>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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