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Learning object 7
1. JennyGu
11779148
Physics 101 Learning Object
Considertwosourcesof sound,eachemittingsoundof wavelength1m.Imagine Source 2 is6m south of
Source 1, anda personisstandingtothe east of the sources,creatingan equilateraltrianglewiththe
sources.
a. How many wavelengthsawayisthe personfromSpeaker1 andSpeaker2?
b. At the pointwhere the personisstanding,is perfectconstructive interference, perfect
destructive interference,orneitheroccurring? Explain.
c. What isthe pathdifference betweenthe twosourcesandthe person?
d. If the personwere towalkina straightline west,whattype of interference wouldthey
experience?
e. If the personwere towalktowardsone of the sourcesof sound,wouldtheyencounterapoint
where interferenceisperfectlyconstructive,orperfectlydestructive?
Solution
a. The personis 6 wavelengthsfromSpeaker1,and6 wavelengthsfromSpeaker2.
b. At the pointwhere the personisstanding,constructiveinterferenceisoccurringbecause the
path lengthsof eachof the twowavestothe pointwhere the personisstandingare integer
multiplesof the wavelength.
c. ∆d = d2 – d1 = 6λ - 6λ = 0
d. If the personwalkedwest,theywouldcontinue toexperience constructive interference asthe
path differencesateverypointof thatline wouldbe zero.
e. For the interference tobe perfectlyconstructive orperfectlydestructive,the pathlengthsmust
be integermultiplesof the wavelength,orthe pathdifference mustbe ahalf-integermultipleof
the wavelength,respectively.
In the diagrambelow,itisassumedthaty isequal to 5.5m, 5m, 4.5m, etc. if the interferenceis
constructive ordestructive atthatpoint.Usingthe cosine law (c2
= a2
+ b2
– 2abcosθ),x can be
determinedasfollows:x = sqrt[y2
+ 62
– 2(y)(6)cos(π/3)].Thiscanbe solvedbyhand, or using
Excel.
2. JennyGu
11779148
The results correspondingx andyintegervaluesatthe initial positionof the person,andatthe position
of the sourcesof sound.Thismeansthat there isperfectlyconstructive interference atthose two
locations.However, there isnootherpointof perfectconstructive ordestructiveinterference alongthe
path fromthe person’sinitial positiontoanyof the twosourcesof sound.Thisisbecause there are no
correspondingintegerorhalf-integervaluesof x tothose of y alongthat path.
![JennyGu
11779148
Physics 101 Learning Object
Considertwosourcesof sound,eachemittingsoundof wavelength1m.Imagine Source 2 is6m south of
Source 1, anda personisstandingtothe east of the sources,creatingan equilateraltrianglewiththe
sources.
a. How many wavelengthsawayisthe personfromSpeaker1 andSpeaker2?
b. At the pointwhere the personisstanding,is perfectconstructive interference, perfect
destructive interference,orneitheroccurring? Explain.
c. What isthe pathdifference betweenthe twosourcesandthe person?
d. If the personwere towalkina straightline west,whattype of interference wouldthey
experience?
e. If the personwere towalktowardsone of the sourcesof sound,wouldtheyencounterapoint
where interferenceisperfectlyconstructive,orperfectlydestructive?
Solution
a. The personis 6 wavelengthsfromSpeaker1,and6 wavelengthsfromSpeaker2.
b. At the pointwhere the personisstanding,constructiveinterferenceisoccurringbecause the
path lengthsof eachof the twowavestothe pointwhere the personisstandingare integer
multiplesof the wavelength.
c. ∆d = d2 – d1 = 6λ - 6λ = 0
d. If the personwalkedwest,theywouldcontinue toexperience constructive interference asthe
path differencesateverypointof thatline wouldbe zero.
e. For the interference tobe perfectlyconstructive orperfectlydestructive,the pathlengthsmust
be integermultiplesof the wavelength,orthe pathdifference mustbe ahalf-integermultipleof
the wavelength,respectively.
In the diagrambelow,itisassumedthaty isequal to 5.5m, 5m, 4.5m, etc. if the interferenceis
constructive ordestructive atthatpoint.Usingthe cosine law (c2
= a2
+ b2
– 2abcosθ),x can be
determinedasfollows:x = sqrt[y2
+ 62
– 2(y)(6)cos(π/3)].Thiscanbe solvedbyhand, or using
Excel.](https://image.slidesharecdn.com/learningobject2-150315231317-conversion-gate01/85/Learning-object-7-1-320.jpg)
