On the next page I present experimental data supporting the results predicted by the analysis.
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| Doppler shifts in loudspeaker. Fact or fiction? | ||||||||||||||||||||||||
| Updated Novermber 24, 2004 | ||||||||||||||||||||||||
| The document below presents a brief analysis of wave form distortion in loudspeaker dynamic drivers when reproducing both a single tone as well as 2 arbitrary tones such that the different frequencies are related as Fh = n Fl, where n is any number greater than 1.0. The single tone analysis shows that when a driver is subject to a single sine wave input, the acoustic output will under go a distortion of the wave form. The level of this distortion is dependent on the driver displacement. In the two tone case, it is shown that in addition to the wave form distortion present for a single tone, there is also a frequency shift in the higher frequency. The amount of frequency shift is primarily dependent on the excursion of the driver associated with the lower of the 2 frequencies, and completely independent of the excursion related to the higher frequency. If the frequency shift is give by df, then it is shown that the higher frequency tone oscillates about the input frequency Fh as F = Fh + df sin(2*Pi*Fl*T). It is also shown that the magnitude of df asymptotes to a limiting value as the ratio of the frequencies, n, gets large. The frequency shift is shown to result in the creation of intermodulation sidebands, thus rsulting in IM distortion of the input signal. The document is in MS Word format in compressed zip form, about 73k and down loads quickly. On the next page I present experimental data supporting the results predicted by the analysis. |
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| Download Original Article (Written Feb. 2001) | ||||||||||||||||||||||||
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| As of Noverber 24, 2004 I have added a second paper where I revisit wave form distortion arising from Doppler effects. This new paper, which parallels the analysis below, is much simpler and easier to follow than the previous paper and yields similar results. This new paper is available for download at the link below. The paper is in MS Work format in compressed zip form, about 29k. | ||||||||||||||||||||||||
| Download New Article (Written Nov. 2004) | ||||||||||||||||||||||||
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| The figure to the left shows the results of the analysis above for a modulation frequency of 1, a frequency ratio of 10 and a modulation index of 0.5. The thin green line is the displacement due to the modulation signal. The black line is the sum sin(T) + sin(10xT). The red line is the sum of sin(T) + the distorted signal. The orange line is the instantaneous frequency of the distorted signal. Note that the frequency is a maximum at the zero crossing of the modulation signal (green line). The blue line is the time dependent phase of the distorted signal. Note that it is a maximum at the peak displacement of the modulation signal and is consistent with the measured data of Rod Elliott. However, Mr. Elliot's conclusion that this indicates the shift is not a result of Doppler effects is incorrect as the maximum frequency shift does occur at the poit of zero crossoing where the velocity due to the modulation signal is a maximum, a Doppler result. | ||||||||||||||||||||||||