The Interference of Sound Waves

The Principle of Superposition The Principle of Superposition states that when 2 waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location. Example:

The Principle of Superposition Each pulse has a constant speed of 1 cm/s. When t=2sec, what is the height of the resultant pulse at (a) x=3cm and (b) x=4cm?

Constructive Interference The sum of two crests is referred to as a supercrest. The sum of two troughs is referred to as a supertrough.

Destructive Interference Complete destructive interference results in nodes. Demo

The Effect of Interference An increase in amplitude indicates an increase in energy, which for sound waves means an increase in the intensity or volume of the sound.

2-Source Interference Two sources (here, two speakers) will produce an interference pattern.

2-Source Interference Two sources (here, two speakers) will produce an interference pattern. Areas of constructive interference will experience an increase in volume.

2-Source Interference Areas of destructive interference (the grey lines, called nodal lines) will experience a decrease in volume.

2-Source Interference When 2 waves always meet condensation to condensation and rarefaction-to-rarefaction, they are said to be exactly in phase. When 2 waves always meet condensation-to- rarefaction, they are said to be exactly out of phase.

2-Source Interference Auditoriums and many other public spaces are designed with walls (and ceilings and baffles) that will trap and absorb sound energy rather than reflect it so the reflections cannot interfere with the original waves and distort the sound.

2-Source Interference For 2 wave sources vibrating in phase: Constructive interference occurs when the difference in path lengths is 0 or an integer number of wavelengths.

2-Source Interference For 2 wave sources vibrating in phase: Destructive interference occurs when the difference in path lengths is a half integer number of wavelengths.

Noise-Reduction Headphones Noise-reduction headphones cancel ambient sound by producing sound that is ½ wavelength out of phase with the ambient sound (this works best for single frequencies).

Example Two in-phase loudspeakers are separated by 3.2m. A listener is situated at point C, which is 2.4m in front of speaker B. Both speakers are playing identical 214-Hz tones, and the speed of sound is 343 m/s. Does the listener hear a loud sound or no sound?