Distance of hearing a radio station

In summary, the problem involves calculating the distance at which a radio station can be heard based on its power and electric field amplitude. Using the equation S=P/A, where S is the average power and A is the surface area of a sphere, the estimated distance is 65.2 km. Some clarification was needed in the equations used to solve the problem.
  • #1
gillyr2
45
0

Homework Statement


A radio station is allowed to broadcast at an average power not to exceed 24 kW.
If an electric field amplitude of 2.6×10−2 V/m is considered to be acceptable for receiving the radio transmission, estimate how many kilometers away you might be able to hear this station.


Homework Equations



P/A = e_0*c*E^2

The Attempt at a Solution



e_0*c*E^2/P = 1/pi r^2

sqrt(24000/(8.85 *10^-12*3*10^8*pi)) = 65.2 km

help!
 
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  • #2
can anybody help?
 
  • #3
I just had this problem and this is how I solved it

S=P/A where S=(.5)c(permittivity of free space)(E^2) - (this is the average value of S not an instantaneous value. Your equation for S was assuming the instantaneous value)

then a little rearranging:

A=P/S
(4)(pi)(r^2)=P/S - (4pir^2 is the surface area of a sphere, I think you were incorrectly using the area of a circle)

you should be able to solve from here!
 

1. How far can a radio station be heard?

The distance a radio station can be heard varies greatly depending on factors such as the power of the transmitter, the frequency of the station, and the terrain of the area. Typically, AM radio stations can be heard up to 100 miles away, while FM radio stations have a range of about 50-60 miles. However, under certain conditions, a radio station can be heard even farther, sometimes up to 1000 miles away.

2. What is the maximum range of a radio station?

The maximum range of a radio station is determined by the curvature of the Earth. The radio waves travel in a straight line, so the distance they can travel before being obstructed by the Earth's curvature is limited. The maximum range for a typical FM radio station is about 60 miles, while the maximum range for a typical AM radio station is about 100 miles.

3. What factors affect the distance of hearing a radio station?

The distance of hearing a radio station is affected by several factors, including the power and frequency of the station, the terrain and obstacles in the area, and atmospheric conditions. Higher power and lower frequency stations have a longer range, while mountains, buildings, and other obstacles can block or weaken the signal. Atmospheric conditions such as temperature, humidity, and solar activity can also affect the distance a radio station can be heard.

4. How does the power of a radio station affect its range?

The power of a radio station, measured in watts, directly affects its range. The higher the power, the farther the radio waves can travel before losing strength. For example, a 50,000-watt FM radio station can be heard up to 60 miles away, while a 1,000-watt station may only be heard within a 10-mile radius. However, increasing the power of a station also requires a larger transmitter and more energy consumption, making it more expensive to operate.

5. Can a radio station be heard globally?

While it is possible for a radio station to be heard globally, it is not common. In order for a radio station to be heard around the world, it would need an extremely high power and a low frequency. Even then, the signal would need to bounce off the Earth's ionosphere and back down to reach far distances. This phenomenon is known as "skywave" propagation and is limited by atmospheric conditions. Most radio stations are designed to have a local or regional reach and do not have the capability to be heard globally.

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