Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs results in a reduction of amplitude known as destructive interference. When the identical waves are out of phase by 180°, the interference results in complete annulment.
For example, take the case of two speakers being driven by a single signal generator. The sound waves produced by the speakers are in phase and are of a single frequency, and interfere with each other. When two crests or two troughs coincide, there is constructive interference. Similarly, when a trough and a crest coincide, destructive interference occurs. The phase difference is due to the path lengths traveled by the individual waves. If the difference in the path lengths is one wavelength, it leads to total constructive interference and a resulting amplitude equal to twice the original amplitude. If the difference in the path lengths is less than one wavelength but greater than half a wavelength, it results in an amplitude greater than zero and less than twice the original amplitude. Lastly, if the difference in the path lengths is half a wavelength, it leads to total destructive interference and a resulting amplitude equal to zero.
A clever application of interference in everyday situations can be seen in a pair of headphones. In recent times, headphones have been designed to cancel noise with destructive interference by creating a sound wave opposite the incoming sound. These headphones can be more effective than the simple passive attenuation used in most forms of ear protection. Pilots onboard the Voyager aircraft, which holds the record for a nonstop flight around the world, use such headphones to protect their ears against the engine noise.
This text is adapted from Openstax, University Physics Volume 1, Section 17.4: Normal Modes of a Standing Sound Wave.
