1. Vibrations and Waves
Honors Physics

2. Biblical Reference Ephesians 4:14
Then we will no longer be infants, tossed back and forth by the waves.
Ephesians 4:14

3. Simple Harmonic Motion
Back and forth motion that is caused by a force that is directly proportional to the displacement.
The displacement centers around an equilibrium position.

4. Springs – Hooke’s Law
One of the simplest type of simple harmonic motion is called Hooke's Law.
This is primarily in reference to springs.

5. Springs – Hooke’s Law
The negative sign tells us that “F” is a restoring force; it works in the opposite direction of the displacement.

6. Hooke’s Law
Common formulas which are set equal to Hooke's law are Newton’s Second Law and weight.

7. Example
A 0.55 kg mass is attached to a vertical spring, which stretches 36 cm from it’s original equilibrium position. What is the spring constant?

8. Example
A load of 50 N attached to a spring hanging vertically stretches the spring 5.0 cm. The spring is now placed horizontally on a table and stretched 11.0 cm. What force is required to stretch the spring this amount?

9. Conservation of Energy in Springs

10. Springs are like Waves and Circles
The amplitude, A, of a wave is the same as the displacement ,x, of a spring. Both are in meters.
Crest
Equilibrium Line
Trough

11. CREST
Period
Equilibrium Line
Period (T): the time for one revolution or one complete oscillation (one crest and trough).
Oscillations could also be called vibrations and cycles.
Ts = sec/cycle
Trough
In the wave above we have 1.75 cycles or waves (vibrations or oscillations).
Assume that the wave crosses the equilibrium line in one second intervals.
T = 3.5 seconds/1.75 cycles. T = 2 sec.

12. Frequency The Frequency of a wave is the inverse of Period.
That means that the frequency is cycles/sec.
The commonly used unit is Hertz (HZ).

13. Measuring SHM for a Spring
The period of a Spring-Mass System is:
Proportional to 2
Inversely proportional to the square root of the spring constant
Proportional to the square root of the mass on the spring
The greater the mass, the larger the period
The greater the spring constant (more stiff), the smaller the period

14. Example
A 125 N object vibrates with a period of 3.56 seconds when hanging from a spring. Find the spring constant.

15. Remember the Pendulum…

16. Measuring SHM for a Pendulum
The period of a pendulum is:
Proportional to 2 (it’s sweeping out an arc of a circle)
Inversely proportional to the square root of gravity
Proportional to the square root of the length of the pendulum

17. Example
The height of a tower is unknown, but a pendulum, extending from the ceiling almost touches the floor. If the period of the pendulum is 12 s, what is the approximate height of the tower?

18. What is a wave A Wave is a vibration or disturbance in space.
A Medium is the substance that all sound waves travel through and need to have in order to move.

19. Longitudinal Waves 2 areas:
Longitudinal Wave - A fixed point will move parallel with the wave motion
2 areas:
Compression - an area of high molecular density and pressure
Rarefaction - an area of low molecular density and pressure

20. Transverse Waves
Transverse Wave - A fixed point will move perpendicular with the wave motion.
Wave parts: Crest, Trough, Wavelength, Amplitude, Frequency, Period

21. All waves have 4 basic properties:
Properties of Waves
All waves have 4 basic properties:
Amplitude
Wavelength λ lambda
Frequency f
Speed c

22. Properties of Waves
Amplitude – the maximum distance the wave moves up and down.
The more energy a wave has the greater the amplitude.

23. Properties of Waves
Wavelength – the distance between two corresponding parts of a wave
Short Waves can complete more cycles than Long Waves in the same amount of time.

24. Properties of Waves
Frequency – the number of complete waves that pass a given point
Frequency is measured in the unit called Hertz (Hz).
A wave that occurs every second has a frequency of 1 Hz.

25. Properties of Waves
Speed – the distance a wave travels in a given amount of time.
The speed of sound through air is 331 m/s.

26. Wave Speed
You can find the speed of a wave by multiplying the wave’s wavelength in meters by the frequency (cycles per second).
Since a “cycle” is not a standard unit this gives you m/s.

27. Example
A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength?

28. Wave Behavior Superposition - The combination of two overlapping waves
Interference - The result of superposition

29. Standing Waves Two main parts of standing waves:
A standing wave is produced when a wave that is traveling is reflected back upon itself.
Two main parts of standing waves:
Antinodes – Areas of maximum amplitude
Nodes – Areas of zero amplitude

30. Interference Interference is the interaction between waves that meet
There are two types of interference: Constructive and Destructive

31. Reflection
When an object hits a surface it can not pass, it bounces back.
This is called reflection.

32. Refraction
The bending of waves due to a change in speed is called refraction.

33. Diffraction
When a wave moves around a barrier or through an opening in a barrier, it bends and spreads out. This is known as diffraction.