Radio & Conservation of Energy

Is there a limit to how many radios can receive the same signal? Wouldn’t the law of conservation of energy predict that there is such a limit? And yet, how is it possible so many can all listen to the same station within a densly populated metropolitan area?

First off, the transmitter uses and sends out the same energy in every direction no matter whether there’s a receiver antenna to pick it up in a particular spot or not.

On the other hand, the energy in the signal that needs to be received by a modern radio with its own power source for the amplifier has to be very very miniscule. (Probably that was different for very old transistor radios that had no battery of their own.)

I’m not even sure if a radio antenna will absorb enough of the radio signal energy that passes through it that another antenna that is in the same ‘line of sight’ would not be able to produce sound from the same signal - it would interfere with the reception, probably, but how much would depend on many factors.

I hope that this helps. Let us know if you have follow-up questions. :smiley:

Interesting question. I assume there is a limit, but that the degeneration over distance (proportional to the square of the distance for radio, IIRC) is a much more significant factor.


Each radio only sucks energy out of the broadcast for a distance something like one wavelength around its antenna, if that. For FM radios, it’s just a few meters. You may not be able to tightly pack radios on the inside surface of a huge confining sphere, but you could space them a few steps apart.

Most of the energy is just lost to space or absorbed by the ground and other things.

By the way, transmitters don’t radiate in all directions, generally. They aim the signal to make the best use of its power, which is expensive. They might aim it specifically at a nearby city, or they might confine it to radiate fairly horizontally. Shortwave transmitters are often trying to get the signal to echo around between layers of the atmosphere, which forms a sort of vertical channel to guide the signal around the globe. In the field close to the transmission tower, signal strength doesn’t fall off according to the inverse square, though if you get far enough away it does.

This is the understatement of the century.

Let’s say, for example, a radio station pumps out 50,000 W from its antenna. If there are 100,000 listeners, and each radio receives (converts) 10 microwatts of power on average, then 99.998% of the power transmitted by the radio station’s antenna is effectively wasted.

Radio and TV are extremely inefficient methods for broadcasting information.