# Confusion on wording of a dimension problem

the speed v of sound waves in a gas can be express in terms of the pressure p and the density q (mass per unit volume) of the gas, as v=ap^bq^c, where a, b, and c are dimensionless constants. The dimensions of pressure are m/((LT)^2). What must be the values of b and c.

I am confused on what to write for the dimensions of q. Would it be m/L^3 as in mass/volume?

## Answers and Replies

berkeman
Mentor
the speed v of sound waves in a gas can be express in terms of the pressure p and the density q (mass per unit volume) of the gas, as v=ap^bq^c, where a, b, and c are dimensionless constants. The dimensions of pressure are m/((LT)^2). What must be the values of b and c.

I am confused on what to write for the dimensions of q. Would it be m/L^3 as in mass/volume?

Welcome to the PF.

Could you add some parenthesis to your equation to eliminate the ambiguities?

"v=ap^bq^c"

v=a(p^b)(q^c)

berkeman
Mentor
v=a(p^b)(q^c)

Ah, that helps. Now can you fill in the units for each term? I usually use square brackets to indicate the units like v[m/s].

v=[L/T], p=[M]/[L][T^2]

Chestermiller
Mentor
Read up on the Buckingham Pi Theorem. That is what is involved here.

Chet