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| May 1, 2005 The Doppler Debate: A New Shift The Doppler debate has been a bit of a sleeper in audio for many years, but has always remained a favorite of mine. It’s the elephant in the room that no one will acknowledge. Stereophile-bashing will have to take a back seat around here for a few minutes to allow me to praise Keith Howard for his tour-de-force article "Red Shift," in the November 2004 Stereophile. This is a daring and rather comprehensive attempt to reignite the Doppler debate in the right way: working up from the physics and down from the listening experience. Bravo, Keith.Naturally, such an ambitious effort on a topic that is a hobbyhorse of mine could not fail to disagree with my own point of view at some point, and so it has. But before getting to that, some background is required. Most people are familiar by experience with the elementary physical phenomenon of Doppler shift: Sounds coming from objects moving away from you are shifted downward in frequency, while sounds coming from objects moving toward you rise in pitch. The reason for the effect is interpretable by common sense. Sound consists of cyclical variations in air pressure, so a stationary sound source will put out cycles separated by a given interval in time. If the source moves away from you, the time interval between the cycles will be the original time, plus the extra time it takes for a cycle to reach you due to the fact that the source is now farther away. The effect of increasing the total time between cycles is, by definition, a lower frequency. For a source moving toward you, the distance between cycles is the original time minus the time shaved off the arrival of the cycle due to the fact that the source is now closer, so the sound is higher in frequency. The Doppler effect applies to all waves, including light (in which case it’s called red shift). In the case of a microphone detecting a sound source, the effect is given by the equation:
Notice that the amount of shift is linearly proportional to the speed of relative movement between source and listener. The musical scale, on the other hand, is not linear but logarithmic with respect to frequency; i.e., the frequency distance between whole tones is much smaller for lower tones than it is for higher tones. This fact becomes important, as we shall see. Because Doppler effects occur whenever a source is moving with respect to the listener, moving speaker diaphragms are not exempt. Keith Howard’s main thesis deals with the effect of the speaker diaphragm’s movement on the sounds produced. Imagine a speaker playing a low tone at the same time as a high tone. Because the high tone is being launched from a platform that is already moving back and forth with the low tone, the frequency of the high tone will warble up and down due to the Doppler effect as the diaphragm moves toward and away from the listener. The technical term for this effect is frequency intermodulation. Howard points out that the distortion caused by this effect is two orders of magnitude (100 times) greater than the effect of the dreaded jitter, a widely accepted form of distortion from digital audio sources. He then goes through an elaborate experimental procedure involving listening to simulated Doppler sidebands. His conclusion, which I find convincing, is that Doppler intermodulation should be audible. The effect is at its worst in single-driver speakers, where all the higher frequencies are modulated by all the lower frequencies, but diminishes with two-way speakers, and diminishes even more with three-ways. Finally, we have a good explanation for why single-driver speakers, which should be ideal from the point of view of having no crossover, still possess a nagging quality in their sound. The other point in the recording chain where Doppler distortion may play a role is at the microphone diaphragm. A microphone picking up a higher-frequency tone while already in motion as a result of a lower-frequency tone would be expected to Doppler-shift the higher tones. Such shifts would then be inherent in every recording that uses microphones with diaphragms; i.e., every recording. In relation to this, Howard quite properly debunks the myth that the DiAural crossover can correct for Doppler distortion at the microphone. (DiAural has sought to distance itself from this myth.) I’ve read the DiAural patent and wholeheartedly agree. Not only is this circuit incapable of correcting Doppler effects, but, as far as I can see, no real-world analog circuit could. The correction requires dynamically shifting the time base of portions of the signal, which for practical purposes can be accomplished only by using digital processing. Howard goes further than this, however, and implies that microphone excursions are too small to result in velocities great enough to cause noticeable distortion. Here I must respectfully disagree. Let’s illustrate the Doppler effect with a few examples. Take a microphone diaphragm with an excursion of 1mm moving in response to a 100Hz sinewave. At maximum velocity, the diaphragm is moving at only 0.2m/s. According to the Doppler equation, if a middle-C tone at 256Hz were superimposed on this movement, it would be Doppler-shifted between 255.9Hz and 256.1Hz. This is much smaller than a quartertone at this portion of the musical scale and could very well be inaudible.
In general, very-high-frequency tones superimposed on very-low-frequency tones will produce minimally perceptible Doppler shifts, because of the low diaphragm velocities of the latter and the large frequency difference between tones of the former. On the other hand, moderately low (lower-midrange) tones modulating moderately high (upper-midrange) tones will produce larger Doppler shifts. These happen to occur in the crucial frequency band containing the human voice and most solo instruments. Interestingly, speaker drivers wired in correct phase move in a direction opposite to that of the microphone diaphragm when the recording was made. Therefore, there is a potential for the Doppler distortion introduced at the microphone to be corrected to some extent by the opposite velocities of the speaker driver. Howard makes the valid point that perfect correction would depend on a perfect match between microphone diaphragm speed and speaker driver speed, which is unlikely. On the other hand, because the Doppler effects are small, even a partial correction may reduce Doppler shifts to the point of inaudibility. Again, hats off to Keith Howard for pointing out the complexities of Doppler effects in the audio chain and for reigniting the debate. Doppler distortion effects may well represent a kind of final frontier, one of the last really important unsolved mysteries of good audio. As a bonus, I now realize how naïve my concept of "The Ideal Speaker" using a single driver was. Ah, well -- back to the drawing board. Look for a new and equally impossible ideal speaker design soon. ...Ross Mantle
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If you posit a loud 1000Hz
tone producing a 2mm diaphragm excursion, however, and modulating a 4000Hz tone, the
diaphragm moves at 4m/s maximum speed and the tone would be modulated between 3954Hz and
4047Hz. This 93Hz difference approaches a quartertone in that region of the scale and
would definitely be audible.