# Confusion on wording of a dimension problem

• camillevoll
In summary: The dimensions of pressure are m/((LT)^2) and the dimensions of density are m/L^3. To determine the values of b and c, we can use the Buckingham Pi Theorem.
camillevoll
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?

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

## 1. What is a dimension problem?

A dimension problem is a type of mathematical problem that involves finding the measurement or size of an object or space. This can include measurements such as length, width, height, area, or volume. Dimension problems often require the use of formulas and equations to solve.

## 2. Why is wording important in dimension problems?

Wording is important in dimension problems because it can affect how the problem is interpreted and solved. A slight change in wording can result in a completely different problem with a different solution. It is important to pay close attention to the wording and make sure it is clear and precise.

## 3. How can I avoid confusion in dimension problems?

To avoid confusion in dimension problems, it is important to read the problem carefully and identify the key information and measurements that are given. It can also be helpful to draw diagrams or visualize the problem to better understand it. If you are still unsure, you can ask for clarification or seek assistance from a teacher or tutor.

## 4. What are some common mistakes made in dimension problems?

Common mistakes in dimension problems include incorrect unit conversions, misinterpreting the wording, using the wrong formula or equation, and making calculation errors. It is important to double-check your work and make sure all measurements and calculations are accurate.

## 5. How can I improve my skills in solving dimension problems?

The best way to improve your skills in solving dimension problems is to practice regularly. You can also review mathematical concepts and formulas, and seek help from a teacher or tutor if needed. It can also be helpful to work on problems step-by-step and identify any areas where you may need additional practice or clarification.

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