impedance and empericism

Marc Damashek mdamashek@erols.com
Sun, 18 Jun 2000 17:03:50 -0400


>In a message dated 6/18/2000 1:34:56 AM, Marc wrote:
>
><<Once the sound is launched, if the signal speed changes over a path
>-- whether gradually or abruptly, due to changes in temperature,
>pressure, density, composition (as in a thermocline) -- the
>wavelength changes but the frequency doesn't.>>
>
>Marc;
> Yep I agree..... but it is the wavelength that is perceived and not the
>frequency, isn't it?
> Isn't temperature density shift analogous  to the red/blue shift thingee? I
>am not real sure here but the light given off by a moving object shifts red
>or blue, or doesn't shift at all depending on where the observation is
>made..correct? The source has not changed in character, or pitch as it were,
>but the perceived result has and has done so depending upon position of
>perception ....correct?
>
> But shucks what do I know?, I still get get confused by ohms, amps, volts
>and watts! :-)
>Jim Bryant (FL)

Jim:

Imagine a left-handed thread on a right-handed bolt... NO, WAIT, 
THAT'S THE WRONG PROBLEM!!

Lots of room for confusion. The questions are on target. Let's take 
another stab at it...

Whether the signal is sound or light, the key idea is that energy and 
momentum conveyed by a signal is transferred locally, not globally -- 
I'll make this clearer in a bit. For instance, energy and momentum 
are deposited by a signal in some detector (a cone in the retina, a 
hair cell in the ear, a silver grain on film) in a very small volume, 
more or less instant by instant. [We're gonna ignore things like the 
Heisenberg Uncertainty Principle here in order to stay on track -- 
quantum mechanics is irrelevant.]

The coordinated activity in a traveling wave, where lots of small 
elements move in a highly correlated way, leads to the concept of 
wavelength. Easiest analogy: a ripple in a pond that's launched by 
throwing in a small pebble. The pebble crashes into a bunch of water 
molecules when it hits, transfers energy and momentum to them, which 
they then transfer to their nearest neighbors, and so on, leading to 
a circularly spreading disturbance (with up and down wave motion 
caused by overshoot of the displaced water, which falls back under 
gravity, only to overshoot in the opposite direction, ...). The 
motion at one part of the disturbance is closely related to the 
motion everywhere else, and we can even talk about the wavelength of 
the ripples that are generated.

What happens when the spreading wavefront first hits an insect 
floating on the undisturbed surface? He, She, or It rises and falls 
with the instantaneous surface displacement. At any single point on 
the surface, the up-and-down motion is roughly a (damped) sine wave 
in time. And amazingly enough, at any given instant, a radial cross 
section of the surface centered on the pebble is roughly a (damped) 
sine wave in space. But the floating insect doesn't know a thing 
about wavelength, because it can only monitor its immediate (local) 
environment, and it would need to survey a big patch of space, with 
dimensions of the same order as the wavelength, to make a wavelength 
measurement -- it would basically have to infer the activity at a lot 
of points in space at some instant of time. Locally, it can even 
close its baby blue eyes and measure just the acceleration, which 
will certainly give it the period of the passing disturbance. Keep in 
mind that the rise and fall rate at the detector -- the received 
frequency -- is exactly equal to the speed of the wave divided by its 
wavelength: a faster-moving wave bounces the insect more times per 
second, and so does one with closer spacing of the peaks. Change the 
speed or the wavelength IN A WAY THAT CHANGES THEIR QUOTIENT (not so 
easy) and you'll have a frequency change too.

Doppler shifts @#$*^$%?? You want Doppler shifts??!! Is that what the 
wheels on the bottom of a piano are for?? OK, OK: leave the air 
temperature alone, dammit, and let the source of sound be moving 
toward the observer. When the second wave crest is emitted by the 
source it will be closer to the first than it would have been with no 
motion because the emitter has caught up to the first crest a little 
by chasing it toward the observer. In other words, the crests are 
still evenly spaced, but more closely than for a stationary source -- 
the wavelength is shorter. Also, the speed of the wave in air hasn't 
changed. The received frequency -- with more bumps per second 'cuz 
they've been crowded together by the source -- is higher than it 
would have been. Source moving away from observer 'stretches' the 
distance between successive peaks, and at constant sound speed 
produces a lower received frequency. CAREFUL!! With a stationary 
source, changing the air temperature sure does change the speed of 
sound, BUT that change in speed alters the spacing of the peaks in 
exactly the right way to change the wavelength and leave the received 
frequency (= speed/wavelength) constant. The key to the Doppler shift 
in frequency is radial (distance-changing) motion between source and 
observer -- you can have a moving observer instead of source (or 
both) and get the same result. Now, DO NOT ASK why light is red- and 
blue-shifted; relativity is off limits in pianotech. There's a little 
funny business involved, but it turns out the net effect is just 
about the same.

Now for the payoff: many objects that we think of as generators or 
detectors of sound or light are really large-scale arrays of a huge 
number of small elements (emitters or collectors) whose activity is 
coordinated in time and space (sometimes because that's how we 
designed them in the first place -- a loudspeaker or antenna, for 
instance). The wavelengths that they most easily either produce or 
detect are closely related to their physical size and configuration: 
if you make sure the elementary oscillators are coordinated in the 
right way, the sum of their contributions to the signal will 
selectively reinforce or inhibit each other in certain predictable 
ways, and might even allow only a certain range of frequencies to be 
transmitted or received. It's the collection apparatus (radio 
antenna, large flat sound baffle) that's large and 
wavelength-sensitive, funneling a whole bunch of different frequency 
components to the detector with a variety of possibly altered phases 
and amplitudes to duke it out when they hit the tiny, 
frequency-sensitive detectors at the end of the road, which ride the 
local crests and troughs that stream on by.

I liked the left-handed thread problem better, even though I got the 
answer wrong.

Cheers,

Marc Damashek
Hampstead, MD



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