Re: Speed of sound at altitude and temp

[brian whatcott <inet@intellisys.net>]

At 01:23 7/16/97 EDT, David Dockstader wrote:
> Why do you suggest that the value I read from the graph is incorrect?
> I presume the equation you give is for sea level and there is no reason
> to expect it to give the correct answer for 35,000 feet is there?

There is a rumor abroad, that no matter how poorly physics students
are taught, the arrogance element in the course work always gets through.
  This is doubtless a calumny in the general case, but speaking for 
myself I see that the epithet has merit, in connection with my attempted
explanation of speed of sound in air.

    Here are the facts: speed of sound in atmospheric air is almost 
independent of pressure but acutely sensitive to air temperature 
for a given air composition.
   If much water vapor is added (a material of lower density than dry 
air), the speed again changes.

As c is quite well established at standard temperature and pressure
as 331.4 m/s    (i.e at sea level) it is easy to tell if a mistake
is made in computing its value at elevated positions because:

 cooler = slower  
  and
 higher = cooler

  (this last rule which is capsulated for pilots as -2 degC per 1000 ft.
holds on average until the tropopause where temperature stabilizes,
 and even higher, t begins to rise again, towards space.)
 So higher means a lower value of c until great heights are attained.

I realise you have probably been seduced by the deceptive (but true)
expression: c = root ( K / rho )
where K  is the appropriate elastic constant ( the bulk modulus of 
elasticity)  and rho is the normal density of the medium.

You need not feel unduly put down by this contretemps - it happens 
that Newton also examined this question, and concluded (not 
unreasonably) that the appropriate value for K was that for isothermal
conditions.
   It turns out and  experiment confirms that the appropriate value 
is in fact the adiabatic one.

This has the effect of canceling the pressure/density effect on c
until very high experimental pressures are reached. These are not to 
be found in the real atmosphere.

I hope you will find this discourse more modest and more understandable.
 I would commend you purchase a dictionary of science or physics.
You will find many such questions are readily answered here.
I can recommend Valerie Pitt's 'The Penguin Dictionary of Physics',
a paper-back, but there are many others, I am sure.

Lest arrogance be found entirely missing from this note, I will not 
forbear to add this advice:
 "If you hear a teacher derogate the value of science books in general,
including dictionaries, you may confidently assume she has lost the 
meaning of the love of knowledge and is better avoided."

Regards



brian whatcott <inet@intellisys.net>
Altus OK