of Microprocessors

16 MUSICAL APPUCATIONS OF MICROPROCESSORS
The Amplitude Parameter
The other parameter that describes a sine wave is the amplitude. The
amplitude parameter is related to the height of the wave in a plot such as in
Fig. 1-2A. In the air, amplitude would actually relate to the degree of
change in air pressure, whereas in an electronic circuit it would relate to the
voltage or current in the circuit.
The most obvious way to specify the amplitude ofa sine wave is to find
the minimum voltage and the maximum voltage in the course of one cycle
and express the amplitude as the difference between the extremes. This is
termed the peak-to-peak amplitude. Another method is to specify the average
amplitude, which is the long time average difference between the instantaneous
waveform voltage and the baseline. A typical voltmeter would respond to
this average rather than the actual peaks of the waveform. A third method
relates the amount of heat produced in a resistor connected to the source of
the sine wave voltage to the amount of heat produced when the same resistor
is connected to a source of constant dc voltage. The dc voltage required to
produce the same amount ofheat is called the effective voltage of the sine wave
or its root-mean-square value which is abbreviated rms. Of the amplitude
specification methods, the rms technique most accurately correlates with
what the ear hears, whereas the peak-to-peak: method most accurately predicts
the possibility of unwanted distortion in electronic recording and synthesis
equipment.
The most common unit for amplitude specification when a waveform is
being examined is simply the volt. In rare cases, a current waveform may be
of interest so the amplitude would be specified in milliamperes or amperes.
When a signal is being delivered to a speaker, however, the amplitude is
usual!y expressed as power in watts. The power in a signal can be calculated
in several ways. The simplest is to multiply the instantaneous voltage by the
instantaneous current and average the product over one repetition of the
waveform. Another method is to square the rms voltage of the waveform and
divide the result by the speaker impedance, which is accurate only if the
speaker impedance is purely resistive.
The human ear is capable of responding to a very wide range of sound
amplitudes. The amount of sound power at 2,000 Hz that can be listened to
without undue discomfort is about a trillion (0 12 ) times greater than the
power in a barely audible sound. For convenience in working with such a
wide range of power, the bel scale (named after Alexander Graham Bell) of
sound intensity was developed. Like musical pitch units the bel scale is
relative. The bel unit refers to a ratio of 10 between the power oftwo sounds.
Thus, sound B contains 1.0 bel more power than sound A if it is 10 times as
powerful. Conversely, sound A would be 1 bel less powerful or -1.0 bel
with respect to sound B. Expressed using the bel scale, the range of hearing
would be 12 bels.