Page 27 - The Master Handbook Of Acoustics

2 CHAPTER ONE

The same situation exists between intensity and loudness. The rela-
tionship between the two is not linear. This is considered later in more
detail because it is of great importance in high fidelity work.
Similarly, the relationship between waveform (or spectrum) and
perceived quality (or timbre) is complicated by the functioning of the
hearing mechanism. As a complex waveform can be described in
terms of a fundamental and a train of harmonics (or partials) of various
amplitudes and phases (more on this later), the frequency-pitch inter-
action is involved as well as other factors.

The Simple Sinusoid

The sine wave is a basic waveform closely
related to simple harmonic motion. The
5
weight (mass) on the spring shown in Fig.
1-1 is a vibrating system. If the weight is
pulled down to the 5 mark and released,
0 W
the spring pulls the weight back toward 0.
The weight will not, however, stop at zero; its
inertia will carry it beyond 0 almost to 5.
5
The weight will continue to vibrate, or oscil-
FIGURE 1-1 late, at an amplitude that will slowly
A weight on a spring vibrates at its natural frequency decrease due to frictional losses in the spring,
because of the elasticity of the spring and the iner- the air, etc.
tia of the weight. The weight in Fig. 1-1 moves in what is
called simple harmonic motion. The pis-
ton in an automobile engine is connected to the crankshaft by a con-
necting rod. The rotation of the crankshaft and the up-and-down
motion of the pistons beautifully illustrate the relationship between
rotary motion and linear simple harmonic motion. The piston position
plotted against time produces a sine wave. It is a very basic type of
mechanical motion, and it yields an equally basic waveshape in sound
and electronics.
If a ballpoint pen is fastened to the pointer of Fig. 1-2, and a strip of
paper is moved past it at a uniform speed, the resulting trace is a sine
wave.
In the arrangement of Fig. 1-1, vibration or oscillation is possible
because of the elasticity of the spring and the inertia of the weight.