This question might better be posed on an acoustics group, but my guess is that someone here will know the answer. I have been told by knowledgeable acoustics people that when a sound wave travels through a solid rather than air, the speed of propagation varies with the frequency (I believe acoustics folks talk about "bending" as the mechanicsm for propagation). To me this means that if I mix 2 frequencies together and couple them into a solid, the phase relationship between the two frequencies will vary as I move my pickup point along the surfacfe of the solid. My question is this; does the statement that the speed of propogation is frequency-dependant also imply non-linearity, and therefore have I generated new frequencies when I mix several frequencies together? Do I get distortion with only a single frequency excitation? If it is non-linear, assuming that I knew the relationship between the propagation speed and the frequency (for single frequencies), how would I characterize such a system mathematically? Thanks for any tips! Bob Adams
linearity of mechanical coupling
Started by ●April 3, 2008
Reply by ●April 3, 20082008-04-03
Robert Adams wrote:> I have been told by knowledgeable acoustics people that when a sound > wave travels through a solid rather than air, the speed of propagation > varies with the frequency (I believe acoustics folks talk about > "bending" as the mechanicsm for propagation). To me this means that if > I mix 2 frequencies together and couple them into a solid, the phase > relationship between the two frequencies will vary as I move my pickup > point along the surfacfe of the solid.Surface waves are a separate question from waves through a bulk solid.> My question is this; does the statement that the speed of propogation > is frequency-dependant also imply non-linearity, and therefore have I > generated new frequencies when I mix several frequencies together? Do > I get distortion with only a single frequency excitation?I believe it implies non-linearity, but it may be so small you don't see any mixing.> If it is non-linear, assuming that I knew the relationship between the > propagation speed and the frequency (for single frequencies), how > would I characterize such a system mathematically?If the speed changes fairly slowly with frequency, just the speed vs. frequency curve will be enough. Consider that optical materials also change speed with frequency, but away from resonances they can usually be considered linear. Non-linear optics is done at high amplitude where things do go non-linear. The displacement of the electrons is large enough that non-linear effects become significant. -- glen
Reply by ●April 3, 20082008-04-03
On Apr 3, 2:37 pm, Robert Adams <robert.ad...@analog.com> wrote:> This question might better be posed on an acoustics group, but my > guess is that someone here will know the answer. > > I have been told by knowledgeable acoustics people that when a sound > wave travels through a solid rather than air, the speed of propagation > varies with the frequency (I believe acoustics folks talk about > "bending" as the mechanicsm for propagation). To me this means that if > I mix 2 frequencies together and couple them into a solid, the phase > relationship between the two frequencies will vary as I move my pickup > point along the surfacfe of the solid. > > My question is this; does the statement that the speed of propogation > is frequency-dependant also imply non-linearity, and therefore have I > generated new frequencies when I mix several frequencies together? Do > I get distortion with only a single frequency excitation? > > If it is non-linear, assuming that I knew the relationship between the > propagation speed and the frequency (for single frequencies), how > would I characterize such a system mathematically? > > Thanks for any tips! > > Bob AdamsBob I think the effect of the sound speed as a function of frequency is dispersion. I don't think it implies nonlinearity at low amplitudes. Here are a couple of documents that discuss measurements. Improved Surface Wave Dispersion Models and Amplitude Measurements ADA422916 http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=ADA422916&Location=U2&doc=GetTRDoc.pdf Discrimination, Detection, Depth, Location, and Wave Propagation Studies Using Intermediate Period Surface Waves in the Middles East, Central Asia, and the Far East ADA417753 http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=ADA417753&Location=U2&doc=GetTRDoc.pdf Even if the topics aren't an exact match to your interest, take a look at the introductory sections. Direct use of non-linearity at high drive levels is used in "parametric" oscillators and amplifiers. Take a look at the discussion of the non-linearity in this document as an example. http://www.sea-acustica.es/Sevilla02/ult04021.pdf Dale B. Dalrymple
Reply by ●April 3, 20082008-04-03
Hi Joe, I don't think that this implies non-linearity or the creation of sum and difference frequencies. Between any two locations the audio transmission should be defined by an impulse response and a frequency response, just as any linear system. As you mention, the frequency response will be a constant amplitude and a changing phase, with respect to frequency. Off hand, I don't see any reason that this cannot be linear (someone smarter might correct me!). Regards, Steve
Reply by ●April 3, 20082008-04-03
Robert Adams wrote:> This question might better be posed on an acoustics group, but my > guess is that someone here will know the answer. > > > I have been told by knowledgeable acoustics people that when a sound > wave travels through a solid rather than air, the speed of propagation > varies with the frequency (I believe acoustics folks talk about > "bending" as the mechanicsm for propagation). To me this means that if > I mix 2 frequencies together and couple them into a solid, the phase > relationship between the two frequencies will vary as I move my pickup > point along the surfacfe of the solid. > > My question is this; does the statement that the speed of propogation > is frequency-dependant also imply non-linearity, and therefore have I > generated new frequencies when I mix several frequencies together? Do > I get distortion with only a single frequency excitation? > > If it is non-linear, assuming that I knew the relationship between the > propagation speed and the frequency (for single frequencies), how > would I characterize such a system mathematically?Propagation velocity being a function of wavelength is called "dispersion" whether in optics or acoustics. Snell's law applies in either case. Acoustic lens structures exist and have been used to focus and disperse sounds. Non-linearity, if involved at all, is a side effect and not fundamental to the phenomenon. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 3, 20082008-04-03
On Apr 3, 9:18�pm, Jerry Avins <j...@ieee.org> wrote:> Robert Adams wrote: > > This question might better be posed on an acoustics group, but my > > guess is that someone here will know the answer. > > > I have been told by knowledgeable acoustics people that when a sound > > wave travels through a solid rather than air, the speed of propagation > > varies with the frequency (I believe acoustics folks talk about > > "bending" as the mechanicsm for propagation). To me this means that if > > I mix 2 frequencies together and couple them into a solid, the phase > > relationship between the two frequencies will vary as I move my pickup > > point along the surfacfe of the solid. > > > My question is this; does the statement that the speed of propogation > > is frequency-dependant also imply non-linearity, and therefore have I > > generated new frequencies when I mix several frequencies together? Do > > I get distortion with only a single frequency excitation? > > > If it is non-linear, assuming that I knew the relationship between the > > propagation speed and the frequency (for single frequencies), how > > would I characterize such a system mathematically? > > Propagation velocity being a function of wavelength is called > "dispersion" whether in optics or acoustics. Snell's law applies in > either case. Acoustic lens structures exist and have been used to focus > and disperse sounds. Non-linearity, if involved at all, is a side effect > and not fundamental to the phenomenon. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������- Hide quoted text - > > - Show quoted text -My problem is that if I think of a linear mechanical system, I should be able to define a spatial R-L-C lumped approximation, and once I have done that I don't see how propagation speed could depend on wavelength (propagation speed in not the same as group delay at a given spatial point; I am assuming no effects from rolloffs, the system is flat at all frequencies that are injected). Try to think of a R-L-C transmission line model where the propogation speed varies with frequency; I can't think of how this could happen in a linear system. Bob
Reply by ●April 3, 20082008-04-03
Robert Adams wrote:> On Apr 3, 9:18 pm, Jerry Avins <j...@ieee.org> wrote: >> Robert Adams wrote: >>> This question might better be posed on an acoustics group, but my >>> guess is that someone here will know the answer. >>> I have been told by knowledgeable acoustics people that when a sound >>> wave travels through a solid rather than air, the speed of propagation >>> varies with the frequency (I believe acoustics folks talk about >>> "bending" as the mechanicsm for propagation). To me this means that if >>> I mix 2 frequencies together and couple them into a solid, the phase >>> relationship between the two frequencies will vary as I move my pickup >>> point along the surfacfe of the solid. >>> My question is this; does the statement that the speed of propogation >>> is frequency-dependant also imply non-linearity, and therefore have I >>> generated new frequencies when I mix several frequencies together? Do >>> I get distortion with only a single frequency excitation? >>> If it is non-linear, assuming that I knew the relationship between the >>> propagation speed and the frequency (for single frequencies), how >>> would I characterize such a system mathematically? >> Propagation velocity being a function of wavelength is called >> "dispersion" whether in optics or acoustics. Snell's law applies in >> either case. Acoustic lens structures exist and have been used to focus >> and disperse sounds. Non-linearity, if involved at all, is a side effect >> and not fundamental to the phenomenon. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> �����������������������������������������������������������������������- Hide quoted text - >> >> - Show quoted text - > > > > My problem is that if I think of a linear mechanical system, I should > be able to define a spatial R-L-C lumped approximation, and once I > have done that I don't see how propagation speed could depend on > wavelength (propagation speed in not the same as group delay at a > given spatial point; I am assuming no effects from rolloffs, the > system is flat at all frequencies that are injected). Try to think of > a R-L-C transmission line model where the propogation speed varies > with frequency; I can't think of how this could happen in a linear > system.Dispersion occurs on transmission lines also. They can be modeled (below some critical frequency) with R-L-C components and no others. Instead of my writing a treatise on transmission lines, try Google. Start with http://www.ece.uci.edu/docs/hspice/hspice_2001_2-269.html Waveguides are also dispersive. Unlike with transmission lines, it is not even theoretically possible to avoid it. All optical fibers show dispersion. The propagation velocity is the inverse of the refractive index, and refractive index is a function of wavelength. No distortion is involved. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●April 4, 20082008-04-04
On Apr 3, 10:56�pm, Jerry Avins <j...@ieee.org> wrote:> Robert Adams wrote: > > On Apr 3, 9:18 pm, Jerry Avins <j...@ieee.org> wrote: > >> Robert Adams wrote: > >>> This question might better be posed on an acoustics group, but my > >>> guess is that someone here will know the answer. > >>> I have been told by knowledgeable acoustics people that when a sound > >>> wave travels through a solid rather than air, the speed of propagation > >>> varies with the frequency (I believe acoustics folks talk about > >>> "bending" as the mechanicsm for propagation). To me this means that if > >>> I mix 2 frequencies together and couple them into a solid, the phase > >>> relationship between the two frequencies will vary as I move my pickup > >>> point along the surfacfe of the solid. > >>> My question is this; does the statement that the speed of propogation > >>> is frequency-dependant also imply non-linearity, and therefore have I > >>> generated new frequencies when I mix several frequencies together? Do > >>> I get distortion with only a single frequency excitation? > >>> If it is non-linear, assuming that I knew the relationship between the > >>> propagation speed and the frequency (for single frequencies), how > >>> would I characterize such a system mathematically? > >> Propagation velocity being a function of wavelength is called > >> "dispersion" whether in optics or acoustics. Snell's law applies in > >> either case. Acoustic lens structures exist and have been used to focus > >> and disperse sounds. Non-linearity, if involved at all, is a side effect > >> and not fundamental to the phenomenon. > > >> Jerry > >> -- > >> Engineering is the art of making what you want from things you can get. > >> �����������������������������������������������������������������������- Hide quoted text - > > >> - Show quoted text - > > > My problem is that if I think of a linear mechanical system, I should > > be able to define a spatial R-L-C lumped approximation, and once I > > have done that I don't see how propagation speed could depend on > > wavelength (propagation speed in not the same as group delay at a > > given spatial point; I am assuming no effects from rolloffs, the > > system is flat at all frequencies that are injected). Try to think of > > a R-L-C transmission line model where the propogation speed varies > > with frequency; I can't think of how this could happen in a linear > > system. > > Dispersion occurs on transmission lines also. They can be modeled (below > some critical frequency) with R-L-C components and no others. Instead of > my writing a treatise on transmission lines, try Google. Start withhttp://www.ece.uci.edu/docs/hspice/hspice_2001_2-269.html > > Waveguides are also dispersive. Unlike with transmission lines, it is > not even theoretically possible to avoid it. All optical fibers show > dispersion. The propagation velocity is the inverse of the refractive > index, and refractive index is a function of wavelength. No distortion > is involved. > > Jerry > -- > Engineering is the art of making what you want from things you can get. > �����������������������������������������������������������������������- Hide quoted text - > > - Show quoted text -I think this is different. Consider the following experiment. I drive a narrow and thin strip of plastic at one end with a transducer of some sort. I dial the frequency to 1KHz, and then I measure the PHYSICAL wavelength somewhere near the end of the strip by moving 2 pickup microphones around until their outputs are in-phase. The propogation speed is then calculated by dividing the physical wavelength by 1ms. Let's say the wavelength turns out to be 1 cm. Now I double the input frequency to 2KHz, and repeat the experiment. This time, though, the physical wavelength comes out to be .4cm instead of the expected .5cm. indicating that the propogation speed has changed. I could run the exact same experiment with a transmission line, and I would argue that no matter how much dispersion you get, the measured wavelength will always be equal to the propogation velocity divided by the frequency.
Reply by ●April 4, 20082008-04-04
On Apr 3, 5:37�pm, Robert Adams <robert.ad...@analog.com> wrote:> I have been told by knowledgeable acoustics people that when a sound > wave travels through a solid rather than air, the speed of propagation > varies with the frequencyIs it TRULY frequency dispersion, or is it amplitude dispersion? I find brief mention of the difference here: "http:// imamat.oxfordjournals.org/cgi/content/abstract/1/3/269". I seem to recall from my SONAR work, for example, that water exhibits amplitude dispersion, which causes sinusoidal waveforms to turn into sawtooth waveforms. That does not, however, address frequency dispersion for non-sinusoidal waveforms in that medium.> My question is this; does the statement that the speed of propogation > is frequency-dependant also imply non-linearity, and therefore have I > generated new frequencies when I mix several frequencies together? Do > I get distortion with only a single frequency excitation?Again referring to the abstract mentioned above, media that are linear but dispersive seem to be possible. If a medium is linear but dispersive, I think that it can be treated like a linear filter with nonlinear phase response -- the kinds of filters that we encounter routinely.> If it is non-linear, assuming that I knew the relationship between the > propagation speed and the frequency (for single frequencies), how > would I characterize such a system mathematically?Perhaps characterize the nonlinearities and the dispersion separately; nonlinearities as distortion products, and dispersion as filters (as above)? Greg
Reply by ●April 4, 20082008-04-04
Robert Adams wrote: ...>> Waveguides are also dispersive. Unlike with transmission lines, it is >> not even theoretically possible to avoid it. All optical fibers show >> dispersion. The propagation velocity is the inverse of the refractive >> index, and refractive index is a function of wavelength. No distortion >> is involved.I should add that transmission lines need some dissipation in order to exhibit dispersion, but waveguides don't. They *always* exhibit dispersion, which (to first order) is independent of loss.> I think this is different. Consider the following experiment. I drive > a narrow and thin strip of plastic at one end with a transducer of > some sort. I dial the frequency to 1KHz, and then I measure the > PHYSICAL wavelength somewhere near the end of the strip by moving 2 > pickup microphones around until their outputs are in-phase. The > propogation speed is then calculated by dividing the physical > wavelength by 1ms. Let's say the wavelength turns out to be 1 cm. > Now I double the input frequency to 2KHz, and repeat the experiment. > This time, though, the physical wavelength comes out to be .4cm > instead of the expected .5cm. indicating that the propogation speed > has changed.Propagation velocity is wavelength times frequency by definition.> I could run the exact same experiment with a transmission line, and I > would argue that no matter how much dispersion you get, the measured > wavelength will always be equal to the propogation velocity divided by > the frequency.That's true by definition. How do you conclude from it that the propagation velocity is independent of frequency? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
