The speed v of sound waves depends on the pressure p and density d.?

Question

Using dimensional analysis, find an expression for v in terms of p and d. Thanks for your help. I was stomped on this one.

Answer 1

Sound is the result of molcular collision between molecules.
The Intensity of a sound wave depends on the density of the medium and the energy used to create the disturbence in the medium.
The Energy formula to create sound wave required to disturb the medium is as follows;
Es = Md x Vf^2
Where Es is the Max energy used to create the disturbance.
Md is the amount of mass disturbed.
Vf is the final velocity of the disturbed mass during one oscillation.
Va = average velocity =Vf/2

The formula for Vf^2= Es/Md

The dimensions in the formula balances as folows

Es(kg m^2/sec^2)/Md(kg)
canceling out the Units yields =m^2/sec^2 which is final velocity(Vf) squared.

Pressure is Energy per unit volume.=kg /sec^2 m
and distance is force per unit energyis the wavelength in units of meters.
frequency is the inverse of time period of the moving force of the wave.

Md Vf^2 /Volume = Pressure
solve for Vf ^2=Pressure x volume /Md
Yield Vf^2= Pressure /density of the disturbed mass. dimensional analysis yields the following;

Pressure[(kg/(sec^2x m) ]/density(kg/m^3)
canceling like units we obtain m^2/sec^2 which is Vf^2

Answer 2

It relies upon on the temperature considering the fact that with the increasing temperature air molecules shuttle at greater desirable speeds bumping against one yet another greater generally. Sound strikes speedier in such medium because of the fact it communicates with the molecules that carry the sound. whilst the temperature is going down molecules decelerate, interactions between them are rarer and sound passes by way of gaps of empty rely searching for molecules, that are its carriers; the sound is dispersing itself by way of area.