Why is the intensity of waves in destructive interference still 2(A^2)?

[desmond iking]

Homework Statement

i don't 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?

Homework Equations

The Attempt at a Solution

 

[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.

 

[NascentOxygen]

Agree---pics too small.

 

[desmond iking]

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.

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

i don't 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

 

[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.

 

[desmond iking]

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.

sorry. i still don't understand. can you explain further? i can't 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)

 

[desmond iking]

why average intensity is used? and i don't understand how is the average intensity calculated.

 

[Simon Bridge]

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

 

[desmond iking]

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

intensity=power/area

why average intensity is used? and i don't understand how is the average intensity calculated.

why can't the phase difference of pi/3 leads to constructive intefreence?

 

[Simon Bridge]

intensity=power/area

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 )
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.

 

[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 ?

 

[desmond iking]

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 )
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.

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?

 

[NascentOxygen]

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)?

 

[desmond iking]

0...

 

[desmond iking]

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)?

i can understand why phase angle 160=200.. for the second diagram, i can also say that 120=240 degree... but this doesn't comply with the statement that the phase difference between A1 and A2 is 60

 

[NascentOxygen]

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

 

[Simon Bridge]

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 ?

Go back t the question - what does it say?