Calculating radio station frequency given distances

[aeliand]

Sorry if I posted this in the wrong location, it seemed like the most appropriate board.

Homework Statement

As you drive down the highway, you notice that the dial on your stereo is not functioning. You have the radio tuned to a station that uses two transmission towers that are 175.0 m apart. The towers are 25.00 km from your present location. You wish to estimate the frequency setting of your radio using the interference pattern set up by two towers. You notice that the signal reception fluctuated between maximums as you drive a distance of 0.4500 km parallel to the line joining the two towers. What is the frequency of the station to which you are listening?

Homework Equations

This is supposed to test at how well we can find out data about upcoming units, so I had to guess at which equations would be most relevant since we have yet to learn them. This formula is the only one I know of that I figured would help in any way.

velocity = frequency * lambda

The Attempt at a Solution

I assumed by maximums, it means 0.45/2 on each side of the "present location", so I calculated the distance to the points from each tower.

I drew out the diagram, which made an isoceles triangle with dimensions 0.1750 km, 25 km and 25 km, then split the triangle in half to figure out the distance between the line created by the two receivers and the highway, and using Pythagorean theorem I got a value around 24.99984687 km. I then used that value to find out the distance from the maximums to the towers. From either point to the tower farthest from it, it would be 25.00179994 km away, and to the tower closest it would be 25.000225 km.

I calculated the time to reach each tower, and the values were 0.073520961 s to the closest tower and 0.073534705 s to the farthest.

I assume from here it would do something with resonance but I can not think of the correct formula to use to calculate that. I don't necessarily need a full answer, but a step in the right direction would be very helpful. Thanks in advance!

 

[eggman1965]

Sorry if I posted this in the wrong location, it seemed like the most appropriate board.

Homework Statement

As you drive down the highway, you notice that the dial on your stereo is not functioning. You have the radio tuned to a station that uses two transmission towers that are 175.0 m apart. The towers are 25.00 km from your present location. You wish to estimate the frequency setting of your radio using the interference pattern set up by two towers. You notice that the signal reception fluctuated between maximums as you drive a distance of 0.4500 km parallel to the line joining the two towers. What is the frequency of the station to which you are listening?

Homework Equations

This is supposed to test at how well we can find out data about upcoming units, so I had to guess at which equations would be most relevant since we have yet to learn them. This formula is the only one I know of that I figured would help in any way.

velocity = frequency * lambda

The Attempt at a Solution

I assumed by maximums, it means 0.45/2 on each side of the "present location", so I calculated the distance to the points from each tower.

I drew out the diagram, which made an isoceles triangle with dimensions 0.1750 km, 25 km and 25 km, then split the triangle in half to figure out the distance between the line created by the two receivers and the highway, and using Pythagorean theorem I got a value around 24.99984687 km. I then used that value to find out the distance from the maximums to the towers. From either point to the tower farthest from it, it would be 25.00179994 km away, and to the tower closest it would be 25.000225 km.

I calculated the time to reach each tower, and the values were 0.073520961 s to the closest tower and 0.073534705 s to the farthest.

I assume from here it would do something with resonance but I can not think of the correct formula to use to calculate that. I don't necessarily need a full answer, but a step in the right direction would be very helpful. Thanks in advance!

This is a classic two source interference problem:

The 450m is the 'delta X' distance between minima, the 25km is the 'L' distance from the source, the 175m is 'd' the slit separation for double slit intereference (think Young's exp).

Use the relation: 'lambda' over 'd' = 'delta X' over 'L' and solve for Lambda. Use this wavelength to solve for 'f' (frequency) keeping in mind that v = c = 3.0x10^8 m/s