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Mostly Mozart


70 Watts
Posted December 26, 2000

Mostly Mozart is sponsored by Comfort and Joy, a unique children's store.

I talked about how FM broadcasting works in my second show, or maybe it was my 4th or 6th show depending on when and how you start counting. In this show I will try to deal with a question about wattage, raised by Paddy and Courtney on last Wednesday's Creatures For Awhile show. The question is, how does a 70 watt radio transmitter reach so much further than a 70 watt light bulb? I've thought of a few possible answers to that, but before I get to that, I think we should all listen to a Mozart horn concerto.

I was telling Paddy last Wednesday about why I like Mozart so much. One thing that came up was that the role played by solo instrument in a Mozart concerto, is very similar to the role played by a voice in a Mozart aria. This accounts for two things that surprised me when I started listening to Mozart; first of all, the solos sounded way more coherent, and showed more spontaneity and freedom of expression, than any of the guitar solos from my favourite classic rock songs. But even better, I started to like Mozart operas.

When I was growing up, my parents were both opera lovers, but I always secretly hated it. Then, at some point I noticed that if I listened to the voices as if they were just more instruments in the orchestra, with their own subtle sonic characteristics, then I enjoyed opera just as much as orchestral music. So far, this has only happened in the case of Mozart; I still dislike everyone else's operas. But it's a big step in the right direction.

Here is a horn concerto which might help to illustrate the resemblance between the role of the solo instrument in a concerto, and the role of a voice in an aria.

--- dennis brain horn concerto 1-2-3

--- flanders & swann

Kootenay Co-op Radio would like to thank Comfort and Joy for sponsoring Mostly Mozart.

No doubt you recognized Michael Flanders and Donald Swann, from the song about thermodynamics I played two weeks ago. That one was called "ill wind," and yes, Mozart's music is in the public domain, so you can get away with stuff like that.

And for purposes of comparison: this is from the Magic Flute, which is somewhat more authentic.

--- magic flute

OK, I know what you're thinking... Why does a 70 watt FM transmitter reach so much further than a 70 watt light bulb?

Well, there are several advantages to being an FM radio wave rather than a light wave. There's efficiency; there's the spectrum; there's the atmosphere; and there's the receiver. Also, a 70 watt light bulb has a pretty good range under ideal conditions.

I've mentioned before that light waves and radio waves are just electromagnetic waves at different frequencies. So it makes sense to compare 70 watts of radio power to 70 watts of light power. Except for one thing. A 70 watt light bulb consumes 70 watts of electrical power, but it doesn't necessarily give out 70 watts of light. A 70 watt fluorescent bulb produces significantly more light than a 70 watt incandescent bulb. The trouble with incandescent bulbs, which is also the reason why they're called incandescent, is that they work by putting so much electricity through a small filament that it gets hot enough to glow. The reason that hot things glow will have to be the subject of another thermal physics lesson, but the important thing here is that a good portion of the 70 watts of energy ends up being absorbed as heat instead of light. One reason there's a vacuum inside every light bulb, is that heat can't travel by convection or conduction in a vacuum. So almost all of the energy that leaves the filament is radiated, which means it's still in the form of light. But as soon as it gets to the glass bulb, a lot of the radiant energy gets absorbed, and serves only to heat up the space around the bulb. So, just based on the difference in brightness between fluorescent and incandescent bulbs, let's assume we lose half our power to heat, which leaves us with 35 watts. The radio antenna doesn't seem to radiate much heat, judging by the sheet of ice it's wearing right now, so we'll assume we've still got nearly 70 watts of broadcast power there.

That should deal with the efficiency problem. The next problem I said was the spectrum. A light bulb is at a huge disadvantage here because it has to produce white light, which really means red light plus violet light plus everything in between. Incandescent bulbs generate a spectrum that's much wider than necessary. They radiate lots of extra low frequency light that doesn't propagate the same way as visible light, and you never see it anyway unless you're wearing infrared goggles. But even fluorescent bulbs have to produce light that's spread fairly evenly throughout the visible spectrum. By contrast, a radio antenna has to generate only one frequency. In the case of FM, there is a small range of frequencies that it needs to cover, but it only transmits one specific frequency at any given moment. So all 70 watts is allocated to that frequency, instead of being shared across a spectrum. As a conservative estimate, let's say that 1/50 of a light bulb's power is concentrated at its strongest frequency, and the remainder is spread across the visible spectrum. So we're down to less than 1 watt at a particular frequency.

Now, I don't know if you noticed, but I just pulled a fast one on you. It's not fair to take power away from the light bulb just because it's generating light at other visible frequencies. After all, those extra frequencies do help to make the light bulb visible, and we're trying to figure out why you can't see a light bulb 10 miles away, even though your radio still picks up KCR. So, shouldn't we take all of the visible light into account? Well, no, because what you see, and what your radio receiver sees, is determined by contrast, not absolute brightness. And you get more contrast by concentrating all your power into one frequency, and looking only for that one frequency. If you look across a wide frequency, then you also increase the amount of random noise you see behind the signal. So it is fair after all to restrict ourselves to one frequency with 1 watt of a particular hue of red light.

I still want to talk about the atmosphere and how radio receivers work differently than your eyes, but first I'll take a little break for some more opera. And a reminder that I'm Tom Clegg, and Mostly Mozart is sponsored by Comfort and Joy, a unique children's store.

--- magic flute

What does the atmosphere have to do with radio waves? Well, it's full of all kinds of particles including hydrogen, oxygen, nitrogen, water molecules, and a huge array of byproducts from common chemical reactions, collectively referred to as smog. All of these particles are really good at absorbing certain frequencies of EM radiation, and also reflecting or diffusing it in random directions. They're also roughly arranged in layers, with more of the heavier particles at low altitudes and so on. This layering produces some convenient reflective effects, which make it possible to hear shortwave radio signals from other continents, and it also plays a part in the aurora borealis, better known as Northern Lights. All of this absorption and reflection happens at different rates, depending on the frequency of the radiation. The Northern Lights and shortwave radio are both somewhat sporadic phenomena, so it's probably best not to assign any special advantage to either light bulbs or radio antennas based on atmospheric effects. Just two observations though: first, FM radio frequencies can pass through walls, even though light can't, and that is because of the difference in frequencies; also, diffused radio waves can be intercepted by a radio receiver, but your eyes filter out everything that's not coming from one particular direction, and assume that it's coming from some other source besides the light bulb.

Finally, the question of the receiver. Unlike your eye, an FM radio receiver has an antenna, which works as an amplifier by collecting all of the signals over a fairly large area. If one part of the antenna is collecting a signal with lots of noise, another part will be contributing the same signal with less noise. This is a way of exploiting the fact that a good portion of the interfering noise comes from nearby sources like the radio's own electrical circuitry. It also helps to pick up signals that are strong in some places and weak in others, due to filtering effects of the building and other nearby objects.

Another big advantage enjoyed by the radio receiver is that it can easily block out all frequencies except the one it's tuned to. This is something your eye doesn't do very well. If you're standing next to a bright light, your eyes will refuse to open their apertures enough to let you see low light against a dark background. So, to make things fair, we should assume that we're looking at our 70 watt light bulb on a dark night, and there are no other lights on. This should be fair to say, because in the case of FM radio, you need a license to generate significant amounts of radiation that might interfere with FM broadcasts. This stuff is regulated by Industry Canada and the Canadian Radio-television and Telecommunications Commission, also known as the CRTC. One of Industry Canada's jobs is to make sure that electrical devices don't generate too much noise at the same frequency as local radio stations. You can often find Industry Canada stickers on telephones, televisions, and computers, to indicate that they've screened them for any propensity to interfere with radio signals.

I figure that under the favourable conditions I just described, you can see a 70 watt light bulb from a kilometre away. And I've calculated that it will only output one hundredth of its input power at its strongest frequency. So, even without taking into account atmospheric effects, and the fact that radio antennas are much bigger than eyeballs, we've got a hundred times as much usable power coming out of our antenna as we have coming out of the light bulb. The next question is, of course, how much extra distance do you get when you use a hundred times as much power?

Unfortunately for KCR, you don't get a hundred times as much distance. You only get ten times as much. Why? If you're ten times as far from the antenna, your receiving antenna will cover one tenth as much vertical space, and also one tenth as much horizontal space, as viewed from the transmitting antenna. So you'll only receive one hundredth as much signal. And that's assuming that the atmosphere doesn't absorb anything along the way, which will reduce the signal strength even more.

So according to this lengthy argument, we should expect a 70 watt FM transmitter to reach about ten kilometres, if a 70 watt light bulb reaches one kilometre. I've done some informal tests using my car radio, and our range seems to be between 10 and 20 kilometres. This could be more of a coincidence, than an indication of the accuracy of my explanation, but it's probably as good as it's going to get.

If you liked that explanation, you should seriously consider phoning me in the studio in the next few minutes to make a request. If you want to know why steam burns hurt so much, or how they make those after dinner mints with the goo inside a hard shell, or why salt makes ice melt, call me at 352-3706 and ask me, and I'll try to give you the answer in next week's show. I'd also be happy to hear from you if you have a favourite scientific field of your own and you'd like to be a guest expert on the show. I'll bring the Mozart if you don't have any.

Speaking of Mozart, I've got yet another horn concerto in E flat, that I'd like to play. But first I'll warn you that up next, at 8:00 we have a special edition of the Polka Power Hour, featuring Stephanie, Brad, and Catherine. So don't go away.

This is CJLY nelson, 93.5 fm.

Kootenay Co-op Radio would like to thank Comfort and Joy for sponsoring Mostly Mozart.

That's it for today; see you next week. Don't forget to make your requests, at 352-3706.