Table of contents
- 0. Math Review(0)
- 1. Intro to Physics Units(0)
- 2. 1D Motion / Kinematics(0)
- Vectors, Scalars, & Displacement(0)
- Average Velocity(0)
- Intro to Acceleration(0)
- Position-Time Graphs & Velocity(0)
- Conceptual Problems with Position-Time Graphs(0)
- Velocity-Time Graphs & Acceleration(0)
- Calculating Displacement from Velocity-Time Graphs(0)
- Conceptual Problems with Velocity-Time Graphs(0)
- Calculating Change in Velocity from Acceleration-Time Graphs(0)
- Graphing Position, Velocity, and Acceleration Graphs(0)
- Kinematics Equations(0)
- Vertical Motion and Free Fall(0)
- Catch/Overtake Problems(0)
- 3. Vectors(0)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(0)
- Adding Vectors Graphically(0)
- Vector Composition & Decomposition(0)
- Adding Vectors by Components(0)
- Trig Review(0)
- Unit Vectors(0)
- Introduction to Dot Product (Scalar Product)(0)
- Calculating Dot Product Using Components(0)
- Intro to Cross Product (Vector Product)(0)
- Calculating Cross Product Using Components(0)
- 4. 2D Kinematics(0)
- 5. Projectile Motion(0)
- 6. Intro to Forces (Dynamics)(0)
- 7. Friction, Inclines, Systems(0)
- 8. Centripetal Forces & Gravitation(0)
- Uniform Circular Motion(0)
- Period and Frequency in Uniform Circular Motion(0)
- Centripetal Forces(0)
- Vertical Centripetal Forces(0)
- Flat Curves(0)
- Banked Curves(0)
- Newton's Law of Gravity(0)
- Gravitational Forces in 2D(0)
- Acceleration Due to Gravity(0)
- Satellite Motion: Intro(0)
- Satellite Motion: Speed & Period(0)
- Geosynchronous Orbits(0)
- Overview of Kepler's Laws(0)
- Kepler's First Law(0)
- Kepler's Third Law(0)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(0)
- Gravitational Potential Energy for Systems of Masses(0)
- Escape Velocity(0)
- Energy of Circular Orbits(0)
- Energy of Elliptical Orbits(0)
- Black Holes(0)
- Gravitational Force Inside the Earth(0)
- Mass Distribution with Calculus(0)
- 9. Work & Energy(0)
- 10. Conservation of Energy(0)
- Intro to Energy Types(0)
- Gravitational Potential Energy(0)
- Intro to Conservation of Energy(0)
- Energy with Non-Conservative Forces(0)
- Springs & Elastic Potential Energy(0)
- Solving Projectile Motion Using Energy(0)
- Motion Along Curved Paths(0)
- Rollercoaster Problems(0)
- Pendulum Problems(0)
- Energy in Connected Objects (Systems)(0)
- Force & Potential Energy(0)
- 11. Momentum & Impulse(0)
- Intro to Momentum(0)
- Intro to Impulse(0)
- Impulse with Variable Forces(0)
- Intro to Conservation of Momentum(0)
- Push-Away Problems(0)
- Types of Collisions(0)
- Completely Inelastic Collisions(0)
- Adding Mass to a Moving System(0)
- Collisions & Motion (Momentum & Energy)(0)
- Ballistic Pendulum(0)
- Collisions with Springs(0)
- Elastic Collisions(0)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(0)
- 12. Rotational Kinematics(0)
- 13. Rotational Inertia & Energy(0)
- More Conservation of Energy Problems(0)
- Conservation of Energy in Rolling Motion(0)
- Parallel Axis Theorem(0)
- Intro to Moment of Inertia(0)
- Moment of Inertia via Integration(0)
- Moment of Inertia of Systems(0)
- Moment of Inertia & Mass Distribution(0)
- Intro to Rotational Kinetic Energy(0)
- Energy of Rolling Motion(0)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(0)
- Torque with Kinematic Equations(0)
- Rotational Dynamics with Two Motions(0)
- Rotational Dynamics of Rolling Motion(0)
- 14. Torque & Rotational Dynamics(0)
- 15. Rotational Equilibrium(0)
- 16. Angular Momentum(0)
- Opening/Closing Arms on Rotating Stool(0)
- Conservation of Angular Momentum(0)
- Angular Momentum & Newton's Second Law(0)
- Intro to Angular Collisions(0)
- Jumping Into/Out of Moving Disc(0)
- Spinning on String of Variable Length(0)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(0)
- Angular Momentum of a Point Mass(0)
- Angular Momentum of Objects in Linear Motion(0)
- 17. Periodic Motion(0)
- 18. Waves & Sound(0)
- Intro to Waves(0)
- Velocity of Transverse Waves(0)
- Velocity of Longitudinal Waves(0)
- Wave Functions(0)
- Phase Constant(0)
- Average Power of Waves on Strings(0)
- Wave Intensity(0)
- Sound Intensity(0)
- Wave Interference(0)
- Superposition of Wave Functions(0)
- Standing Waves(0)
- Standing Wave Functions(0)
- Standing Sound Waves(0)
- Beats(0)
- The Doppler Effect(0)
- 19. Fluid Mechanics(0)
- 20. Heat and Temperature(0)
- Temperature(0)
- Linear Thermal Expansion(0)
- Volume Thermal Expansion(0)
- Moles and Avogadro's Number(0)
- Specific Heat & Temperature Changes(0)
- Latent Heat & Phase Changes(0)
- Intro to Calorimetry(0)
- Calorimetry with Temperature and Phase Changes(0)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(0)
- Phase Diagrams, Triple Points and Critical Points(0)
- Heat Transfer(0)
- 21. Kinetic Theory of Ideal Gases(0)
- 22. The First Law of Thermodynamics(0)
- 23. The Second Law of Thermodynamics(0)
- 24. Electric Force & Field; Gauss' Law(0)
- 25. Electric Potential(0)
- 26. Capacitors & Dielectrics(0)
- 27. Resistors & DC Circuits(0)
- 28. Magnetic Fields and Forces(0)
- 29. Sources of Magnetic Field(0)
- Magnetic Field Produced by Moving Charges(0)
- Magnetic Field Produced by Straight Currents(0)
- Magnetic Force Between Parallel Currents(0)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops and Solenoids(0)
- Toroidal Solenoids aka Toroids(0)
- Biot-Savart Law (Calculus)(0)
- Ampere's Law (Calculus)(0)
- 30. Induction and Inductance(0)
- 31. Alternating Current(0)
- Alternating Voltages and Currents(0)
- RMS Current and Voltage(0)
- Phasors(0)
- Resistors in AC Circuits(0)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(0)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(0)
- Phasors for Inductors(0)
- Impedance in AC Circuits(0)
- Series LRC Circuits(0)
- Resonance in Series LRC Circuits(0)
- Power in AC Circuits(0)
- 32. Electromagnetic Waves(0)
- 33. Geometric Optics(0)
- 34. Wave Optics(0)
- 35. Special Relativity(0)
18. Waves & Sound
Velocity of Longitudinal Waves
18. Waves & Sound
Velocity of Longitudinal Waves: Study with Video Lessons, Practice Problems & Examples
14PRACTICE PROBLEM
Imagine a longitudinal wave traveling through a steel rod. The wave has a frequency of 8000 Hz. What is the wavelength of this wave as it propagates through the steel rod?
![Table of elastic moduli for various materials including steel and iron.](data:image/png;base64,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)
![Table of densities for substances like aluminum and copper.](https://static.studychannel.pearsonprd.tech/courses/physics/thumbnails/cb29b2a2-874f-44d2-af81-5a22b7b1655e)
Imagine a longitudinal wave traveling through a steel rod. The wave has a frequency of 8000 Hz. What is the wavelength of this wave as it propagates through the steel rod?