Page 273 - The Master Handbook Of Acoustics

248 CHAPTER ELEVEN

1
For an answer, the work of Huygens is consulted. He enunciated a
principle that is the basis of very difficult mathematical analyses of
diffraction. The same principle also gives a simple explanation of how
sound energy is diverted from the main beam into the shadow zone.
Huygens’ principle can be paraphrased as:
Every point on the wavefronts of sound that has passed through an
aperture or passed a diffracting edge is considered a point source radi-
ating energy back into the shadow zone.
The sound energy at any point in the shadow zone can mathemati-
cally be obtained by summing the contributions of all of these point
sources on the wavefronts.
In Fig. 11-2A, each wavefront passing through the aperture
becomes a row of point sources radiating diffracted sound into the
shadow zone. The same principle holds for Fig. 11-2B except that the
aperture is very small and only a small amount of energy passes
through it. The points on the limited wavefront going through the hole
are so close together that their radiations take the form of a hemi-
sphere.

Diffraction of Sound by Obstacles

In Fig. 11-3A the obstacle is so small compared to the wavelength of
the sound that it has no appreciable effect on the passage of sound. In
Fig. 11-3B, however, the obstacle is many wavelengths long and it has
a definite effect in casting a shadow behind the obstacle. Each wave-
front passing the obstacle becomes a line of new point sources radiat-
ing sound into the shadow zone.
A very common example of an obstacle large compared to the
wavelength of the impinging sound is the highway noise barrier
shown in Fig. 11-4. If the wavelength of the impinging sound is indi-
cated by the spacing of the spherical wavefronts hitting the barrier, the
barrier size is acoustically great. At higher frequencies the barrier
becomes even larger, and at lower frequencies it becomes acoustically
smaller. First, the sound reflected from the wall must be noted. It is as
though the sound were radiated from a virtual image on the far side of
the wall. The wavefronts passing the top edge of the wall can be con-
sidered as lines of point sources radiating sound. This is the source of
the sound penetrating the shadow zone.