Physics 7E Prof. D. Casper

Course Stuff Web Site MasteringPhysics: Lecture slides posted through Chapter 14 Solution to this week’s discussion problems posted MasteringPhysics: Next long homework assignment (Chapter 14) is due next Thursday Chapter 15 long homework and optional problems will be posted over the weekend.

Forced Oscillation An oscillator is forced when a driving force acts on it Very common physical situation! In steady state, the system will ALWAYS oscillate at the driving frequency 𝜔 𝑑 regardless of its natural frequency 𝜔 0 It is still a harmonic oscillator, but the frequency is set by that of the driving force Resonance occurs when the driving frequency 𝜔 𝑑 is set close to the natural frequency 𝜔 0

Resonance Amplitude Applied Force: Amplitude: 𝐹= 𝐹 𝑑 cos⁡( 𝜔 𝑑 𝑡) 𝐴= 𝐹 𝑑 𝑚 𝜔 0 2 − 𝜔 𝑑 2 2 + 2𝛾 𝜔 𝑑 2 Very large when: 𝜔 0 ≈ 𝜔 𝑑 , and 𝛾≈0

Chapter 15: Mechanical Waves Learning goals: What is meant by a mechanical wave, and the different varieties of mechanical waves. How to use the relationship between speed, frequency and wavelength for a mechanical wave. How to interpret and use the mathematical expression for a sinusoidal periodic wave. How to calculate the speed of waves on a rope or string. How to calculate the rate at which a mechanical wave transports energy. What happens when mechanical waves overlap and interfere. The properties of standing waves on a string, and how to analyze these waves. How stringed instruments produce sounds of specific frequencies.

Waves are Everywhere! Sound waves and light waves are the primary means by which we collect information from the world around us Quantum mechanics tells us that electrons, atoms and molecules all have wave-like behavior

Mechanical vs. Electromagnetic Waves A disturbance propagating through a physical medium. Disturbance can be transverse or parallel (longitudinal) to direction of motion Examples: Sound waves Earthquakes Ocean waves Vibrating strings Electromagnetic A disturbance of the electric and magnetic fields. EM waves can pass through vacuum. Disturbance is always transverse to direction of motion. Examples: Visible light Radio WiFi X-rays

How Mechanical Waves Move

What Moves? In a wave, what travels from one end to the other? A) Particles with mass B) The medium C) Energy D) Forces of motion Wave motion transports energy over a distance Matter (the medium) is not transferred

Transverse Wave Pulse The pulse moves to the right Disturbance passes through each element of the medium, carrying kinetic energy through it The medium only moves up and down, transverse to the pulse direction The pieces of the string do not move to the right with the pulse

Longitudinal Wave Pulse Again the pulse moves to the right Again the disturbance passes through each element of the medium, carrying kinetic energy through it Here the medium moves longitudinally, parallel to the direction of the disturbance Particles of the fluid still do not have any net displacement to the right

Example: Seismic Waves Fastest, least destructive Slowest, most destructive

Be the Wave! (Part One) Was the “wave” you just did: A) A transverse wave B) A longitudinal wave C) Not really a wave

Be the Wave! (Part Two) Is there another way to do a transverse stadium (or lecture hall) wave? Is there a way to do a longitudinal lecture hall wave?

Requirements for a Mechanical Wave Must have: A physical medium for the disturbance to propagate through A source of disturbance that excites the medium Some mechanism that allows elements of the medium to influence each other and transmit the disturbance

Waves and Oscillation 𝑥 𝑡 =𝐴 cos⁡(𝜔𝑡+𝜙) A mechanical wave can be treated an interaction between coupled harmonic oscillators Each particle of the medium undergoes Simple Harmonic Motion Interactions cause one oscillator to influence its neighbors, allowing the disturbance to propagate 𝑥 𝑡 =𝐴 cos⁡(𝜔𝑡+𝜙)