Klarinet Archive - Posting 000883.txt from 1997/05

From: Stephen Froehlich <shorthnd@-----.edu>
Subj: RE: Ligatures - OK Please explain
Date: Fri, 30 May 1997 17:09:05 -0400

On Fri, 30 May 1997, Adam Calabrese wrote:

> At 10:32 AM 5/30/97 -0500, Stephen Froehlich wrote:
> >
> > There is an interesting article (I don't think its on sneezy but
> >its referenced from there) on the fact that the instrument walls are 30db
> >(that 10000 times) softer than the air column. Therefore, wall vibrations
> >are negligble, and therefore in terms of sound, material. The main pro to
> >grenedalia, as I understand it, is its relatively low cooeficent of
> >thermal expansion, and low specific heat compared to metals.
> >
> > Sincerely,
> > Stephen Froehlich
>
> Perhaps there was a typo and you meant 1000, not 10000? dB are used when
> comparing things (like pressue, intensity, etc). Also, walls are softer
> than the air column? What is the measurement for "softer"? I'll have to
> check the referenced articl if possible. However, that won't stop me from
> adding a few cents here. For intensity the definition of the decibels is
>
> db=10*log(G)
>
> where G is the gain (intensity ratio). 30 dB is a factor of G=1000 times
> greater. For pressure comparisons the definition is

You are, of course correct. Dividing by 10 in the wrong place.
That's what I get for not using paper and pencil. Still a factor of 1000
or 500 is enough to make it inaudible.

> Also, the thermal expansion statement seems reasonable enough to me without
> checking the numbers. However, I'm not sure what the specific heat
> statement means (ie, it may be irrelevant). The definition of specific heat
> comes from the 1st law of thermodynamics. Add a little heat and see what
> the temperature change is at a constant volume or pressure.
>
> sp heat = (1/nu)*(dQ/dT) (nu is the amount of substance in moles)

The specific heat is proportional to the time required for the
horn to "warm up". If it follows Newton's heating law, or even Fourier's,
the specific heat should fall out of the integral and be a direct
proportion to the characteristic time.

> My CRC actually doesn't give specific heats for wood. It gives thermal
> conductivity. All wood has a much lower thermal conductivity than metals
> (silver@-----. So
> grenadilla wood (from the mpingo tree - did anyone ever see the
> educational TV (Discovery, Learning Channel, PBS?) special about how
> wood from the mpingo tree is harvested? very interesting) would have one
> of the higher specific heats of the woods.

Please elaborate.

> OK, where was I going? Oh yeah - I don't think the specific heat statement
> makes sense. Maybe you meant thermal conductivity? My judgement is that the
> specific heat of wood would be higher than that of metal. Specific heat of
> silver at room temp is about 0.056 cal/(g deg K). Specific heat of carbon
> in graphite form is about 0.17 cal/(g deg K). Granted wood isn't all
> carbon, and it's a different form, but I think this is a good indication.
> Silver and gold (0.038) have relatively small specific heats compared to
> most of the elements.

I concede. On the other hand, a low thermal conductivity would
imply a larger temp difference through the wall, more stress, etc. (not
to mention that metal clarinets have much thinner walls) On the other
hand, consider the respective densities of the two materials. We're
really worried about specific heat per unit volume, aren't we?

> Sorry I got so long-winded. I think I'm preparing my scientific side to get
> involved in the acoustics discussions....

I'm actually just an undergrad in fizix. Thanks for straightening
me out. You might find the article interesting. I'll have to look up the
URL later. We're back to the question of why do different ligatures
behave differently? What is the mode of vibration that dissipates
differently with different metals? Perhaps its interference going around
the ligature?

Sincerely,
Stephen Froehlich