18. Waves & Sound

Wave Functions & Equations of Waves

Physics - Mechanics: Mechanical Waves (10 of 21) The Wave Equation in 1-Dimension

Wave Equation

Physics - Mechanics: Mechanical Waves (9 of 21) The Wave Equation

y = (7.5 cm) cos[(1.26 cm−1)x − (44.9 s−1)t]

y = (7.5 cm) cos[(2.51 cm−1)x − (89.8 s−1)t]

y = (7.5 cm) sin[(1.26 cm−1)x − (44.9 s−1)t]

y = (7.5 cm) sin[(2.51 cm−1)x − (89.8 s−1)t]

Write the mathematical representation of the wave graphed in the following two figures.<img src="https://static.studychannel-prd.pearsonprd.tech/courses/physics/thumbnails/images/184a92ee"alt=""/>

The Wave Function

The Mathematical Description Of A Wave

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mtext>.3</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x2009;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>positive</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mtext>.1</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x2009;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>positive</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mtext>.76</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x2009;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>negative</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mtext>.3</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x2009;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>negative</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>2</mn><mtext>.1</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x00A0;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>negative</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

<math display=“inline” xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mtext>.76</mtext><mtext>&#x00A0;</mtext><mtext>m/s</mtext><mo rspace="thickmathspace">&#x2009;</mo><mi mathvariant="normal" class="MathML-Unit">in</mi><mtext>&#x00A0;</mtext><mtext>the</mtext><mtext>&#x00A0;</mtext><mtext>positive</mtext><mtext>&#x00A0;</mtext><mi>x</mi><mtext>-direction</mtext></mrow></math>

The vertical displacement of a wave moving along the x-axis is given by <math display=“inline”><mrow><mi>y</mi><mrow><mo>(</mo><mrow><mi>x</mi><mo>,</mo><mi>t</mi></mrow><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mrow><mrow><mn>0.045</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow></mrow><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mrow><mrow><mo>(</mo><mrow><mrow><mn>3.4</mn><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">Hz</mi></mrow></mrow><mo>)</mo></mrow><mi>t</mi><mo>&#x2212;</mo><mrow><mo>(</mo><mrow><mn>4.5</mn><mtext>&#x00A0;</mtext><msup><mrow><mo rspace="thickmathspace">&#x2062;</mo><mi mathvariant="normal" class="MathML-Unit">m</mi></mrow><mrow><mo>&#x2212;</mo><mn>1</mn></mrow></msup></mrow><mo>)</mo></mrow><mi>x</mi></mrow><mo>)</mo></mrow></mrow></math>. What is the wave speed and in what direction is it traveling?

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t)=2.30mm cos[(16.98 rad/m^)x+(742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x, t)=2.30mm cos[(16.98 rad/m^)x+(742 rad/s)t]. Being more practical, you measure the rope to have a length of 1.35 m and a mass of 0.00338 kg. You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength; (d) wave speed; (e) direction the wave is traveling; (f) tension in the rope; (g) average power transmitted by the wave.

Introduction to Wave Function

vT(7cm, 2s) = 23.3 m/s; vT,max = 157 m/s; aT,max = 7854 m/s2

vT(7cm, 2s) = 23.3 m/s; vT,max = 25 m/s; aT,max = 1250 m/s2

vT(7cm, 2s) = 70.8 m/s; vT,max = 157 m/s; aT,max = 7854 m/s2

vT(7cm, 2s) = 70.8 m/s; vT,max = 157 m/s; aT,max = 49,298 m/s2

vT(7cm, 2s) = 107.2m/s; vT,max = 157 m/s; aT,max = 7854 m/s2

vT(7cm, 2s) = 107.2 m/s; vT,max = 157 m/s; aT,max = 49,298 m/s2

The function for some transverse wave is ? = (0.5 m) sin [(0.8 m−1)x − 2?(50 Hz)t + π/3]. What is the transverse velocity at t=2 s, x=7 cm? What is the maximum transverse speed? The maximum transverse acceleration?

Periodic Traveling Wave Motion as a Function of x AND t | Doc Physics

Velocity Of A Wave

Phase Angle

A transverse wave is represented by the following function:y = (18 cm) sin [2π (x/2cm) − t/5s + 1/4)]. What is the phase angle of this wave?

Graphs Of Mathematical Representation of Wave

Learn the toughest concepts covered in Physics with step-by-step video tutorials and practice problems by world-class tutors

Patrick

Physics

https://static.studychannel-prd.pearsonprd.tech/courses/physics/thumbnails/physics

#FFFFFF

Doc Schuster

DrPhysicsA

Andrey K

Patrick Ford

Michel van Biezen

Jennifer Cash

Bozeman Science

1. Intro to Physics Units

2. 1D Motion / Kinematics

3. Vectors

4. 2D Kinematics

5. Projectile Motion

6. Intro to Forces (Dynamics)

7. Friction, Inclines, Systems

8. Centripetal Forces & Gravitation

9. Work & Energy

10. Conservation of Energy

11. Momentum & Impulse

12. Rotational Kinematics

13. Rotational Inertia & Energy

14. Torque & Rotational Dynamics

15. Rotational Equilibrium

16. Angular Momentum

17. Periodic Motion

19. Fluid Mechanics

20. Heat and Temperature

21. Kinetic Theory of Ideal Gases

22. The First Law of Thermodynamics

23. The Second Law of Thermodynamics

24. Electric Force & Field; Gauss' Law

25. Electric Potential

26. Capacitors & Dielectrics

27. Resistors & DC Circuits

28. Magnetic Fields and Forces

29. Sources of Magnetic Field

30. Induction and Inductance

31. Alternating Current

32. Electromagnetic Waves

33. Geometric Optics

34. Wave Optics

35. Optical Instruments

36. Special Relativity

[BOOK PHYS] !CLUTCH

The Doppler Effect

Sound Waves

Standing Waves

Intro to Waves

Standing Sound Waves

Wave Interference

Beats

Sound Intensity

Velocity of Transverse Waves (Strings)

General Chemistry

Jules

Study the key concepts of Physics with descriptive videos, questions, and more

General Biology

Jason

Financial Accounting

Brian

Dive deep into Psychology with videos, practice problems, and more.

Psychology

Microeconomics

The first in a two-course sequence introduces the basic structure and functions of the human body

Anatomy & Physiology

College Algebra covers algebraic topics and skills necessary to succeed in college-level math

College Algebra

Organic Chemistry

Johnny

Genetics

Kylia

GOB Chemistry

Microbiology

Cell Biology

Analytical Chemistry

Study topics incliding trogonometric functions, identities and equations, solutions of triangles, complex numbers, and other topics as time permits

Trigonometry

Learn the toughest concepts covered in Precalculus with step-by-step video tutorials and practice problems by world-class tutors

Precalculus

Biochemistry

Macroeconomics

Chemistry

Biology

Math

Business

Social Sciences

Michelle Barry Franco

Building Great Presentations

Eric Zackrison, PhD

Critical Thinking And Problem Solving

Sam Bennett

Embracing Times Of Uncertainty

Nicole Tetreault, PhD

Emotional Intelligence Basics

Eugene Choi, PharmD

Enhancing Your Critical Thinking Skills

Jason Richardson, PsyD

Habits To Win Every Day

Alyssa Lowery, PhD

Having Powerful Advanced Conversations

Don Gilman, EdD

How To Influence & Persuade

Amy Matthews

Leadership Skills For Rising Stars

Listening To Lead

Michael Shermer, PhD

Making Decisions Under Uncertainty

Lynne Hurdle

Mistakes To Avoid When Resolving Conflict

Michael Veltri

Overcoming Decision Making Traps

Mike Vardy

Prioritizing Effectively

Secrets Of Effective Prioritization

Strategies To Build Up Your Creativity

Tools For Decision Making

Tutti Taygerly

Unleash And Advance Your Creativity

Winning Collaboration: How To Work More Effectively With Different Personalities

Writing Emails People Want To Read

Critical Thinking

Self Management

Digital Literacy

Collaboration

Communication

Analytical Thinking

Leadership

Flexibility/Adaptability

Innovation

Eric Zackrison

Nicole Tetreault

Dive deep into Python with videos and more.

Introduction to Python

Arianne Dee

Agile Project and Product Management

Agile & Product Management

Mariya Breyther 

Introduction to Microsoft Power BI

Microsoft Power BI

Chris Sorensen

Data Analysis Fundamentals with Excel

Data Analysis - Excel

Chris Sorensen & Ammul Shergill

Getting Started with  and Cryptocurrency

Introduction to Blockchain

George Levy

Learn Enough HTML, CSS and Layout to be Dangerous

HTML, CSS & Layout

Lee Donahoe & Michael Hartl

Learn Enough JavaScript to be Dangerous: A Tutorial Introduction to Programming with JavaScript