phy1020.DVI

Table 11-1. Speed of sound in several fluids. (All data are for 20 ıC.)

Medium Bulk modulusB(Pa) Density (kg/m^3 ) Speed of sound

Air 1:42 105 1.204 343

Helium 1:69 105 0.1663 1008

SF 6 1:35 105 6.069 149

Water 2:2 109 1000 1497

A common laboratory demonstration is to inhale some helium gas and then try to talk; the amusing result
is an abnormally high-pitched voice. The opposite effect can be demonstrated by inhaling sulfur hexafluo-
ride (SF 6 ), which results in an abnormally low voice. (You shouldnotattempt to do this yourself, as both
demonstrations are potentially dangerous.) As you can see from the table, all three gases have similar bulk
moduli; they differ mainly by their densities, which results in different speeds of sound for each gas. It is
these differences in the sound speed that is responsible for the high and low pitches of one’s voice in each
gas.
The bulk modulus and density of a gas are also functions of temperature. We can find the an explicit
expression for the speed of sound in a gas as a function of temperature as follows: the bulk modulusBof an
ideal gas is given by

BD

p; (11.4)

wherepis the pressure of the gas, and is the ratio of the heat capacity at constant pressure (CP) to the heat
capacity at constant volume (CV):

D

CP

CV

: (11.5)

It can be shown from thermodynamics that:

• For a monatomic gas: D^53 D1:67


• For a diatomic gas, or other gas with linear molecules: D^75 D1:40


• For a gas with nonlinear molecules: D^43 D1:33

Now substituting Eq. (11.4) into the Newton-Laplace equation (11.3), we have

vsndD

r



p

: (11.6)

Now using the ideal gas law

pVDNkBT (11.7)

(whereVis the volume of gas,Nis the number of atoms or molecules of gas,kBD1:3806488 10 ^23 J
K^1 is the Boltzmann constant, andTis the absolute temperature in kelvins) to substitute for the pressurep,
we have

vsndD

s



NkBT

V

: (11.8)