Speed of sound in a metal rod

My guess is that it relates to specific stiffness. Beryllium is very high in specific stiffness; steels, magnesium, and aluminum alloys are medium; and lead is very low.

I think you'd find silicon carbide also very high, and alumina ceramics to be moderately high.

Taking the extreme case, a perfectly stiff material would transmit sound instantaneously.

"Taking the extreme case, a perfectly stiff material would transmit sound instantaneously. "

Faster than the speed of light?

Excellent question! I don't have an answer. A perfectly stiff material (and especially a perfect "specific stiffness" material -- i.e., one with 0 density) does not exist, so we won't be able to do the experiment.

But suppose we have an infinitely stiff rod of 1000 km length. If we push on it, the other end must move at exactly the same time. Likewise, if we pull on it. So if we push and pull at, let's say, 100 times per second, then there will be a sound at the other end. And the start of that sound will be precisely at the same time as the start of the sound at our push-pull end. The motion of the material itself, however, would be much slower. (If the amplitude is 1mm, then the material motion is only 200 mm per second.) So we are not violating the prohibition against matter moving at greater than the speed of light.

So, yes, I guess then the speed of sound in this material (assuming longitudinal waves) would be higher than the speed of light. The speed of the matter would be much lower.

In order to propagate, sound proceeds by streching and compressing atomic bonds. If those bonds are very stiff, they will be very hard to strech or compress. If the rod can displace freely (without any friction or energy dissipation) then the "sound" pressure will diplace it "as a whole"...the transmission of the motion will be indeed instantaneous...but can we really think of a propagating wave in this case? If the bonds are very very stiff the rod might simply be modelled as a point mass.

The propagation of a wave is function of two physical parametres of the material considered:

the stiffness and

the specific mass

When you mention only one then you neglegt the other it is compulsory to look at the two AT SAME TIME and consider their interaction.

A rod can be considered as a series of small masses bound together with a series of springs. In a vibrating system one does not consider only spri,g rate but also the inertia of the parts the same in a vibrating rod or wire the difference is only related to the fact that in surrounding systems we are more confronted with discrete systems and a rod behaves as continous system.

A rod can be considered as a series of small masses bound together with a series of springs.

Absolutely agree. Only, if the springs cannot be strecheted or compressed (case of infite stiffness)...you may substitute all the small masses by a single one.

hi mtcuberes,

the greeks said that all flows, as an engineer you know that there is no undeformable stuff.

Sound transmission is MICROSCOPIC and not MACROSCOPIC. To consider a rod as a whole is a MACROSCOPIC simplification used often in mechanical analysis at low frequencies when the MICROSCOPIC aspects can be neglected. It is by the way possible going from the diffrential equation for continuum to determine when the rod can be considered as a whole.

I am sorry to insist that a model MUST be coherent with the conditions it is thought for if not it is NOT of any use since it leads to wrong results. This is the problem of extrapolations done for domains out of the validity limits.

Hi Nick Name

I agree with both you and mtcuberes, in slightly different ways.

This is an interesting problem, posed first as a thought problem in response to my saying that a material with infinite specific stiffness (infinitely high stiffness and infinitely low mass) would transmit sound instantly. Then someone questioned, "faster than the speed of light?"

As the stiffness of this rod increases, eventually, it moves as a whole, so we can't detect any wave motion in the rod (there is just the macroscopic oscillation). One end moves in and out... the other end moves in and out... perfectly in phase. I think, that, even in real world terms, with a very stiff but light rod (pultruded carbon fiber, for example) operating at low sound frequency (let's say 100 Hz) that the "sound transmission" speed could be greater than light speed. (from playing around with such rods, I know that the resonant frequency, longitudinally, is relatively high -- in other words, if you tap the end with a hammer aligned lengthwise, the rod rings at a relatively high pitch.)

Suppose you drove one end of the rod with a transducer, and put a similar transducer at the opposite end as a sensor. You compare the waveform at the end of rod with the waveform transmitted through wire a distance equal to the rod. I'd guess that the rod-conducted signal might be faster than the wired signal (and that you could see a phase difference on a pretty fast scope).

So I think sound transmission can be by macroscopic means, rather than just microscopic means. As the medium becomes stiffer and lighter, the effect is more macroscopic.

to Blink

if you understand by "sound" the transmission of mechanical energy it is ok. What I wanted to make clear is that a model must be accorded to the physics of the phenomenom one wants to modelize. The problem is the ratio between own frequency and the disturbing one. The higher this ratio is the more the body will behave as a "whole". But we cannot part elasticity from inertia in a vibrating system.

In fact we are all of us right providung we specify in which range we think. I agree with you as you see.

Thanks for your viewpoint, Nick Name.

Nevertheless, still many things that I do not understand...The stiffer the material (i.e. the higher its own frequency), the easier it is that sound propagates throught it...Nevertheless, a stiffer material would made the ration "own frequency versus disturbing frequency" ration higher, and hence one would expect that the material should behave as a "whole" and hence, just experience a displacement but NOT "PROPAGATE" A WAVE...perhaps the problem with sound is the high wavelength of soundwaves with compared with interatomic distances...

it is a misunderstanding:

when the own frequency is high with resoect to the disturbing frequency then the disturbance will have a low frequency and the rod will behave as (or near as) a whole.

If the disturbing frequency is high then the waves manifest themselves stronger. I doubt that we have to go as far as the interatomic distances since in usual mechanics we will never reach such frequencies(so high). When I used MICROSCOPIC I thought about small with respect to the overall dimensions of the body. I assumed that the wave length is small with respect to the rod length.

it is the crystalline structure. that could be sussed from diamond's attrib. vs lead

speed of sound is proportional to (E/ρ)^0.5 where E= young modulus and ρ= specific mass (density). So you can compute the differences = the lower the density and the higher the intrinsic stiffness the higher the speed.

Reminds me of a physics lab from college where we had to measure the speed of sound in brass and steel rods. I think the TA had not experienced the lab previously. We were given instructions to rub the rods with shammies to get them to vibrate. For a long time no one got the idea and we looked foolish rubbing these metal rods until someone hit the natural frequency of the rod and then it was like the elevated train was making a turn in the physics lab. Especially when all the metal rods were screeching.

As mentioned above, It is the Chrystaline structure - the way the atoms align with each other,

Berylium has a hexagonal structure. See

http://environmentalchemistry.com/yogi/periodic/Be.html#Atomic

Boron does the same thing, it has a Rhombohedral structure see

http://environmentalchemistry.com/yogi/periodic/B.html#Atomic

Diamond also has a hexagonal structure.

http://environmentalchemistry.com/yogi/periodic/C.html#Atomic

As far as I remember graphite has the hexagonal structure but NOT diamond which has a tetrahedral structure.

This is the reason why grphite is used as solid lubricant - it shears along the planes of higher atomic density- and diamond has the highest hardness because of its pyramidal structure.

Or may be I am wrong? it is always good to have a doubt about own knowledge.