![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)
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- 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.