- #1

- 11

- 0

## Homework Statement

Two shortwave radio antennas broadcast identical, in-phase signals at the same frequency. The transmitters are 176.0 m north, and 176.0 m south of Western Ave, respectively, as shown (that is, they are separated by 352.0 m). Western Ave is 452.0 m long. Starting at the end of that avenue, a car drives north along Negundo Street, which lies parallel to the line joining the two radio antennas. The car first encounters a minimum in reception after it travels 124.0 m. What is the wavelength of the radio waves? Assume that the car and the transmitters are all at the same altitude.

http://www.instantimagehosting.com/storage/Untitled_6.jpg [Broken]

## Homework Equations

2-slit interference for dark fringes (minimums)

sin[tex]\theta[/tex]=[(m+.5)[tex]\lambda[/tex]]/d

## The Attempt at a Solution

First encounters a minimum of reception means the first dark spot from the midpoint. Therefore m, the fringe number=0.

Solving for the angle of separation between the first dark spot at 124m and the midpoint. We have two sides of a triangle so arctan(124/452)= 15.3408908 degrees

sin(15.3408908)=[(.5)[tex]\lambda[/tex]]/352

2*sin(15.3408908)*352=[tex]\lambda[/tex]=186.251202 m

However this is incorrect! Any help you can give me would be excellent!

http://www.instantimagehosting.com/storage/Untitled_6.jpg [Broken]

Last edited by a moderator: