Wave Interference For complete destructive interference to occur, two pulses must have: the same ____________________ and equal magnitude but opposite direction ________________ ________________

Wave Interference For complete destructive interference to occur, two pulses must have: the same pulse width or wavelength and equal magnitude but opposite direction amplitude (height) amplitude (height)

The Interference of Sound Waves 3U Physics

Minds-ON Question We talked yesterday about ear bud dangers. If common wisdom is that noise-reduction headphones are advisable, provide an explanation for how they work We talked yesterday about ear bud dangers. If common wisdom is that noise-reduction headphones are advisable, provide an explanation for how they work

Superposition Not superimposing…. which is the adding of images with one of them covered permanently Superposition is “The displacement of a medium caused by two or more waves is the algebraic sum of the amplitudes of the waves” Superposition is “The displacement of a medium caused by two or more waves is the algebraic sum of the amplitudes of the 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, 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:

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

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.

The Effect of Interference An increase in amplitude indicates an increase in ?

The Effect of Interference An increase in amplitude indicates an increase in energy, which for sound waves means an increase in the ?

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.

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).

Very Different Frequencies If two very different frequencies are sounded at the same time, the resulting interference pattern will be repeating and therefore sound musical (consonant) if the ratio between the frequencies is a small whole-number ratio:

Very Different Frequencies Frequencies in the ratio of 2:1 are an octave.

Very Different Frequencies The resulting interference pattern will be non- repeating and therefore dissonant if the ratio between the frequencies is not a small whole- number ratio:

Slightly Different Frequencies What if we have two sources with slightly different frequencies? Sometimes the interference will be constructive (increased intensity) and sometimes destructive (decreased intensity).

Different Frequencies This variation in intensity is heard as a variation in volume known as “beats.”

Different Frequencies The beat frequency is equal to the difference between the two frequencies. E.g. if tuning forks of 255 Hz and 257 Hz are struck simultaneously, beats will be heard at a frequency of 2 Hz (2 per second). The closer the frequencies, the lower the beat frequency.

Doppler and Beats Example A car with a siren of 550-Hz is driving toward an observer at a speed of 5 m/s. Another car with a siren of 550 Hz is parked beside the observer. What is the beat frequency heard by the observer? Assume the speed of sound in air is 344 m/s.

Doppler and Beats Example A car with a siren of 550-Hz is driving toward an observer at a speed of 5 m/s. Another car with a siren of 550 Hz is parked beside the observer. What is the beat frequency heard by the observer? Assume the speed of sound in air is 344 m/s.

Doppler and Beats Example A car with a siren of 550-Hz is driving toward an observer at a speed of 5 m/s. Another car with a siren of 550 Hz is parked beside the observer. What is the beat frequency heard by the observer? Assume the speed of sound in air is 344 m/s.

Interference and the Listener Of course, what is heard by the listener will depend on the location of the listener....

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 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.

More Practice The Interference of Sound Waves: The Interference of Sound Waves: An Inquiry Activity Homework Set 11: Sound Interference Homework Set 11: Sound Interference