dvorak (11/15/82)
A recent comment on this newsgroup stated that humans could discriminate a sine wave from a square wave when the fundamental was 15kHz. This is contrary to my understanding of our auditory system. How is this so? Aliasing? IM distortion? Uncalibrated equipment? Would someone please elucidate (or argue that it is not true) ? --Chuck Dvorak BTL Holmdel (Houxp!dvorak) P.S> FYI, some similarity exists in the Fourier domain between vision and audition. In vision, of course, one is concerned with SPATIAL frequency (cycles per degree of visual angle). In vision, a high-frequency (~50 c/deg.) squarewave is, I believe, NOT distinguishable from a sine wave.
CSvax:Physics:hal (11/17/82)
#R:houxp:-15200:pur-phy:3300001:000:923 pur-phy!hal Nov 16 08:25:00 1982 In general, a square wave is distinguishable from a sine wave of the same frequency because the square wave contains overtones. To be precise, a sqaure wave of frequency f is composed of the following sine wave compon- ents; f + 1/3(3f) + 1/5(5f) + 1/7(7f) + ... that is, the fundamental frequency and odd harmonics. The ear detects the presence of these overtones and so the square sounds "different". Now for a fundamental frequency of 15kHz, the third harmonic is 45kHz and well beyond the range of hearing. This may be the reason for expecting a square wave and sine wave to sound the same at this frequency. However, just because a 45kHz tone can not be heard I'm not at all sure this means it cannot be sensed. I have read that people radiated with ultrasonics are affected (a sense of forboding, or that they are being watched) even though they don't hear anything. Hal Chambers pur-ee!pur-phy!hal
mike (11/20/82)
Ok, even if we CAN'T hear the overtones of the 15 kHz square ware, couldn't the ear detect the difference between the sine and square waves via wave shape, transient response, or other related mechanisms? I remember an experiment where a sound was synthesized two different ways, each of which had the same spectral components, at least concerning frequency and magnitude. One sound had the phases juggled so that it was "smooth" (you know what I mean), and the other was just summed to give a delta approximation. In any event, the two sounds were judged to be different. Could it just be that the square wave "hurts" more? I sure can't stand listening to them any more... Coo roo coo coo... ...we13!uniq!mike Mike Hall