How Far from the Midpoint is the First Point of Constructive Interference?

[kendie16]

Homework Statement

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.

Homework Equations

w=wavelength
w=v/f

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.

 

[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?

 

[kendie16]

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

 

[cookt]

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

 

[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 wavelength longer than the wave from speaker one, right?

 

[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?

 

[LowlyPion]

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

 

[cookt]

i keep getting it incorrect... i don't know what I am 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...? I've tried both and it doesn't work. what am i not understanding?

 

[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

 

[Delphi51]

At what distance from that midpoint is that first point?

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