Radio waves: constructive and destructive interference 1-dimension

[kelaroo24]

Homework Statement

Two coherent sources of radio waves, A and B, are 5.00 m apart. Each source emits waves
with wavelength 6.00 m. Consider points only along the line connecting the two sources.
(a) At what distance from source A is there constructive interference between points A and
B?
(b) At what (two) distances from source A is there destructive interference between points
A and B?

Suppose the two sources differ in phase by 90 instead.
(c) At what point(s) between the two sources do we get constructive interference?
(d) What is the nearest point to source A, but on the other side from source B, where we
get destructive interference?

Homework Equations

constructive: m*2pi= 2pi delta x / wavelength + phase constant
destructive: (m+1/2) *2pi= 2pi delta x / wavelength + phase constant

The Attempt at a Solution

for parts a/b, i am using phase constant = 0.
i used 0,1,... for m, and plugged into the equation to solve for delta x.
2pi= 2pi delta x / 6m + 0
delta x= 0m, 6m then is 0m the only distance from a where there is constructive interference?

how do you take into account that the sources are 5m apart?

for parts c/d, i am using phase constant = 90
2pi= 2pi delta x / 6m + pi/2
delta x= 9/2 m, 21/2 m is 4.5 m the distance from a for constructive interference?

i am assuming there's something I'm missing since the hints from the problem suggest 1 answer to part a, 2 distances for part b, etc.

 

[Delphi51]

Curious, that formula doesn't work BETWEEN the two sources where the solutions lie.

 

[kelaroo24]

Is there a different formula to use for interference?

 

[Delphi51]

Between the sources, for part (a) it is
distance from A = distance from B
x = 5 - x

 

[kelaroo24]

ok, so for part a, i found delta x equals 0, so i set that equal to 5 -2x = 0 and got x=2.5 m.

for part b, i got delta x= 3, so 5-2x=3, and x= 1m and 4m. is this correct?

for part c, i used 2pi= 2pi delta x / 6m + pi/2 and got x=.25m and x=4.75m.

for part d, would i use 2pi(m +1/2)= 2pi delta x / 6m + pi/2?

 

[Delphi51]

I'm sure you have a, b, and c.
I don't see any solutions for d. The A to B distance amounts to 300 degrees, so the waves will always be 300 + 90 or 300 - 90 degrees out of phase.

 

[kelaroo24]

thanks. for part d, when m=1, 3pi= 2pi delta x/ lambda + pi/2
so delta x = 7.5 m.
I said this would be the answer since 7.5 m is greater than 5 so this would be the distance from source A.

 

[Delphi51]

I don't see how delta x can be anything other than 5.