Interference between two waves problem

[lemin_rew]

Homework Statement

Assume that the waves from the sources are emitted in phase, and that at the point P, amplitude of the disturbance is zero. what is the wavelength of the traveling wave emitted by the sources? (there is more than one possible answer here,but provide the largest possible wavelength.)
Known:
r1=15.4cm
r2=16.2cm
d=1.8cm
θ=26.3°

Homework Equations

Δr=nλ

The Attempt at a Solution

maximum wavelength, n=0
Δr=|16.2cm-15.4cm|
=0.8cm
I am lost, please help me.

 

[TSny]

Note that when the waves combine at point P, the total distrubance has zero amplitude.

Is this constructive or destructive interference?

Are the two waves "in phase" or "out of phase" at point at point P?

What does the path difference Δr need to be in terms of λ in order to produce the answer to the previous question?

 

[lemin_rew]

Note that when the waves combine at point P, the total distrubance has zero amplitude.

Is this constructive or destructive interference?

Are the two waves "in phase" or "out of phase" at point at point P?

What does the path difference Δr need to be in terms of λ in order to produce the answer to the previous question?

it is destructive because the it has nodes(minimum amplitude), and they are out of phase.
the path difference Δr need to be the multiple of λ? I am not sure how to approach from now on...

 

[TSny]

it is destructive because the it has nodes(minimum amplitude), and they are out of phase.

Yes, that's right, they must be out of phase.

the path difference Δr need to be the multiple of λ?

No, this isn't correct. Suppose you draw two waves side by side with the same λ so that they are in phase (i.e., crest of one wave beside crest of the other wave). Now suppose you shift one wave by λ; that is, slide one wave by the distance λ relative to the other wave. Are the waves now in phase, out of phase, or something else?

 

[lemin_rew]

Yes, that's right, they must be out of phase.


No, this isn't correct. Suppose you draw two waves side by side with the same λ so that they are in phase (i.e., crest of one wave beside crest of the other wave). Now suppose you shift one wave by λ; that is, slide one wave by the distance λ relative to the other wave. Are the waves now in phase, out of phase, or something else?

so...then the waves are now in phase?
sorry i don't think I am understanding it...fully

 

[TSny]

so...then the waves are now in phase?
sorry i don't think I am understanding it...fully

Yes, if you slide one wave a distance λ relative to the other, then you will still have wave crests next to each other. So, they would still be in phase.

You want the waves to be out of phase. How far would you need to shift one wave in order to get it to be out of phase with the other wave?

 

[lemin_rew]

Yes, if you slide one wave a distance λ relative to the other, then you will still have wave crests next to each other. So, they would still be in phase.

You want the waves to be out of phase. How far would you need to shift one wave in order to get it to be out of phase with the other wave?

1? so then m=1 and
the equation becomes Δr=(m+1/2)λ
0.8cm (1+1/2)λ
λ=0.53?? is this right??...

 

[TSny]

No, not quite right yet. If two waves start out in phase and you want to get them out of phase, then one wave will need to be shifted so that a crest of one wave is now next to a trough of the other wave. Since the distance between a crest and a trough is (1/2)λ, you need to shift one of the waves by (1/2)λ. Or, you could shift by (1 + 1/2)λ, (2+1/2)λ, (3+1/2)λ, etc. In general, the waves will end up out of phase if the shift is (m+1/2)λ where m can be 0, 1, 2, 3, ...

So, you need the path difference Δr to be one of these possible shifts. Pick the shift that gives the largest λ for the answer.

 

[lemin_rew]

No, not quite right yet. If two waves start out in phase and you want to get them out of phase, then one wave will need to be shifted so that a crest of one wave is now next to a trough of the other wave. Since the distance between a crest and a trough is (1/2)λ, you need to shift one of the waves by (1/2)λ. Or, you could shift by (1 + 1/2)λ, (2+1/2)λ, (3+1/2)λ, etc. In general, the waves will end up out of phase if the shift is (m+1/2)λ where m can be 0, 1, 2, 3, ...

So, you need the path difference Δr to be one of these possible shifts. Pick the shift that gives the largest λ for the answer.

so then, when m=0 gives the biggest wavelength.
hence, 0.8cm=(0+1/2)λ
λ=1.6cm.
is this correct?

 

[TSny]

OK, so you will chose m = 0 to get the longest wave. I'm not sure if you have the correct answer yet, since I'm not sure of the meaning of r1 and r2. Are they the distances from the sources to the point P. What does the angle 26.3^o represent in the problem?

 

[lemin_rew]

OK, so you will chose m = 0 to get the longest wave. I'm not sure if you have the correct answer yet, since I'm not sure of the meaning of r1 and r2. Are they the distances from the sources to the point P. What does the angle 26.3^o represent in the problem?

yes r1 and r2 is are the distances from point p. and the angle is between the midpoint of d(distance of the slits) to p. it was needed for the other question for calculating dsinθ.
i don't think the angle is involved in the question i posted here.

 

[TSny]

OK, I think you have the correct answer.

 

[lemin_rew]

OK, I think you have the correct answer.

Thank you so much for your time and help. i really appreciate it!:)