# Distance between two speakers

1. Feb 1, 2009

### kendie16

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

Two in-phase loudspeakers are 2.35 m apart. They emit sound with a frequency of 425.0 Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 342 m/s.

2. Relevant equations

w=wavelength
w=v/f

3. The attempt at a solution

I used the above equation to find the wavelength (0.805m), divided the distance between the speakers by 2 (2.35/2= mid point) and then subtracted one wavelength from this to get what I thought would be the answer (0.370m). But it is not correct and I am really lost. I know there is another old thread like this but that person did the same as me and never got the right answer.

2. Feb 2, 2009

### LowlyPion

Welcome to PF.

Consider that since the sound arriving at the midpoint at the same time, shouldn't a half λ to each side experience constructive interference, because the wave at that point will be delayed from arriving from one speaker by 1/2λ and from the other speaker will require another 1/2λ longer?

Last edited: Feb 2, 2009
3. Feb 2, 2009

### kendie16

Thanks so much, I understand now and got the right answer. It didn't occur to me that there would be a delay.

4. Feb 2, 2009

### cookt

i have a similar question, although diff values, on my physics assignment, but even with the help given im confused and can't seem to get the correct answer.

5. Feb 2, 2009

### Hannisch

At the midpoint, the distance from speaker 1 is the same as the distance from speaker 2 - the difference between the distances is 0. Constructive interferance occurs when the difference is 0, λ, 2λ, 3λ etc., so a point before the midpoint would be where the wave from speaker 2 has traveled one wavelenght longer than the wave from speaker one, right?

6. Feb 2, 2009

### cookt

ok....so i've got my midpoint, and i've got my wavelength... are you telling me to add my wavelength onto my midpoint?

7. Feb 2, 2009

### LowlyPion

The points of constructive interference I think should be 1/2*λ to each side of the midpoint.

8. Feb 2, 2009

### cookt

i keep getting it incorrect... i dont know what im doing wrong.

my midpoint= 1.95
my λ= 0.824

im adding 1/2*0.824 to both sides of 1.95 to give me: 3.16m?
just adding one...? ive tried both and it doesnt work. what am i not understanding?

9. Feb 2, 2009

### LowlyPion

Sorry, I don't know what your problem statement is.

But as to the constructive interference I'd look for it at ± ½*λ from the mid point.

That would be for what you've presented so far more along the lines of 1.95 ± .412

10. Feb 2, 2009

### Delphi51

With this wording, the answer would be 0.412, not 3.16.