# Homework Help: Waves and light (problem solving)

1. Oct 16, 2011

### lemin_rew

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

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?

2. Relevant equations

Xn/L = (n-1/2)λ/d

or

Δx/L = λ/d

3. The attempt at a solution

i know d=30cm
L=40cm
and n=2
but i dont know where to get Xn (if that is the proper equation to use for this question)

thank you

2. Oct 16, 2011

### Staff: Mentor

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

3. Oct 16, 2011

### lemin_rew

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?

4. Oct 16, 2011

### Staff: Mentor

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.)

5. Oct 16, 2011

### lemin_rew

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

6. Oct 16, 2011

### Staff: Mentor

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

7. Oct 16, 2011

### lemin_rew

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?

8. Oct 16, 2011

### Staff: Mentor

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

9. Oct 16, 2011

### lemin_rew

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

Last edited: Oct 16, 2011
10. Oct 16, 2011

### Staff: Mentor

Exactly right.

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