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Natural Science Forum / Physics / Acoustics / December 2004Sound in Solids
Could someone please explain why sound travels at different speeds depending on frequency through a solid, but not through air? Of course the easy answer is that the wavelength changes (for all but one frequency), but why does that happen? > Could someone please explain why sound travels at different speeds > depending on frequency through a solid, but not through air? Of > course the easy answer is that the wavelength changes (for all but one > frequency), but why does that happen? Hi, check my post in few days back discussion, please, about sound absopbtion and you will get an idea! http://groups.google.com/groups?hl=en&lr=&safe=off&threadm=2a22a434.0411110627.5 6df439d%40posting.google.com&prev=/groups%3Fhl%3Den%26lr%3D%26ie%3DUTF-8%26safe% 3Doff%26group%3Dalt.sci.physics.acoustics Good luck, Alex > Hi, > check my post in few days back discussion, please, about sound > absopbtion and you will get an idea! > Good luck, > Alex I read that thread and it doesn't address my basic question. I understand what happens to sound in solids, I want to know why. Why is it that different frequencies travel at different speeds in a solid, but not in air? Is it that they actually do travel at different speeds in air, but the difference is so small as to be negligible? I have looked in all my acoustic texts and Googled for this answer. Everyone and their dog can talk about coincident dip, but no one ever explains the fundamental principle behind it beyond just saying the speed and wavelength change on a frequency dependent basis which creates a sympathetic coupling at one frequency between the wall and air. > I read that thread and it doesn't address my basic question. I > understand what happens to sound in solids, I want to know why. Why > is it that different frequencies travel at different speeds in a > solid, but not in air? Is it that they actually do travel at > different speeds in air, but the difference is so small as to be > negligible? There are lots of things that can't be explained in words, only maths. I rather think this is one of them (although I would like some of the cleverer people who post in this group to prove me wrong). I think you're referring to bending waves in solid materials which have significant stiffness. For these waves to propagate, the solid bar or sheet must be elastic, i.e., springy when bent. It is quite a different propagation mechanism to sound in air, which propagates by compression waves. So it's not that surprising that they behave differently. Solid bars of material can also support longitudinal waves, in which the velocity is not dependent on frequency. All this is dealt with in books on fundamental acoustic theory. Incidentally and for the record, the velocity of sound in air is not quite constant with frequency, but that has nothing to do with vibrations in solids. Don't assume that a simple theory covers all vibrations. For accurate calculations you need to know exactly what is going on, and in the case of a gas that involves the individual molecules. Tony W > > I read that thread and it doesn't address my basic question. I > > understand what happens to sound in solids, I want to know why. Why [quoted text clipped - 21 lines] > > Tony W Hi, OK, will try to make more direct answers on your questions. BTW, I don't recommend you to search for answers for so complex questions in Internet. Unfortunately, no sites I know so far when you can read full text of theory of continuum media. University library IMHO is the best source so far about the topic. Now is my answer. Go math, please, and do wave equation. I assume you are familiar with hyperbolic dispersive waves equation. The answer is writing there. The speed of sound is the group speed from that equation and is function from local disturbance. Without math at this point you know the gas or open air has very light inter-molecule forces, and applying just acoustic frequencies could be difficult to get stronger local disturbance. The solids or metals for your question specifically have stronger intermolecular forces and sounds possible to get local disturbance stronger by changing source frequency. That is the reason for effects you are asking about. Now we have the idea and have to proof one by math. If you take open air, ideal gas with isentropic movements could relatively good approximation. Do the math for small perturbation in ideal gas and no relations to perturbation frequency could be discovered. In reality, gas has at least some order Van-der-Vaalse shifts, but because of small magnitude of the shift it is difficult to measure one in experiments. In result speed of sound in gases doesn't affect by small variations in sound frequency. For solids/metals task conditions are different and you have to write acoustic wave Lagrangian. Solving Lagrangian you see sound wave speed dependences from frequency. If you want to make all math by yourself feel free, to ask more questions. Good luck, Alex > Why > is it that different frequencies travel at different speeds in a > solid, but not in air? This is called "dispersion" (also termed in optics). The sound variety arises in solid materials. Liquids and gases cannot support shear loads, so the dispersion does not occur there except at the molecular level (ultrasound in carbon dioxide, for instance). Solids support permanent shear loads, so a sound wave can be by bending as well as compression when traveling in solids. I do not have further expression of that at the moment. > Is it that they actually do travel at > different speeds in air, but the difference is so small as to be > negligible? It occurs to a slight extent at the molecular level (ultrasound in carbon dioxide, for instance). > I have looked in all my acoustic texts and Googled for > this answer. Everyone and their dog can talk about coincident dip, > but no one ever explains the fundamental principle behind it beyond > just saying the speed and wavelength change on a frequency dependent > basis which creates a sympathetic coupling at one frequency between > the wall and air. In a resilient panel (window, gypsum board, etc.), there can be bending waves aka shear waves. The wavelength of that wave varies as some power of the frequency (not the first power), the thickness and the density of that panel. There can always be found a frequency where the wavelength in air is equal to the wavelength of the bending waves in any resilient panel. when that frequency is in the audio range, we say that coincidence transmission is governing the transmission loss. It also the case that when the direction of arrival of the sound wave is not parallel to the plate, the air wavelength projection of the plate gets longer, so it takes a higher frequency to have the waves match. As the angle increases from tangential to normal, the coincidence frequency rises rapidly. In a glass pane I have observed perhaps 500 Hz at grazing, rising to perhaps 10 kHz at an angle of about 20 degrees (someone here can calculate it precisely). Test laboratory data shows one broad dip, since it uses diffuse sound, arriving at a wide variety of angles down to perhaps 20 degrees from grazing (70 degrees from the normal). Angelo Campanella > This is called "dispersion" (also termed in optics). The sound variety > arises in solid materials. Liquids and gases cannot support shear loads, > so the dispersion does not occur there except at the molecular level > (ultrasound in carbon dioxide, for instance). Surface waves in a fluid travel at speeds dependent on their wavelength, so you see dispersion there. Cheers Greg Discussing this topic is really interesting. I have a simple explaination on internet : "... Depending on what the propagation medium is, the sound speed can change with frequency. Non-Dispersive Medium – Sound speed is independent of frequency, therefore the speed of energy transport and sound propagation are the same. Air is a non-dispersive medium. Dispersive Medium – Sound speed is a function of frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at each its own phase speed, while the energy of the disturbance propagates at the group velocity: Cg. Water is an example of a dispersive medium. .... " The paragraphs are extracted from J. S. Lamancusa, Penn State ( www.me.psu.edu/lamancusa/me458/5_physics.pdf ) > Discussing this topic is really interesting. I have a simple > explaination on internet : [quoted text clipped - 14 lines] > The paragraphs are extracted from J. S. Lamancusa, Penn State > ( www.me.psu.edu/lamancusa/me458/5_physics.pdf ) Bobby, The text your citate is right, but is not too good. The author postulate some points as an axioms. To understand topic more interesting to know _WHY_ author says that, but not what he actually says. Like why math of sound is different for non-dispersive medium and not depends from frequency then in dispersive ones and depend from frequency in them. If he could focused on understanding of physics, not bringing some set of facts up, he could make more work in his text. For advance course for high school students it is good, but for serious adults who is going to be an engineer shortly and takes classes in boundary problems of mathematical physics in parallel with acoustics, the author could provide more detail proofs for his statements. At least, author could ask students to make their own exercise and to prove _all_ formulas mentioned in the text. That makes difference between the Bible book and book in science like physics is about. Good luck, Alex The first task is to identify the type of waveform. Mechanical structures such as beams, plates and shells have longitudinal, bending, and torsional waves, among other types. The Earth has P-waves, S-waves, Rayleigh waves, Loves Waves, among other types. Some of these mechanical and seismic waveforms tend to be dispersive, others are non-dispersive. Some good references are: 1. Structure Borne Sound : Structural Vibrations and Sound Radiation at Audio Frequencies by L. Cremer, M. Heckl, E.E. Ungar. 2. Modern Global Seismology (International Geophysics Series) by Thorne Lay, Terry C. Wallace Tom Irvine www.vibrationdata.com > The first task is to identify the type of waveform. Mechanical > structures such as beams, plates and shells have longitudinal, [quoted text clipped - 15 lines] > > Tom Irvine Hi Tom, You count material properties, but that has not refrence to direct answer for question: Why sound in gases does not have dispersions, but the one in solids has dispersion? The answer is: because sound in gases is isentropic disturbance, but in solids it is not isentropic one. Source of sound in solids is entropy source. This is fundamental difference defineded by natural differences between phases of matter. Sound in gases does not changes gas structure, but in solids does. Normally professors at Universities ask students to prove that point and that is fun problem to calculate medium entropy change in sound source of given sound frequency. Alex > Why sound in gases does not have dispersions, but > the one in solids has dispersion? The answer is: because sound in [quoted text clipped - 5 lines] > and that is fun problem to calculate medium entropy change in sound > source of given sound frequency. But the dispersive surface waves in an infinitely deep fluid under gravitational constraints are not damped. They are reversible. Therefore your argument (which I don't much like anyway) is demonstrably wrong, for at least one class of dispersive waves. I do not think the dispersive character of the weaves has anything much to do with the internal damping of the medium, which I think is the gist of your argument. Oh, by dispersive I mean that waves of different frequency travel at different speeds. Cheers Greg Locock > > Why sound in gases does not have dispersions, but > > the one in solids has dispersion? The answer is: because sound in [quoted text clipped - 11 lines] > Therefore your argument (which I don't much like anyway) is demonstrably > wrong, for at least one class of dispersive waves. Original question was why sounds in gases has different behaviour then in solids. When you try to put attention to some particular case, like water under some specific curcumstances you dump the topic. Stay focused, please, on general medium and do not take some specific boundary condition, try to think about medium in continuum. > I do not think the dispersive character of the weaves has anything much > to do with the internal damping of the medium, which I think is the gist > of your argument. When God created :))) this World, he used basic laws of nature, like conservation energy, etc and basic math like wave equations. To figure out the whole picture, try to describe some medium what takes the whole continuum and has internal disturbance source. Put dsome diturbance restrictions in place, please, like sound range as opposite of shock waves and describe the disturbance propagations across the medium to get an answer why speed of sound in gas is _not_ function from disturbance frequency. Try to be abstract, please, from what 'you think', please, but rely on math havily. That is not rocket science, acoustics was developed well enough to the beginning of 20 century. If you just repeat steps what the greatest people did early you will see the answer for the problem and you will agree with my previous post when I shortly summarized the math and physical nature of solid, inlcluding fluids, and gas mediums. Good luck, Alex > Oh, by dispersive I mean that waves of different frequency travel at > different speeds. > > Cheers > > Greg Locock >>> Why sound in gases does not have dispersions, but >>>the one in solids has dispersion? The answer is: because sound in [quoted text clipped - 31 lines] > from disturbance frequency. Try to be abstract, please, from what 'you > think', please, but rely on math havily. I gave you a specific real example of an undamped dispersive system. Therefore all your windbag philosophy is moot. Cheers Greg Locock > >>> Why sound in gases does not have dispersions, but > >>>the one in solids has dispersion? The answer is: because sound in [quoted text clipped - 38 lines] > > Greg Locock Can you see the difference between "Could someone please explain why sound travels at different speeds depending on frequency through a solid, but not through air?" and your example "the dispersive surface waves in an infinitely deep fluid under gravitational constraints". The question was not about deep fluids in gravitational field. Good luck, Alex >>>>>Why sound in gases does not have dispersions, but >>>>>the one in solids has dispersion? The answer is: because sound in [quoted text clipped - 46 lines] > Good luck, > Alex Wrong, you claim damping is essential to dispersion, I gave an example where it is not. Can you see your error? Cheers Greg Locock > > Can you see the difference between "Could someone please explain why > > sound travels at different speeds depending on frequency through a [quoted text clipped - 12 lines] > > Greg Locock One more time: if you want discuss "the dispersive surface waves in an infinitely deep fluid under gravitational constraints", just create new thread with this topic and I will explain you physics in the phenomena. This discussion tread is about "Could someone please explain why sound travels at different speeds depending on frequency through a solid, but not through air?" and is not specific to deep fluids or suface waves, but covers gases, liquids, solids and plasma. We discuss spead of sound in continuum media here. To discuss something different, like surface waves are, just create new thread with topic about speed of surface wave in deep water, please. Be specific about your question, please, because, I hope you know the difference between surface wave in media and sound wave at least from Lamb Hydrodynamic book. Have a nice Thanksgiving, Alex >Wrong, you claim damping is essential to dispersion, I gave an example >where it is not. > >Can you see your error? Isn't this the same Alex who recognized the difference between physiologic acoustics and psychacoustics only after many posts? Give him time. The mathematical rebuttal to his claim that damping is essential to dispersion is to compare the Burgers and Korteweg-deVries equations. Both have propagating wave terms. (Nonlinear, but that's just an extra.) The Burgers equation has a second derivative term, which is clearly dissipative (omega-squared in the frequency domain), while Korteweg-deVries has a corresponding third derivative term (i-omega-cubed) which is clearly not dissipative but does represent dispersion. Don't tell him about the connection of K-dV to water waves and we'll be fine. :-) Ken Plotkin > >Wrong, you claim damping is essential to dispersion, I gave an example > >where it is not. [quoted text clipped - 18 lines] > > Ken Plotkin Nice humor. Ken, you probably, could brings distinguishes between sound wave and surface wave much better then I'm :)). With your humor it is easy to explain, isn't it? :-) Second, I expect you can do all details clear. :-) Alex > Dispersive Medium – Sound speed is a function of frequency. The spatial > and temporal distribution of a propagating disturbance will continually > change. Each frequency component propagates at each its own phase speed, > while the energy of the disturbance propagates at the group velocity: > Cg. Water is an example of a dispersive medium. .... " A Story: Way back when my home town, wilkes-Barre, PA still had electric buses (after street car tracks were removed), Some work was being done on the overhead trolley electric wire. The line passed our 2nd story living room, and that window was open (no A/C then) I heard a chirp- chirp- chirp sound outside the window, pretty loud, and definitely not a bird! I stuck my head out, looking for the source, and it saw that it was that electric line, a stretched bare copper cable about a half inch in diameter. A block or two on my right, I could see a work crew using a lift truck to work on that cable. They were changing the cleats that were soldered to the top of that cable, repositioning them, perhaps to accommodate the 2-wire line needed for the rubber tire electric busses. The cleats were removed cold, by hammering a chisel into the soldered gap. Each blow sent a mechanical impulse into the stretched cable. Normally a "click" should be all that is heard, but in this case it was a chirp, sweeping from high to low audio frequencies. It was clear that either one of two things was happening: Either the cable was dispersive, and the high frequencies arrived first, likely that the high speed waves were compressive, while the low speed waves were lateral shear (bending) waves; or that doppler was going on where a single frequency "ring" was traveling at a moderate speed toward me, passing and then departing, and the chirp was as expected from the Doppler effect. Anyone else ever have this experience? Angelo Campanella > > Dispersive Medium Sound speed is a function of frequency. The spati > al [quoted text clipped - 39 lines] > > Angelo Campanella I think, you did hear some electrical discharge between trolly wire and equipment, or because wire was little moved around its normal support points discharges between wire and and points of wire support when isolation was not too good. Certainly, may be something else. Actually, interesting phenomena. >>electric line, a stretched bare copper cable about a half inch in >>diameter. A block or two on my right, I could see a work crew using a [quoted text clipped - 3 lines] >>The cleats were removed cold, by hammering a chisel into the soldered >>gap. Each blow sent a mechanical impulse into the stretched cable. > I think, you did hear some electrical discharge between trolly wire > and equipment, or because wire was little moved around its normal Not so (though it may also occur under your circumstances). No trolleys or busses were nearby when I heard and saw it occur. The workman clearly was causing the chirp with each hammer blow. Here, Karl Uppiano correctly referenced this phenomenon with his Star-Wars laser shot sound, crescent wrench blow method. That was exactly what I heard circa 1950. > support points discharges between wire and and points of wire support > when isolation was not too good. Certainly, may be something else. > Actually, interesting phenomena. Now I want to see us here correctly analyze and characterize it! Angelo Campanella  Signature--------- www.CampanellaAcoustics.com --------- > >>electric line, a stretched bare copper cable about a half inch in > >>diameter. A block or two on my right, I could see a work crew using a [quoted text clipped - 21 lines] > > Angelo Campanella Yup. Could be nice to see :)). Far away from my home in Oregon :). Alex Bobby Nelson wrote: > Dispersive Medium – Sound speed is a function of frequency. The spatial > and temporal distribution of a propagating disturbance will continually > change. Each frequency component propagates at each its own phase speed, > while the energy of the disturbance propagates at the group velocity: Cg. > Water is an example of a dispersive medium. .... " A Story: Way back when my home town, wilkes-Barre, PA still had electric buses (after street car tracks were removed), Some work was being done on the overhead trolley electric wire. The line passed our 2nd story living room, and that window was open (no A/C then) I heard a chirp- chirp- chirp sound outside the window, pretty loud, and definitely not a bird! I stuck my head out, looking for the source, and it saw that it was that electric line, a stretched bare copper cable about a half inch in diameter. A block or two on my right, I could see a work crew using a lift truck to work on that cable. They were changing the cleats that were soldered to the top of that cable, repositioning them, perhaps to accommodate the 2-wire line needed for the rubber tire electric busses. The cleats were removed cold, by hammering a chisel into the soldered gap. Each blow sent a mechanical impulse into the stretched cable. Normally a "click" should be all that is heard, but in this case it was a chirp, sweeping from high to low audio frequencies. It was clear that either one of two things was happening: Either the cable was dispersive, and the high frequencies arrived first, likely that the high speed waves were compressive, while the low speed waves were lateral shear (bending) waves; or that doppler was going on where a single frequency "ring" was traveling at a moderate speed toward me, passing and then departing, and the chirp was as expected from the Doppler effect. Anyone else ever have this experience? If I remember correctly, the original sound for the Star Wars "laser shots" used in the space ship battle scenes was created by hitting a guy wire on a power pole with a Crescent wrench. It created a rapid high-to-low frequency sweep. >> Dispersive Medium – Sound speed is a function of frequency. The >> spatial and temporal distribution of a propagating disturbance will [quoted text clipped - 29 lines] > > Anyone else ever have this experience? Yes, I've heard it when striking long iron railings. I'm pretty sure it was used as an example in one N&V course I went to. In order to radiate sound they are presumably bending waves. Cheers Greg Locock Hi Derrick, You ask a very interesting and basic question. Let's take the example of transverse waves in a bar. In this case, the wave velocity is proportional to the square root of the wave frequency. The reason for this is that, when you go through the derivation of the equation of motion of the bar, you must balance acceleration forces with shear forces, which in turn depend upon moment (torque) that tend to bend the bar. If you take the simplest case of a freely vibrating bar (no external force) and no friction, the equation of motion for y, deflection of the bar, consists of two terms, one of which represents the restoring force, and this term, because of the moments, has a fourth derivative with respect to x (axial distance along the bar). This is the chief mathematical distinction between this equation and the wave equation, which governs longitudinal vibrations, and which contains only a second derivative for the corresponding term. When you look for simple harmonic solutions in the transverse case, you find that the wave velocity depends upon the frequency. This is the mathematical explanation. The physical explanation proceeds in more detail as follows. Acceleration forces are balanced by net shear forces, which depend upon the rate of change of shear forces. The shear forces depend on net moments (torques), or rate of change of moment, which is rate of change of curvature (third derivative of x). Thus, acceleration forces are balanced by the second derivative of curvature (or fourth power of x). With longitudinal waves in, for example, a taught, uniform, flexible string, the tension is assumed independent of x, and net restoring force depends only upon the curvature (second power of x). In summary, the dependence of wave speed on frequency for transverse waves in a bar is due to the fact that restoring forces, because of the mechanism for applying moment, or torque, are dependent on the higher order derivatives of the wave shape in the bar. This dependency doesn't exist for longitudinal waves in the idealized string, in which purely tension forces are considered. Best regards, Tom www.bluesbox.biz > Could someone please explain why sound travels at different speeds > depending on frequency through a solid, but not through air? Of > course the easy answer is that the wavelength changes (for all but one > frequency), but why does that happen? |
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