The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples of music being performed consist of a single source playing a single frequency for an extended period of time. A single frequency of sound for an extended period might be monotonous to the point of irritation, similar to the unwanted drone of an aircraft engine or a loud fan. Music is pleasant and exciting due to mixing the changing frequencies of various instruments and voices.
An interesting phenomenon that occurs due to the constructive and destructive interference of two or more frequencies of sound is the phenomenon of beats. They look like a single sinusoidal wave with a varying amplitude that goes from a maximum to zero and back. The amplitude variation causes variations of loudness, called beats, and the frequency with which the loudness varies is called the beat frequency. It is defined as the difference between the two frequencies.
Piano tuners can use these beats to tune a piano. A tuning fork is struck, and a note is played on the piano. When the piano tuner tunes the string, the beats have a lower frequency as the frequency of the note played approaches the frequency of the tuning fork.
Beats between two tones can be heard up to a beat frequency of about 6 or 7 Hz. The engines on multi-engine propeller aircraft have to be synchronized so that the propeller sounds do not cause annoying beats, which are heard as loud throbbing sounds. On some planes, this is done electronically; on others, the pilot does it by ear, just like tuning a piano.
