1. Vibrations and Waves

2. Simple Harmonic Motion

3. Useful Definitions
Periodic Motion – A repeated motion. If it is back and forth over the same path, it is called simple harmonic motion.
Examples: Wrecking ball, pendulum of clock
Simple Harmonic Motion – Vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium

4. Useful Definitions
Amplitude – the maximum angular displacement from equilibrium.
Period – the time it takes to execute a complete cycle of motion
Symbol = T SI Unit = second (s)
Frequency – the number of cycles or vibrations per unit of time
Symbol = f SI Unit = hertz (Hz)
T = 1/f or f = 1/T

5. A: B:
Same amplitude; different frequencies

6. Properties of Waves

7. Useful Definitions
Crest: the highest point above the equilibrium position
Trough: the lowest point below the equilibrium position
Wavelength λ : the distance between two adjacent similar points of the wave

8. Wave Motion A wave is the motion of a disturbance.
Medium: the material through which a disturbance travels
Mechanical waves: a wave that requires a medium to travel through
Electromagnetic waves: do not require a medium to travel through

9. Wave Types Pulse wave: a single, non-periodic disturbance
Periodic wave: a wave whose source is some form of periodic motion
When the periodic motion is simple harmonic motion, then the wave is a SINE WAVE (a type of periodic wave)
Transverse wave: a wave whose particles vibrate perpendicularly to the direction of wave motion
Longitudinal wave: a wave whose particles vibrate parallel to the direction of wave motion

11. Transverse wave
Longitudinal Wave

12. Speed of a Wave Speed of a wave= frequency x wavelength v = fλ
Example Problem:
The piano string tuned to middle C vibrates with a frequency of 264 Hz. Assuming the speed of sound in air is 343 m/s, find the wavelength of the sound waves produced by the string.
343 m/s = (264 Hz)(λ)
1.30 m = λ

13. Wave Interactions

14. Constructive vs Destructive Interference
Constructive Interference: individual displacements on the same side of the equilibrium position are added together to form the resultant wave
Destructive Interference: individual displacements on the opposite sides of the equilibrium position are added together to form the resultant wave

16. Ruben's Tube Video 1:57