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)
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- Kepler's Third Law for Elliptical Orbits(0)
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- 9. Work & Energy(0)
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- 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)
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- 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)
34. Wave Optics
Diffraction
34. Wave Optics
Diffraction: Study with Video Lessons, Practice Problems & Examples
16PRACTICE PROBLEM
A music practice room has an entrance consisting of two doorways, each 1.1 m wide and separated by a distance of 3.1 m. Outside the practice room, a tuning fork is struck in the hallway, producing a sound wave with a frequency of 512 Hz.
(i) Find all the angles of θ at which no sound will be heard within the practice room when the tuning fork is struck.
(ii) If a student is standing inside of the practice room as illustrated below when the tuning fork is struck outside of the room, will the student have a good explanation for not hearing the sound? Explain.
Assuming that the speed of sound is 340 m/s and that it has not bounced off the walls inside of the room.
![Diagram showing sound wave diffraction in a music practice room with a student inside.](data:image/png;base64,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)
A music practice room has an entrance consisting of two doorways, each 1.1 m wide and separated by a distance of 3.1 m. Outside the practice room, a tuning fork is struck in the hallway, producing a sound wave with a frequency of 512 Hz.
(i) Find all the angles of θ at which no sound will be heard within the practice room when the tuning fork is struck.
(ii) If a student is standing inside of the practice room as illustrated below when the tuning fork is struck outside of the room, will the student have a good explanation for not hearing the sound? Explain.
Assuming that the speed of sound is 340 m/s and that it has not bounced off the walls inside of the room.