Beat frequencies occur when there are two sine waves (or narrowband signals) close to one another. For example one freq at f Hz and the second at f+100Hz - the ebat would be heard at 100Hz. Does this mean that the ear is non-linear? Naebad
Beat frequencies
Started by ●October 8, 2006
Reply by ●October 8, 20062006-10-08
naebad wrote:> Beat frequencies occur when there are two sine waves (or narrowband > signals) close to one another. For example one freq at f Hz and the > second at f+100Hz - the ebat would be heard at 100Hz. Does this mean > that the ear is non-linear?The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a 1 Hz beat requires no nonlinearity at all. Do you see why? Jerry -- "The rights of the best of men are secured only as the rights of the vilest and most abhorrent are protected." - Chief Justice Charles Evans Hughes, 1927 ���������������������������������������������������������������������
Reply by ●October 8, 20062006-10-08
"Jerry Avins" <jya@ieee.org> wrote in message news:18udndqAR405KLTYnZ2dnUVZ_tadnZ2d@rcn.net...> naebad wrote: > > Beat frequencies occur when there are two sine waves (or narrowband > > signals) close to one another. For example one freq at f Hz and the > > second at f+100Hz - the ebat would be heard at 100Hz. Does this mean > > that the ear is non-linear? > > The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a 1 > Hz beat requires no nonlinearity at all. Do you see why? > > JerryI assume you mean because of the amplitude modulation. However, if the ear was non-linear then an even-tempered scale would sound odd! M. -- Posted via a free Usenet account from http://www.teranews.com
Reply by ●October 9, 20062006-10-09
Major Misunderstanding wrote:> "Jerry Avins" <jya@ieee.org> wrote in message > news:18udndqAR405KLTYnZ2dnUVZ_tadnZ2d@rcn.net... >> naebad wrote: >>> Beat frequencies occur when there are two sine waves (or narrowband >>> signals) close to one another. For example one freq at f Hz and the >>> second at f+100Hz - the ebat would be heard at 100Hz. Does this mean >>> that the ear is non-linear? >> The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a 1 >> Hz beat requires no nonlinearity at all. Do you see why? >> >> Jerry > > I assume you mean because of the amplitude modulation. However, if the ear > was non-linear then an even-tempered scale would sound odd!Every analog system is nonlinear to some degree. With all, nonlinearity increases with higher amplitude. With some -- Class B amplifiers are typical, it also increases at low amplitude. To many musicians, even tempering does sound odd. Jerry -- "The rights of the best of men are secured only as the rights of the vilest and most abhorrent are protected." - Chief Justice Charles Evans Hughes, 1927 ���������������������������������������������������������������������
Reply by ●October 9, 20062006-10-09
Jerry Avins <jya@ieee.org> writes:> naebad wrote: >> Beat frequencies occur when there are two sine waves (or narrowband >> signals) close to one another. For example one freq at f Hz and the >> second at f+100Hz - the ebat would be heard at 100Hz. Does this mean >> that the ear is non-linear? > > The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a > 1 Hz beat requires no nonlinearity at all. Do you see why?No. -- % Randy Yates % "And all that I can do %% Fuquay-Varina, NC % is say I'm sorry, %%% 919-577-9882 % that's the way it goes..." %%%% <yates@ieee.org> % Getting To The Point', *Balance of Power*, ELO http://home.earthlink.net/~yatescr
Reply by ●October 9, 20062006-10-09
naebad wrote:> Beat frequencies occur when there are two sine waves (or narrowband > signals) close to one another. For example one freq at f Hz and the > second at f+100Hz - the ebat would be heard at 100Hz. Does this mean > that the ear is non-linear? >The ear is non-linear in some senses but that's not why you hear beats. If you look at the waveform for f1 + f2 when the difference in frequency between f1 and f2 is small you will see that the envelope of the waveform corresponds to this beat frequency. So evidently the cochlea is able to perform simple envelope detection at low frequencies. Paul
Reply by ●October 9, 20062006-10-09
naebad wrote:> Beat frequencies occur when there are two sine waves (or narrowband > signals) close to one another. For example one freq at f Hz and the > second at f+100Hz - the ebat would be heard at 100Hz. Does this mean > that the ear is non-linear?Interesting question. Consider instead of the ear a linear bandpass filter representing one of the hair cells in the cochlea. Consider as input two sine waves close enough to be in the passband of the filter, and so with a very slow beat. The output of that filter, then, will be exactly the two sine waves. (If they are positioned in the passband such that they come through with equal amplitude.) To be useful to us, though, the signal must be converted to an intensity or power, which is always a non-linear process, in terms of the amplitude of the input signal. You can also consider two laser beams of very close frequency. The beat is only detectable as an intensity change, not through the amplitude, which will see the two separately. This has been done where the beams converge on a microwave diode that can switch at the difference frequency of two lasers. One can pretty much make an optical frequency counter. -- glen
Reply by ●October 9, 20062006-10-09
Jerry Avins wrote:> naebad wrote: > >> Beat frequencies occur when there are two sine waves (or narrowband >> signals) close to one another. For example one freq at f Hz and the >> second at f+100Hz - the ebat would be heard at 100Hz. Does this mean >> that the ear is non-linear? > > > The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a 1 > Hz beat requires no nonlinearity at all. Do you see why? > > Jerry100 Hz is of course within the human hearing range of pitch (slightly sharp low G), so it would not be heard as a beat, but as a difference tone or resultant tone. Low tones of this nature may however not be heard distinctly, but as a sort of low register muddiness, especially where the tone is inharmonic to the generating tones. The term "beat" is really confined to much smaller differences where the beat frequency is perceived as a repeating tremolo (or vibrato, thogh that term is properly reserved or variations of pitch rather than amplitude). That is to say, where the frequency is below the point at which we hear a pitch - say, up to 20Hz maximum. Conventionally a beat is much slower than that, a few Hz. The ear has many non-linear fetures, not least that of frequency-related masking - high pitches will not easily mask a low one, but strong low tones can relatively easily mask higher ones. And of course the frequency sensitivity itself is not linear, c.f. the Fletcher-Munson curve. The transition between perception of beats and perception of pitched tones is termed the "critical bandwidth", characterized by a perceived roughness in the sound - too fast to be heard as a beat, but too slow to be a pitch. Typically, around 12Hz or so. Richard Dobson
Reply by ●October 9, 20062006-10-09
Randy Yates wrote:> Jerry Avins <jya@ieee.org> writes: > >> naebad wrote: >>> Beat frequencies occur when there are two sine waves (or narrowband >>> signals) close to one another. For example one freq at f Hz and the >>> second at f+100Hz - the ebat would be heard at 100Hz. Does this mean >>> that the ear is non-linear? >> The ear is nonlinear. 100 Hz is harder to hear than say, 10. Hearing a >> 1 Hz beat requires no nonlinearity at all. Do you see why? > > No.Imagine equal amplitudes of 500 and 500.05 Hz, both starting at zero and going positive at t = 0. At first, they very nearly match, and the overall amplitude is twice either. By the time 10 seconds have elapsed, the peaks of one will coincide with the troughs of the other, and they will cancel. Your ear or a perfectly linear sound meter will detect a sound level that varies smoothly between maximum and zero amplitude every ten seconds. I'm sure you use that effect to tune your guitar. Jerry -- "The rights of the best of men are secured only as the rights of the vilest and most abhorrent are protected." - Chief Justice Charles Evans Hughes, 1927 ���������������������������������������������������������������������
Reply by ●October 9, 20062006-10-09
Richard Dobson wrote:> Jerry Avins wrote:>> ... 100 Hz is harder to hear than say, 10. Hearing a >> 1 Hz beat requires no nonlinearity at all. ... >> >> Jerry > > > 100 Hz is of course within the human hearing range of pitch (slightly > sharp low G), so it would not be heard as a beat, but as a difference > tone or resultant tone. Low tones of this nature may however not be > heard distinctly, but as a sort of low register muddiness, especially > where the tone is inharmonic to the generating tones. The term "beat" is > really confined to much smaller differences where the beat frequency is > perceived as a repeating tremolo (or vibrato, thogh that term is > properly reserved or variations of pitch rather than amplitude). That is > to say, where the frequency is below the point at which we hear a pitch > - say, up to 20Hz maximum. Conventionally a beat is much slower than > that, a few Hz.I didn't mean to imply that 100 Hz would be perceived as an audible beat, but only that it would be a beat in the heterodyne sense. Small periodic variations of pitch are indistinguishable from variations of amplitude. The only difference between amplitude modulation and narrow-band frequency modulation is the shift of the sideband's phases by 90 degrees relative to the carrier. That is the principle behind phase-contrast microscopy, in which variations in the object's refractive index are converted to intensity differences in the image. ... Jerry -- "The rights of the best of men are secured only as the rights of the vilest and most abhorrent are protected." - Chief Justice Charles Evans Hughes, 1927 ���������������������������������������������������������������������
