1. Physics 7E
Prof. D. Casper

2. 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.

3. 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

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

5. 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.

6. 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

7. 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

8. How Mechanical Waves Move

9. 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

10. 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

11. 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

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

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

14. 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?

15. 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

16. 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)