1. Chapter 11
Vibrations and Waves

2. Elasticity
When you hang a weight on a spring, the weight applies a force to the spring and it stretches in direct proportion to the applied force.
According to Hooke’s law, the amount of stretch (or compression), x, is directly proportional to the applied force F.
Double the force and you double the stretch; triple the force and you get three times the stretch, and so on: F ~ ∆x

3. Elasticity
If an elastic material is stretched or compressed more than a certain amount, it will not return to its original state.
The distance at which permanent distortion occurs is called the elastic limit.
Hooke’s law holds only as long as the force does not stretch or compress the material beyond its elastic limit.

4. Free Body Diagrams Revisited

5. Spring force = - (spring constant) (displacement) Felastic = -kx
Hooke’s Law
Spring force = - (spring constant) (displacement) Felastic = -kx

6. Hooke’s Law
If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium, what is the spring constant?

7. Simple Harmonic Motion
Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium

8. Simple Pendulums
Amplitude
Length
Period
Frequency

9. Simple Pendulums

10. Simple Pendulums
At what position in the cycle of a swinging pendulum is the potential energy of the pendulum at a maximum?

11. Simple Harmonic Motion Calculations
For a simple pendulum in simple harmonic motion
For a mass-spring system in simple harmonic motion

12. Waves
Medium – a physical environment through which a disturbance can travel
Mechanical wave – a wave that requires a medium to travel through
Examples Non-examples

13. Transverse Waves
Wave motion is perpendicular to equilibrium

14. Transverse Waves

15. Transerve Waves

16. Longitudinal Waves
Wave motion is parallel to equilibrium

17. Wave Properties Pulse wave Reflection
A wave that is just one interference – no repetition
Reflection

18. Constructive and Destructive Interference
Constructive interference
A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave

19. Constructive and Destructive Interference
A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave

20. speed of a wave = (frequency) (wavelength) v = f λ
1. A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.
2. The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels at the speed of light (3.00 x 108 m/s). Find the frequency of the laser light.

21. De Broglie Waves
Louis de Broglie suggested that all matter has wavelike characteristics.
where h is Planck’s constant, equal to 6.63 x J·s.
This wavelength is too small to notice interference for large objects. This idea becomes important when looking all things at the microscopic level.

22. De Broglie Waves
What is the wavelength of an electron (mass = 9.11 x 10¯31 kg) traveling at 5.31 x 106 m/s?