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

Wave InterferenceWave InterferenceFor complete destructive interference For complete destructive interference

to occur, two pulses must have:to occur, two pulses must have:

the same ____________________the same ____________________

and equal magnitude but opposite and equal magnitude but opposite directiondirection

________________________________

Wave InterferenceWave InterferenceFor complete destructive interference For complete destructive interference

to occur, two pulses must have:to occur, two pulses must have:

the same the same pulse width or wavelengthpulse width or wavelength

and equal magnitude but opposite and equal magnitude but opposite directiondirection amplitude (height)amplitude (height)

The Interference The Interference of Sound Wavesof Sound Waves

3U Physics3U Physics

Minds-ON QuestionMinds-ON Question We talked yesterday about ear bud We talked yesterday about ear bud

dangers. If common wisdom is that dangers. If common wisdom is that noise-reduction headphones are noise-reduction headphones are advisable, provide an explanation for advisable, provide an explanation for how how theythey work work

SuperpositionSuperpositionNot superimposing….Not superimposing….which is the adding of which is the adding of images with one of images with one of them covered permanentlythem covered permanently

Superposition is “The displacement of a Superposition is “The displacement of a medium caused by two or more waves is medium caused by two or more waves is the algebraic sum of the amplitudes of the the algebraic sum of the amplitudes of the waves”waves”

The Principle of The Principle of SuperpositionSuperposition

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

Constructive Constructive InterferenceInterference

The sum of two crests is referred to as a ?The sum of two crests is referred to as a ?

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

Constructive Constructive InterferenceInterference

The sum of two crests is referred to as a The sum of two crests is referred to as a supercrestsupercrest..

The sum of two troughs is referred to as a The sum of two troughs is referred to as a supertroughsupertrough..

Destructive InterferenceDestructive InterferenceComplete destructive interference Complete destructive interference

results in results in nodesnodes..

The Effect of The Effect of InterferenceInterference

An increase in An increase in amplitude amplitude indicates an indicates an increase in ?increase in ?


An increase in An increase in amplitude amplitude indicates an indicates an increase in increase in energy, which energy, which for sound waves for sound waves means an means an increase in increase in the ?the ?


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

Noise-Reduction Noise-Reduction HeadphonesHeadphones

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

Very Different Very Different FrequenciesFrequencies

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


Frequencies in the Frequencies in the ratio of 2:1 are an ratio of 2:1 are an octaveoctave..


The resulting The resulting interference interference pattern will be pattern will be non-repeating and non-repeating and therefore therefore dissonantdissonant if the if the ratio between the ratio between the frequencies is frequencies is notnot a small whole-a small whole-number ratio:number ratio:

Slightly Different Slightly Different FrequenciesFrequencies

What if we have two sources with What if we have two sources with slightlyslightly different frequencies?different frequencies?

Sometimes the interference will be Sometimes the interference will be constructive (increased intensity) and constructive (increased intensity) and sometimes destructive (decreased sometimes destructive (decreased intensity).intensity).

Different FrequenciesDifferent FrequenciesThis variation in intensity is heard as a This variation in intensity is heard as a

variation in volume known as “beats.”variation in volume known as “beats.”

Different FrequenciesDifferent FrequenciesThe beat frequency is equal to the The beat frequency is equal to the

difference between the two frequencies. difference between the two frequencies. E.g. if tuning forks of 255 Hz and 257 Hz E.g. if tuning forks of 255 Hz and 257 Hz

are struck simultaneously, beats will be are struck simultaneously, beats will be heard at a frequency of 2 Hz (2 per heard at a frequency of 2 Hz (2 per second).second).

The closer the frequencies, the lower the The closer the frequencies, the lower the beat frequency.beat frequency.

Doppler and Beats Doppler and Beats ExampleExample

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



Hzf

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sourcemovingtheFor

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sm

sm

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sourcesound

sourcesoundobs

5585344

550344

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Hzf

Hzf

vvfvf

sourcemovingtheFor

obs

sm

sm

sm

obs

sourcesound

sourcesoundobs

5585344

550344

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HzHzHzfrequencyBeat 8550558

Interference and the Interference and the ListenerListener

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

2-Source Interference2-Source InterferenceTwo sources Two sources

(here, two (here, two speakers) will speakers) will produce an produce an interference interference patternpattern..

2-Source Interference2-Source InterferenceTwo sources (here, Two sources (here,

two speakers) will two speakers) will produce an produce an interference interference patternpattern..

Areas of constructive Areas of constructive interference will interference will experience an experience an increase in volume.increase in volume.

2-Source Interference2-Source InterferenceAreas of Areas of

destructive destructive interference interference (the grey lines, (the grey lines, called called nodal nodal lineslines) will ) will experience a experience a decrease in decrease in volume.volume.

2-Source Interference2-Source InterferenceAuditoriums and many Auditoriums and many

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

More PracticeMore Practice The Interference of The Interference of

Sound Waves: Sound Waves: An Inquiry ActivityAn Inquiry Activity

Homework Set 11: Homework Set 11: Sound InterferenceSound Interference

Documents

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