1. Harmonic Motion
Mr. Villa
Physics

2. Harmonic motion Key Question:
How do we describe the back and forth motion of a pendulum?

3. Cycles, systems, and oscillators
A cycle is a unit of motion that repeats.

4. Harmonic motion is common
scommunications
sound
clocks
nature

5. Period and Frequency
Period is the time it takes to move through one cycle.
Period is measured in seconds (s).
Frequency is how many cycles can occur in one second.
Frequency is measured in Hertz (Hz).

7. Amplitude
Amplitude describes the size of a cycle.

8. Amplitude
The energy of an oscillator is proportional to the amplitude of the motion.
Friction drains energy away from motion and slows the pendulum down.
Damping is the term used to describe this loss.

9. Why Things Oscillate
Systems that have harmonic motion move back and forth around a central or equilibrium position.
Equilibrium is maintained by restoring forces.
A restoring force is any force that always acts to pull the system back toward equilibrium.

11. Waves A wave is an oscillation that travels.
A ball floating on water can oscillate up and down in harmonic motion.
The surface of the water oscillates in response and the oscillation spreads outward from where it started.

12. Recognize waves Anytime you see a vibration that moves...
Anything that makes or responds to sound...
Anything that makes or responds to light ...
Anything that transmits information through the air (or space) without wires...
cell phones, radio, and television.
Anything that allows you to “see through” objects...
ultrasound, CAT scans, MRI scans, and X rays

13. Characteristics of waves
Waves have cycles, frequency, and amplitude, just like oscillations.
The amplitude of a wave is the maximum movement from equilibrium.
The frequency of a wave tells how often each point oscillates.
The wavelength of a wave is the length of one complete cycle.

14. Mechanical Waves
A mechanical wave is a physical disturbance in an elastic medium.
Consider a stone dropped into a lake.
Energy is transferred from stone to floating log, but only the disturbance travels.
Actual motion of any individual water particle is small.
Energy propagation via such a disturbance is known as mechanical wave motion.

15. A Transverse Wave
In a transverse wave, the vibration of the individual particles of the medium is perpendicular to the direction of wave propagation.
Motion of particles
Motion of wave

16. A Transverse Wave
Motion of particles
Motion of wave

17. Longitudinal Waves
In a longitudinal wave, the vibration of the individual particles is parallel to the direction of wave propagation. v
Motion of particles
Motion of wave

18. Longitudinal Waves
Motion of particles
Motion of wave

19. Water Waves

20. Water Waves
Motion of wave
Motion of particles
Motion of particles

21. Wavelength l is distance between two particles that are in phase.
Periodic Wave Motion
A vibrating metal plate produces a transverse continuous wave as shown.
For one complete vibration, the wave moves a distance of one wavelength l as illustrated. l B A
Wavelength l is distance between two particles that are in phase.

22. Production of a Longitudinal Wave
An oscillating pendulum produces condensations and rarefactions that travel down the spring.
The wave length l is the distance between adjacent condensations or rarefactions.

23. Velocity and Wave Frequency
The period T is the time to move a distance of one wavelength. Therefore, the wave speed is:
The frequency f is in s-1 or hertz (Hz).
The velocity of any wave is the product of the frequency and the wavelength:

24. Example 1: An electromagnetic vibrator sends waves down a string
Example 1: An electromagnetic vibrator sends waves down a string. The vibrator makes 600 complete cycles in 5 s. For one complete vibration, the wave moves a distance of 20 cm. What are the frequency, wavelength, and velocity of the wave?
f = 120 Hz
The distance moved during a time of one cycle is the wavelength; therefore:
v = fl
v = (120 Hz)(0.2 m)
l = 0.20 m
v = 24.0 m/s