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Constructive/Destructive Interference

  • #1

Homework Statement



A person driving at v = 15 m/s crosses the line connecting two radio transmitters at right angles, as shown in the figure (d1 = 300 m and d2 = 100 m). The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at point A the radio picks up a maximum net signal.

The image: http://www.webassign.net/walker/28-31alt.gif
(a) What is the longest possible wavelength of the radio waves?
(b) How long after the car passes point A does the radio experience a minimum in the net signal? Assume that the wavelength has the value found in part (a).

Homework Equations


l2 - l1 = (m-1/2)(lambda)


The Attempt at a Solution


For part a I got 200 m.

Part B is where I have a problem. I know I need to get the vertical distance and use v = 15 m/s to find the time. Using triangles formed by connecting the vertical distance x to each radio transmitter I have made l2 = (x^2+100^2)^(1/2) and l1 = (x^2 + 300^2)^(1/2). When I subtract both of them and make them equal to 1/2lambda my x's cancel out, :-(.
 

Answers and Replies

  • #2
LowlyPion
Homework Helper
3,090
4

Homework Statement



A person driving at v = 15 m/s crosses the line connecting two radio transmitters at right angles, as shown in the figure (d1 = 300 m and d2 = 100 m). The transmitters emit identical signals in phase with each other, which the driver receives on the car radio. When the car is at point A the radio picks up a maximum net signal.

The image: http://www.webassign.net/walker/28-31alt.gif
(a) What is the longest possible wavelength of the radio waves?
(b) How long after the car passes point A does the radio experience a minimum in the net signal? Assume that the wavelength has the value found in part (a).

Homework Equations


l2 - l1 = (m-1/2)(lambda)


The Attempt at a Solution


For part a I got 200 m.

Part B is where I have a problem. I know I need to get the vertical distance and use v = 15 m/s to find the time. Using triangles formed by connecting the vertical distance x to each radio transmitter I have made l2 = (x^2+100^2)^(1/2) and l1 = (x^2 + 300^2)^(1/2). When I subtract both of them and make them equal to 1/2lambda my x's cancel out, :-(.
First I would note the X2's are part of RSS's and I don't think they exactly cancel out.
But that said ... if the car wasn't moving how long before the next minimum would arrive?
How far could the car have moved in that time at 15 m/s?
How accurate does your answer need to be?
How many digits of precision does your calculator have?
 
  • #3
I only need up to 4 significant digits. We're only allowed to use a one-line calculator on exams so I have my Ti-89 at home and using the Ti-30Xa for my homework. I guess my problem is somewhere in my algebra?
 
  • #4
LowlyPion
Homework Helper
3,090
4
I only need up to 4 significant digits. We're only allowed to use a one-line calculator on exams so I have my Ti-89 at home and using the Ti-30Xa for my homework. I guess my problem is somewhere in my algebra?
Have you figured yet how far the car could have traveled when the minimum reaches where the car was?
 
  • #5
No, I have not.

I still haven't found how many meters away from point A the minimum is. So far I have set up:
(100^2 + x^2)^(1/2) - (300^2 + x^2)^(1/2) = (1/2)(200)

When I solve it by hand I can't get x.
 
  • #6
LowlyPion
Homework Helper
3,090
4
No, I have not.

I still haven't found how many meters away from point A the minimum is. So far I have set up:
(100^2 + x^2)^(1/2) - (300^2 + x^2)^(1/2) = (1/2)(200)

When I solve it by hand I can't get x.
Well the destructive points of interference are given by what?

EDIT: Won't you need to be at a point where the increases in the hypotenuses will create a 180 out of phase with the arriving waves?
 
Last edited:

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