Handbook for Sound Engineers

Fundamentals of Audio and Acoustics 31

summation is determined by the relative phase of the

individual waves. Let’s consider how two waves might

combine at a point of observation. This point might be a

listener seat or microphone position. Two extremes

exist. If there is no phase offset between two waves of

the same amplitude and frequency, the result is a

coherent summation that is twice the amplitude of either

individual wave (+6 dB). The other extreme is a 180°

phase offset between the waves. This results in the

complete cancellation of the pressure response at the

point of observation. An infinite number of intermediate

conditions occur between these two extremes. The

phase interaction of waves is not a severe problem for

analog audio signals in the electromagnetic domain for

sound systems, where the wavelengths at audio frequen-

cies are typically much longer than the interconnect

cables. Waves reflected from receiver to source are in

phase and no cancellation occurs. This is not the case

for video, radio frequency, and digital signals. The

shorter wavelengths of these signals can be dramatically

affected by wave superposition on interconnect cables.

As such, great attention must be given to the length and

terminating impedance of the interconnect cables to

assure efficient signal transfer between source and

receiver. The practice of impedance matching between

source, cable, and load is usually employed.

In sound reinforcement systems, phase interactions

are typically more problematic for acoustical waves

than electromagnetic waves. Phase summations and

cancellations are the source of many acoustical prob-

lems experienced in auditoriums. Acoustic wavelengths

are often short relative to the room size (at least at high

frequency), so the waves tend to bounce around the

room before decaying to inaudibility. At a listener posi-

tion, the reflected waves “superpose” to form a complex

waveform that is heard by the listener. The sound radi-

ated from multiple loudspeakers will interact in the

same manner, producing severe modifications in the

radiated sound pattern and frequency response. Antenna

designers have historically paid more attention to these

interactions than loudspeaker designers, since there are

laws that govern the control of radio frequency emis-

sions. Unlike antennas, loudspeakers are usually broad-

band devices that cover one decade or more of the

audible spectrum. For this reason, phase interactions

between multiple loudspeakers never result in the

complete cancellation of sound pressure, but rather

cancellation at some frequencies and coherent summa-

tion at others. The subjective result is tonal coloration

and image shift of the sound source heard by the

listener. The significance of this phenomenon is applica-

tion-dependent. People having dinner in a restaurant

Figure 2-13. Some surfaces produce focused reflections.
Courtesy Syn-Aud-Con.

Figure 2-14. Simple harmonic motion can be represented
with a sine or cosine wave. Both are viewpoints of the
same event from different angles. Courtesy Syn-Aud-Con.

Concave surfaces focus sound

Convex surfaces scatter sound

Corners return sound to its source