Calculating radio station frequency given distances

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SUMMARY

This discussion focuses on calculating the frequency of a radio station using the interference pattern created by two transmission towers. The towers are spaced 175.0 meters apart and are located 25.00 kilometers from the observer. The observer drives 0.4500 kilometers parallel to the line joining the towers, leading to fluctuations in signal reception. The key formula utilized is the wave equation, velocity = frequency * wavelength, along with the relationship for double-slit interference to derive the wavelength and subsequently the frequency.

PREREQUISITES
  • Understanding of wave mechanics and interference patterns
  • Familiarity with the double-slit experiment and its equations
  • Basic knowledge of trigonometry and the Pythagorean theorem
  • Ability to manipulate algebraic equations for solving frequency and wavelength
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  • Study the principles of wave interference, particularly in two-source systems
  • Learn how to apply the double-slit interference formula: wavelength/distance = delta X/L
  • Explore the relationship between wavelength, frequency, and wave speed in electromagnetic waves
  • Investigate practical applications of radio wave propagation and signal reception
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Students in physics, particularly those studying wave mechanics, engineers working with radio frequency systems, and anyone interested in understanding radio signal behavior and calculations.

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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!
 
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aeliand said:
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
 

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