Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

Speed of Sound in Gases: Dimensional Analysis

5 Questions

0 Views

Speed of Sound in Gases: Dimensional Analysis

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the value of the exponent x in the formula for the speed of sound?

1/2 (correct)

Which equation represents the relationship between the exponents x, y, and z for the speed of sound?

x - 3y + z = -1 (correct)

x + 3y + z = -1

x - 2y + z = -1

x + 2y + z = -1

What is the value of the exponent y?

1/2

-1/2 (correct)

-1

When applying dimensional analysis to the speed of sound, what is the dimension of pressure?

<p>$M L^{-2} T^{-2}$</p> Signup and view all the answers

In the dimensional equation for speed, the term representing volume contributes what value to the overall dimensional analysis?

<p>$L^{3}$</p> Signup and view all the answers

Study Notes

Speed of Sound in a Gas

Sound speed (V) in a gas, pressure (p), density (ρ), and volume (V) are related.
Dimensional analysis is used to find the exponents x, y, and z in the equation V = p^xρ^yV^z.

Dimensional Analysis

Pressure (p) = mass (m) × acceleration (a) / area (A)
p = kg⋅m^-1⋅s^-2 = M L^-1 T^-2
Density (ρ) = mass (m) / volume (V)
ρ = kg⋅m^-3 = M L^-3
Volume (V) = length³ = L³
Speed (V) = length / time = L T^-1
Substituting the units into the equation V = p^xρ^yV^z gives M^x L^-x T^-2x × M^y L^-3y × L^z = M L T^-1
Equating the exponents produces a system of equations to solve for x, y, and z.

Solving for Exponents

Simplifying the equation gives:
- For mass (M): x + y = 1
- For length (L): -x - 3y + z = 1
- For time (T): -2x = -1
Solving the system of equations:
- x = 1/2
- y = 1/2
- z = 0
The equation for the speed of sound in a gas is V = √(γp/ρ).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Explore the relationship between sound speed, pressure, density, and volume in gases through dimensional analysis. This quiz will guide you in deriving the exponents x, y, and z in the equation relating these physical properties. Test your understanding of pressure, density, and how they influence sound speed.