Question

velocity of sound in a gas depends upon pressure and density of the gas. using the dimensional analysis and establish the relation between them

Answer 1

Answer:

Explanation:

The speed of sound c in a gas depends on among other things on the pressure on the gas, the density and probably, possibly on their viscosity. Determine c-

My Variable list:

Pressure p ML^-1T^-2

Density ρ ML^-3

Speed v LT^-1.

By following  matrix:

| | M | L | T |:    | p | 1 | -1 | -2 | :    | ρ | 1 | -3 | 0 |:     | v | 0 | 1 | -1 |

.after a couple of row reductions comes out to be : k = P/(ρv^2) (pi=k)(k = constant) The answer should be v = k(P/ρ)^(1/2).

Hence the relationship.