Waves and light (problem solving)

[lemin_rew]

Homework Statement

two speakers producing exactly the same frequency and always in phase are located on an east-west line emitting sound toward the north. the speakers are 30cm apart and a microphone is loacted 40cm due north of one speaker. which of the following wavelengths would produce sound with the intensity at the locations of the microphone?

Homework Equations

Xn/L = (n-1/2)λ/d

or

Δx/L = λ/d

The Attempt at a Solution

i know d=30cm
L=40cm
and n=2
but i don't know where to get Xn (if that is the proper equation to use for this question)

also the answer is 20cm
please help me, i have no idea how to solve this question to get that answer.
thank you

 

[Doc Al]

Are you looking for constructive or destructive interference? (Most intensity or least intensity?) What wavelengths did they give?

 

[lemin_rew]

Are you looking for constructive or destructive interference? (Most intensity or least intensity?) What wavelengths did they give?

the question i posted above are the only information given to me:
i beieve they are looking for the least intensity at the location of the microphone?

 

[Doc Al]

the question i posted above are the only information given to me:
i beieve they are looking for the least intensity at the location of the microphone?

OK, so do you want destructive or constructive interference? And what's the criteria for each?

Hint: You must compare the path lengths from each speaker to the microphone.

(When I read "which of the following..." I can only assume they gave you a list of choices.)

 

[lemin_rew]

OK, so do you want destructive or constructive interference? And what's the criteria for each?

Hint: You must compare the path lengths from each speaker to the microphone.

(When I read "which of the following..." I can only assume they gave you a list of choices.)

oh yeah sorry, i forgot to add the options:
a)5.0cm
b)1.0cm
c)20cm
d)30cm
e)40cm

and the answer is 20cm

 

[Doc Al]

Good. Now answer my questions:

OK, so do you want destructive or constructive interference? And what's the criteria for each?

Hint: You must compare the path lengths from each speaker to the microphone.

What's the difference in the path lengths from each speaker to the microphone? How does that path length difference relate to phase?

 

[lemin_rew]

Good. Now answer my questions:

What's the difference in the path lengths from each speaker to the microphone? How does that path length difference relate to phase?

so one speaker to the microphone is 40cm
and to the other it is (40^2-30^2 = 700^(1/2) = 26.4cm?)
then the path difference is 40cm - 26.4cm =13.5cm?
is this right?

 

[Doc Al]

so one speaker to the microphone is 40cm

Right.

and to the other it is (40^2-30^2 = 700^(1/2) = 26.4cm?)

No. The distance from the other speaker to the microphone is the hypotenuse of a right triangle. (Draw yourself a diagram.)

 

[lemin_rew]

Right.

No. The distance from the other speaker to the microphone is the hypotenuse of a right triangle. (Draw yourself a diagram.)

oh yeah sorry,
so its 50cm for the other speaker
so the difference in path is 50-40=10cm

then 10cm = (n-1/2)wavelength
and n = 1 therefore the answer becomes 20cm

is this right? thank you so much

 

[Doc Al]

oh yeah sorry,
so its 50cm for the other speaker
so the difference in path is 50-40=10cm

then 10cm = (n-1/2)wavelength
and n = 1 therefore the answer becomes 20cm

is this right? thank you so much

Exactly right.

To get destructive interference, that path length difference must be an odd multiple of λ/2.