The velocity of sound in a gas is 300 m/s. The root mean square velocity of the molecules is of the order of-?

Question

1) 440 m/s
2) 4400 m/s
3) 44 m/s
4) 4.4 m/s
(cp / cv=Gamma=1.4)

Please show me ... how to solve

Answer 1

See the ref.
Vsound = sqrt(gamma/3) * Vm (RMS molecular V), so
Vm = Vsound / sqrt(gamma/3) = 439.2.
Answer is (1).

Answer 2

?

The molecules do not travel
they merely vibrate and pass the wave front to the next molecule

so the velocity is zero

unless they teach it differently in schools now

I'll support my statement a little more, sound travels in solids
what do you suppose the velocity of a molecule is in a solid

you can talk about the wavefront travelling, but not the molecules


But I'm a little curious to know what use the rms value of an oscillating particle is to anyone (it need not be sinusoidal for a start)

Answer 3

1) 440 m/s

In gas molecules are far apart, and move with constant velocities between the collisons.
For this reason the speed of molecules cannot be less than speed of sound, either 44m/s or 4.4 m/s.

If you want exact formula, just google it.

Answer 4

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

hope that helps

I'm going to say 440 m/s because if we take 300*sqrt(2) = 424

its been a long time since college.