From: mar@physics.su.OZ.AU (David Mar)
Subject: Re: Huh? [Re: Dr. Asimov]
Organization: School of Physics, University of Sydney, Australia
Date: Fri, 10 Apr 1992 09:08:18 GMT

> [StM mentions trombones and harmonic resonances as an analogy to quasar
>  light intensity variations: ... ]
>So my question to you is:  Why, in making these estimates do you assume that
>you're looking at the first harmonic?  There may be good reasons for doing so
>of which I'm unaware, but it's a question that must be addressed, and Asimov,
>at his best, would, in my opinion, have at least mentioned this complication.

Danger Mouse thinks carefully, trying to come up with a good way to explain
this.

"Hmmmm...." he begins, "Your analogies to vibrating physical systems are
not valid. Please bear with me and see if I can explain...

"We are not assuming that we are looking at the first harmonic because there
are no harmonics in the system. The size estimate of the trombone in your
analogy comes from a measurement of the frequency of a note it produces
when the air column inside it vibrates. This, it is true, gives you only
a minimum size estimate because of the possibility of harmonics.

"Now, consider what happens when a trombone player varies the loudness of
the note being played. From where you listen to the trombone, you will
hear the volume (or intensity) of the sound go up and down. If the player
varies the intensity in a periodic way, say one cycle of loud-soft-loud
every five seconds, then you can say that the frequency of the intensity
variations is 0.2 hertz. Note that this frequency has nothing to do with
the actual sound frequency, which will probably be several hundred hertz.

"Okay, no problem. But remember that the speed of sound is finite, 330
metres per second. Let's say the trombone tube is 2 metres long (this is
a guess, btw). Now the pressure waves in the tube which cause the sound
travel at that speed, and so take 2/330 = 0.006 seconds to travel the
length of the tube. But the loud-soft-loud cycle is five seconds long
and so we don't notice any effect of this delay.

"Now imagine that the player can produce a loud-soft-loud cycle every
0.012 seconds. (The frequency of the intensity variations is now 83 hertz.)
Okay, the player starts loud, then plays softly - but this only takes
0.006 seconds, and in this time the loud sound has only just reached the
other end of the trombone. So at one end we have loud and at the other
end soft.

"Here is where my extended analogy to a quasar breaks down. In a trombone
you only hear the sound coming out of the end, so you would hear the loud
sound followed by the soft sound 0.006 seconds later.

"In a quasar, we have light intensity variations, not sound ones, and we
can see all parts of the quasar at once. If we replace the speed of sound
with the speed of light, the trombone length with a quasar size of a few
light-days across, and the sound variation with a light intensity variation
with a period of a few days, you can see what will happen. One part of the
quasar will be bright, another part dim - and the total will be smeared
out so that the variations are undetectable to us - since all we will see
is an average of the bright and dim parts at any given time.

"But since we _do_ observe variations in quasar light intensity with a
period of a few days, we must conclude that the light travel time across
the size of the quasar is smaller than a few days, and hence that the
quasar is less than a few light days across. Thus we have an estimate for
the maximum size of the quasar. And I hope you can see that the phenomenon
of harmonic resonance has absolutely nothing to do with this argument."

DM stops speaking, aware of the ranked masses of non-physics folks
staring at him as he raves on like this. He turns to the bar, and the
other patrons slowly return to their pre-lecture conversations.

"It's been a long day, Mike. (No offense, StM - I've enjoyed answering
your question. I'm talking about my RL day.) A nice soothing mug of
spearmint tea, please."

- Danger Mouse.
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