4 Chapter 1
Despite the fact that a gas contains endlessly colliding molecules, a small mass or particle
of gas can have stable characteristics because the molecules leaving are replaced by new
ones with identical statistics. As a result, acoustics seldom need to consider the molecular
structure of air and the constant motion can be neglected. Thus when particle velocity
and displacement are considered, this refers to the average values of a large number of
molecules. In an undisturbed container of gas, the particle velocity and displacement will
both be zero everywhere.
When the volume of a fi xed mass of gas is reduced, the pressure rises. The gas acts like
a spring; it is compliant. However, a gas also has mass. Sound travels through air by an
interaction between the mass and the compliance. Imagine pushing a mass via a spring. It
would not move immediately because the spring would have to be compressed in order to
transmit a force. If a second mass is connected to the fi rst by another spring, it would start
to move even later. Thus the speed of a disturbance in a mass/spring system depends on
the mass and the stiffness. Sound travels through air without a net movement of the air.
The speed of sound is proportional to the square root of the absolute temperature. On
earth, temperature changes with respect to absolute zero ( 273°C) also amount to around
1% except in extremely inhospitable places. The speed of sound experienced by most of
us is about 1000 ft per second or 344 m per second.
1.2 Wavelength
Sound can be due to a one-off event known as percussion, or a periodic event such as
the sinusoidal vibration of a tuning fork. The sound due to percussion is called transient,
whereas a periodic stimulus produces steady-state sound having a frequency f.
Because sound travels at a fi nite speed, the fi xed observer at some distance from the
source will experience the disturbance at some later time. In the case of a transient
sound caused by an impact, the observer will detect a single replica of the original as
it passes at the speed of sound. In the case of the tuning fork, a periodic sound source,
the pressure peaks and dips follow one another away from the source at the speed of
sound. For a given rate of vibration of the source, a given peak will have propagated a
constant distance before the next peak occurs. This distance is called the wavelength
lambda. Figure 1.2 shows that wavelength is defi ned as the distance between any two
identical points on the whole cycle. If the source vibrates faster, successive peaks get
closer together and the wavelength gets shorter. Figure 1.2 also shows that the wavelength