (or some other electro-acoustical device). Because the signal is caused by a sound, the signal strength varies in direct proportion to the sound’s waveform. The computer measures and saves the strength of the electrical signal from the microphone, thus recording the waveform.

There are two important aspects of this measuring process. First is the sampling rate, the rate at which the computer saves measurements of the signal strength. It is a known fact of physics that you must measure, or sample, the signal at a rate at least twice that of the highest frequency you want to capture. For example, suppose you want to record a moderately high note on a violin—say the A whose fundamental frequency is 440 Hz and all overtones up to five times the fundamental. The highest frequency you want to capture is 2,200 Hz, so you need to measure the electrical signal from the microphone at least 4,400 times per second.

Since humans can hear frequencies well above 10 kHz, most sound cards and digital recording systems are capable of sampling at much higher rates than that. Typical sampling rates used by modern musicians and audio engineers are 22 kHz, 44.1 kHz, and 48 kHz. The 44.1 kHz rate is called CD-quality, since it is the rate used by audio compact discs.

The other important aspect of the measuring process is the sampling resolution. The sampling resolution determines how accurately the amplitude of each sample is measured. At present, the music industry has settled on a system that provides 65,536 different values to assign to the amplitude of a waveform at any given instant. Thus, each sample saved by your computer requires 2 bytes (16 bits) to store, since it takes 2 bytes to store a number from –32,768 to 32,767. The scaling of the electrical input signal level to amplitude value is determined by your audio hardware and by the position of your input level control.

What if the amplitude of the sampled signal gets too high, such that a 16-bit number is not large enough to represent it? What typically happens is that the signal is clipped, cut off at the maximum value.

Here is what a clipped waveform might look like:

Clipping is not usually desirable and may have unpleasant audible effects. Sudden irregularities in the waveform of any type can cause clicks, pops, and distortion of the original sound.