(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2Ff%2F0%2Fa%2Ff0aa0a8f1de4bb4cd5c26170954f39b3.png&hash=68b06bc0df75cff00438c5c0a7f0eedc)
where
- cideal is the speed of sound in an ideal gas.
- R (approximately 8.3145 J·mol-1·K-1) is the molar gas constant.
- k is the Boltzmann constant
γ (gamma) is the adiabatic index (sometimes assumed 7/5 = 1.400 for diatomic molecules from kinetic theory, assuming from quantum theory a temperature range at which thermal energy is fully partitioned into rotation (rotations are fully excited), but none into vibrational modes. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at 0 degrees Celsius, for air. Gamma is assumed from kinetic theory to be exactly 5/3 = 1.6667 for monoatomic molecules such as noble gases).
- T is the absolute temperature in kelvins.
- M is the molar mass in kilograms per mole. The mean molar mass for dry air is about .0289645 kg/mole.
- m is the mass of a single molecule in kilograms.
Thus we observe that for a monatomic gas, with three degrees of freedom:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2Fa%2F6%2F9%2Fa6965b5bf23c948de4237fd19b44d91b.png&hash=b4f7ce110dbc807dc66539034fb6b806)
while for a diatomic gas, with five degrees of freedom (at room temperature):
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2F1%2F8%2F6%2F18689553f959854e8fdd5108eb94d6d8.png&hash=03c668849f414c449781ccc1c020e396)
[tqble]
Gas Density (kg/m3) Speed (feet/sec) Standard Deviation (feet/sec) Air 1.2929 1039.7 22.4 Argon 1.7837 957.8 20.3 Carbon Dioxide 1.977 812.4 23.0 Propane 2.009 771.5 21.3
How about a good dose of hypothyroidism! (seriously)
Thus to reduce the speed of sound further, you probably require a gas with a large number of atoms, and a high atomic weight.Would that mean that having too much alcohol (C2H5OH, MW 46) in your breath would lower the pitch of your voice ?
...
I would guess that most molecules that are heavy enough to have a speed of sound 1/3rd the speed of air when a gas, would probably be too heavy to be gaseous at STP.
How about a good dose of hypothyroidism! (seriously)
Probably taking steroids would have the same effect.
So there would be some slight drop in frequency when breathing propane.Not advisable to smokers, however... [:)]
Would that mean that having too much alcohol (C2H5OH, MW 46) in your breath would lower the pitch of your voice ?