Confusion on wording of a dimension problem

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Homework Help Overview

The discussion revolves around the dimensional analysis of the speed of sound waves in a gas, expressed in terms of pressure and density. Participants are examining the relationship defined by the equation v=ap^bq^c, where the dimensions of pressure are provided, and there is uncertainty regarding the dimensions of density.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the correct dimensional representation of density, with one suggesting it might be mass per volume. There is also a request for clarification on the equation's format to reduce ambiguity.

Discussion Status

The discussion is active, with participants providing insights into the dimensional analysis and suggesting the use of notation for clarity. Some guidance has been offered regarding the Buckingham Pi Theorem, indicating a potential direction for further exploration.

Contextual Notes

There is a noted confusion regarding the dimensions of density, and participants are encouraged to clarify their equations to facilitate understanding. The discussion reflects a learning environment where assumptions are being questioned and explored.

camillevoll
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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?
 
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camillevoll said:
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)
 
camillevoll said:
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]
 
Read up on the Buckingham Pi Theorem. That is what is involved here.

Chet
 

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