Homework Help: Destructive inteference

1. Jun 28, 2014

desmond iking

1. The problem statement, all variables and given/known data

i dont understand why the intensity of waves due to destructive inteference is still 2(A^2 ).... since this is destructive inteference why not the wave intensity=0? both waves are of same amplitude but antiphase. Am i right?

2. Relevant equations

3. The attempt at a solution

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2. Jun 28, 2014

Simon Bridge

destructuve interference need not be completely destructive... I think the phase diagram in your second pic shuld make the situation plain.
However, I cannot read the writing in the pics.

3. Jun 29, 2014

Staff: Mentor

Agree---pics too small.

4. Jun 29, 2014

desmond iking

here's the clearer pics. hopefully you can help.

i dont understand why the intensity of waves due to destructive inteference is still 2(A^2 ).... since this is destructive inteference why not the wave intensity=0? both waves are of same amplitude but antiphase. Am i right?
refer to the third pic

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5. Jun 29, 2014

Simon Bridge

Part (b) has two section - one where the phase difference produces total destructive interference and another where the phase difference is one-third that required for total destructive interference.
Since 180deg is required for total destruction, one-third of this is 60deg which is the phase difference shown in the third pic.

6. Jun 29, 2014

desmond iking

sorry. i still dont understand. can you explain further? i cant understand why the average amplitude is as in the photo,

since three vector in the same direction, i would do in this way,
adding up all the vector in clockwise direction, i would get 3(A^2)-(A^2)+(A^2)=3(A^2) magnitude of y1-y2=3(A^2) whereas y1=y2=(A^2)

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Last edited: Jun 29, 2014
7. Jun 29, 2014

desmond iking

why average intensity is used? and i dont understand how is the average intensity calculated.

8. Jun 29, 2014

Simon Bridge

Question b(ii) concerns power carried by the waves.
How is the power related to the intensity?

9. Jun 29, 2014

desmond iking

intensity=power/area

why average intensity is used? and i dont understand how is the average intensity calculated.

why cant the phase difference of pi/3 leads to constructive intefreence?

Last edited: Jun 29, 2014
10. Jun 29, 2014

Simon Bridge

When it is a wave - the intensity is the average power (over one wavelength), per unit area.

$P=I_{ave}A$

http://en.wikipedia.org/wiki/Intensity_(physics [Broken])
http://webpages.ursinus.edu/lriley/courses/p212/lectures/node18.html

The instantaneous intensity is proportional to the instantaneous amplitude squared.
For a stationary target, this will increase and decrease as the wave arrives.
i.e waves arriving at the beach deliver energy in surges, back and forth.

Last edited by a moderator: May 6, 2017
11. Jun 30, 2014

desmond iking

do you mean the author is finding the average intensity of constructive superposition and desrtuctive superposition? where constructive superposition leads to 3A^2 , and destructive superposition leads to A^2 ?

12. Jun 30, 2014

desmond iking

the upper part is for constructive superposition, the lower part is for desrtuctive superposition, the upper part shows phase difference of 60 degree... but the lower part shows phase difference of 120. (but not 60 degree) how can this happen? I know that constructive superposition occurs when phase difference less than 180 degree. Whereas destructive superposition occurs when phase difference more than 180.. is my conceptand working correct?

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13. Jun 30, 2014

Staff: Mentor

A phase difference greater than 180° is the same as a phase difference less than 180°. For example, phase difference of 200° is the same as a phase difference of 160°.

Perhaps generalize the topic this way:

When a pair of sine waves each of amplitude A superimpose at some point such that the resultant sine wave has

(i) an amplitude > A then we have constructive interference;

(ii) an amplitude < A then we have destructive interference;

(iii) an amplitude = A then we have no interference.

Question for desmond iking: What phase difference is needed to give condition (iii)?

14. Jun 30, 2014

desmond iking

0...

15. Jun 30, 2014

desmond iking

i can understand why phase angle 160=200.. for the second diagram, i can also say that 120=240 degree... but this doesnt comply with the statement that the phase difference between A1 and A2 is 60

Last edited: Jun 30, 2014
16. Jun 30, 2014

Staff: Mentor

The second diagram seems to show subtracting one from the other, whereas superposition involves addition.

17. Jul 1, 2014

Simon Bridge

Go back t the question - what does it say?