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CHRISTIAN DOPPLER, an Austrian physicist and mathematician, in his paper, Über das farbige licht der Doppelsterne, published in 1842, described the apparent change of frequency of a wave-type phenomenon due to the relative motion between the emitter and the detector. The wave-type phenomenon includes sound waves, and in this article has to do specifically with apparent change in frequency due to the relative motion between the loudspeaker cone and the listener's ear.
The classic example of the train whistle which decreases in pitch as the train passes is probably well known to most readers. Similarly, a loudspeaker operating simultaneously at two frequencies will, under certain conditions, exhibit the effect because the low-frequency movement of the voice coil, which can be of large amplitude, will "carry" the high-frequency source to and from the listener's ear.
Originally this author felt that the amount of distortion due to the Doppler effect was negligible compared to other problems encountered in audio reproduction; however, when an experiment which is quite easy to perform suggested itself, the following equipment was set up. Utilizing a 6.5-in. high-compliance speaker, a wooden stand, an amplifier, a simple resistive mixer, two audio generators, and a certain amount 'of patience, the experiment is well within the capabilities of many audiophiles. The wooden stand shown in Fig. 1 is merely a platform for stability with two upright arms set into the edges. Spacing must accommodate the speaker used. A depth gauge (Fig. 2) was made from a thick sheet of aluminum for a bracket through which a hole was drilled and tapped for a 0-80 screw. The screw itself had a thin aluminum disk divided into eight equal segments affixed to the underside of its head with a nut and would indicate depth in increments of 1/640 in Interpolation to 1/1280 in. ( .00078 in.) was quite easy. A small compression spring was used between the bracket and the disk to take up play in the threads.
Lack of a baffle allowed considerable low-frequency excursion without appreciable power radiation. Only the low frequency movements of the effect upon the high frequency could be detected, which was exactly as desired. Figure 3 shows a block diagram of the set-up.
According to Doppler, the apparent change in the high frequency depends upon the velocity of the relative motion between the emitter and detector. The maximum velocity is the peak-to-peak amplitude multiplied by times the frequency. For example, a speaker operating at 40 Hz with a total excursion of 0.25 in. will reach a maximum velocity in each direction of approximately 31.4 inches per second or about 1.784 mph. This author felt it was somewhat ridiculous to expect an effect from such a low velocity, but continued with the experiment.
A series of high frequencies was used with 40 Hz as the modulating frequency. Each high frequency was selected and its amplitude adjusted for ease of hearing. The low-frequency amplitude was increased from zero to the point where the high frequency was observed to change and then the high frequency was turned off so the amplitude of low frequency cone movement could be measured with the gauge and noted. Each frequency combination was used, and then the low frequency was changed to 15 Hz so the new combinations could be recorded. The assistant changed places with the listener and the entire test was run and recorded again. The table (with the dimensions rounded off to two significant figures) and the graph show the results.
The most noticeable feature of the results is that the detectable level of amplitude varies widely for both people. One person's ability seems fairly consistent with a modulating frequency of 40 Hz, but there seems to be no pattern to the other runs. Probably background noise level plays an important part. Furnace, traffic, and people noises vied with the test tones, making it necessary to try again in some cases; however, the results may be more typical of home reproduction as a consequence. Homes don't normally feature anechoic chambers.
Maximum velocity is reached at two points during the low-frequency cycle where the cone speeds (1) through the rest positions on its way to or from the listener's ears. Since it is supposed to be reproducing a sine wave it should translate a circular cyclical motion to a reciprocating cyclical motion. Therefore its maximum velocity is the same as the speed of a point revolving at a constant radius around a center at a given frequency.
V =C/unit of time where
C = circum. =pi D
D=diam.=peak to peak amplitude of cone
By substitution: V=Ap-p pi f
At the peaks the velocity reaches zero. At other points in the cycle the velocity changes the high frequency accordingly. The effect is an apparent sweeping below and above the high frequency. A type of warble tone results which, under some circumstances, is quite distinctive. The upper and lower sideband limits of the resultant channel caused by the modulation (note the similarity to a FM carrier in radiotelephony) can be determined by the formula:
S.B.= f1 1129 / 1129 +- V
where f1= high, modulated frequency
f2 = low, modulating frequency
V=Ap_p pi fs
Ap_p =peak to peak amplitude at f2 in feet.
We can consider f1 being multiplied by a "modulation factor" which leads to the conclusion that the actual frequency of f1 is immaterial because the modulation cases a ratio change which our hearing mechanism detects. If the modulation factor were ±2, the warble tone would span a channel two octaves wide, and if the M.F. were ±1.0595 the warble tone would span a channel one whole tone wide. One would expect to hear this much difference. The highest amplitude for detection was 0.18 in. with frequencies of 15 kHz and 15Hz. This represents worst case conditions and would not, with the typical speaker systems, be significant.
It would take a single-voice-coil type of speaker in an enclosure where the speaker load decreases drastically at the very low frequencies so as to allow easy cone movement at 15 Hz-for instance, a phase inversion enclosure of the large-port type. In addition, the input would have to contain frequencies in the 15-Hz region. Much more realistic are the results of the frequency combination of 40 Hz and 400 Hz. One person detected the modulation caused by an amplitude of .094 in. The 400-Hz signal was modulated by a factor of less than 1.00091 It becomes obvious that the amplitude of a low frequency can be very low and still cause detectable change in the high frequency.
It must be remembered that a listener who enjoys large-scale musical works reproduced at super realistic SPL's will be operating speakers so that peak-to-peak amplitudes in the bass region will be of the order of 31 in. or more for even 15 in. speakers. The point is that amplitude of even 0.18 in. as shown in the table are entirely within the realm of normal operation, unless we talk about flute or violin or other instrument without appreciable output in the bass range.
One thing helps the listener: Little in the way of steady-state tones such as were used in this experiment are found in music. The closest to a steady-state tone is probably an organ pedal note. Perhaps the normal variability helps mask the Doppler-effect distortion.
The author wishes to encourage the carrying out of this and similar experiments by others and would appreciate questions, comments, suggestions, corrections, and speculations on this article.
Arguments about Doppler distortion in loudspeakers have been going on for some years now. Many early writers did admit its existence but remained skeptical about the actual effects. In Loudspeakers' published in 1958, Gilbert Briggs said "Some writers still claim that the dividing network avoids Doppler effect but they never furnish proof of having heard the effect or seen evidence of it in a loudspeaker. It seems, on examination to be quite innocuous. If a train passes close to you at 60 m.p.h. with its whistle blowing at about 550 Hz, the pitch will change from about 600 Hz down to 500 Hz to your ear. An airplane travelling at 600 m.p.h. will produce a much greater change of pitch.
But the maximum velocity attained by a voice coil moving l inch at 50 Hz ( which it rarely ever does) is equal to only 4.45 m.p.h., and any resultant change of pitch could not be detected by the human ear. There is actually very little tendency for the Doppler effect to be produced in a moving-coil speaker for the fundamental reason that the velocity of the voice coil goes down with frequency. Thus a movement of ß inch at 25 Hz-where it would be more likely to occur-results in half the velocity produced by the same movement at 50 Hz." Writing in the same book, Raymond Cooke (now of KEF) has this to say ... the Doppler effect with the engine whistle depends on its rapid approach towards and departure from the observer.
The listener to a speaker would therefore have to be directly on axis to receive any pitch variation, which would diminish to zero at the sides, i.e., 90 degrees off axis. Merely standing up or sitting down would destroy much of the effect if it had any audible existence which seems to be more than ever phantasmagorical." Lovely word that. However, in 1967, following a lecture by James Moir to the British Sound Recording Association', Geoffrey Horn wrote' "... Mr. Moir's apparently scientific investigations lead us along nicely, until he comes to subjective assessment when he is on less sure ground. The first part of his article is beyond dispute; certainly there is a Doppler effect, we are all familiar with it; certainly it must apply to loudspeaker cones and obviously it can be measured; but when and under what circumstances can we call it distortion? Mr. Moir sets up his two-tone tests and finds a threshold beyond which he detects unpleasantness but his results are almost unbelievable-in terms of frequency change alone-0.001% error in a watch for example is less than a second a day! ... I have spent some interesting hours in a softly-furnished room of about 2000 cubic feet with a selection of pairs of loudspeakers of different sizes and some suitable Doppler-provoking disks.
Organ proved to be the most illuminating as might be expected; other music provided only occasional examples of the effect, except for a short extract ( which goes a long way) by a `group' where the mightily powerful bass-guitar beat produced a decidedly 'new' sound. In general, the effect of the distortion was not as 'dirty' as had been expected but it was an obviously added noise. From these ever-so-loose and ever-so-subjective tests, I should say that most full range units of 8 inches and below can be expected to produce some signs of this distortion unless they are horn or column loaded in such a way that the diaphragm movement is lessened at low frequencies. I conclude, then that Mr. Moir is correct in saying that quantities of this type of distortion are present in the output of our loudspeakers, but they remain undetected as such because of a number of mitigating or disguising circumstances. Therefore, Briggs was right to dismiss its effect on listening to music and his judgment remains true today. Experiments I carried out myself at Wharfedale in 1965 and at Fisher in 1966 confirmed this point of view. However, if we let Geoffrey Horn have the last word "... the problem is not so far below the surface as we might previously have been inclined to believe, particularly with the development of small 'long throw' loudspeaker units."
-G. W. T.
1. Loudspeakers, by Gilbert Briggs, 1958 Edition. (Cahners Publishing Co., 221 Columbus Ave., Boston, Mass. 02116)
2. Hi-Fi News, January, 1967
3. Hi-Fi News, May, 1967 See also: "Modulation distortion in loudspeakers" by Paul Klipsch, AES Journal, February, 1970 "Loudspeaker performance," Wireless World February, 1970
(Audio magazine, Aug. 1970)
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