1. Waves/Vibrations
Unit 6

2. Simple Harmonic Motion
Any periodic motion that is the result of a restoring force.
Every simple harmonic motion is a back-and-forth motion over the same path
Recall: Hooke’s Law helps us to calculate the restoring force (Spring Force Fs)
Fs= -kx

3. FOR ALL WAVES WE CAN CALCULATE THE PERIOD USING:
Period & Amplitude
The maximum displacement from the equilibrium position is called the amplitude.
Period (T) is the time it takes for an object to complete one full cycle of motion.
After a full period an object is back where it started
measured in seconds
Frequency – f – the number of complete cycles an object goes through per unit of time.
measured in Hertz (Hz)
FOR ALL WAVES WE CAN CALCULATE THE PERIOD USING:
T=1/f

4. Simple Harmonic Motion
At equilibrium position – velocity reaches a maximum. (when the object has a spring displacement of 0)
At maximum displacement, (furthest stretch or compression of the spring), the restoring force (Fs) and acceleration reach a maximum.

5. Period of SHM
We can calculate the period of an oscillating spring mass system using the following formula
T= period of oscillation
m= mass
k= spring constant

6. The Simple Pendulum
The restoring force of a pendulum is a component of the bob’s weight. (Fg)
The only forces acting on the bob (mass at the end of the pendulum) are the force exerted by the string (tension) and the weight of the mass (Fg)

7. The Simple Pendulum
As the displacement of the bob (mass) increases from equilibrium position to maximum to displacement, the Gravitational Potential Energy increases
Therefore, at maximum displacement from equilibrium the bob has the GREATEST gravitational potential energy – because it is at its max height.

8. Period of a Pendulum
We can calculate the period of a simple pendulum by the following formula

9. Types of Waves Transverse Waves
when wave motion is perpendicular to the vibrations of a wave

10. Types of Waves Longitudinal Waves
when wave motion is parallel to the vibrations of a wave.
A longitudinal wave is also called a compression wave

11. Longitudinal Waves

12. Properties of Waves A wave is the motion of a disturbance
There are different mediums in which a wave travels
Ex: Water, Air, Glass etc.
A pulse is a single traveling wave.
Periodic or Traveling Wave – is a series of pulses within a medium creating periodic motion

13. Properties of Waves Amplitude Trough Crest
Maximum displacement of a wave from its equilibrium position
Trough
Lowest point below equilibrium position on a wave
Crest
Highest point above equilibrium position on a wave
Wavelength (λ llambda, measured in meters)
The distance between two adjacent similar points of a wave (crest to crest OR trough to trough)

14. Fundamental Wave Equation
We can relate the speed, frequency and wavelength of a wave with the following equation.
v=fλ
v= velocity (m/s)
f= frequency (Hz)
λ= wavelength (m)

15. Interference of Waves
Two traveling waves can meet and pass through each other without being destroyed or even altered
Waves obey the Superposition Principle
If two or more traveling waves are moving through a medium, the resulting wave is found by adding together the displacements of the individual waves point by point
Actually only true for waves with small amplitudes

16. Constructive Interference
Two waves, a and b, have the same frequency and amplitude
Are in phase
The combined wave, c, has the same frequency and a greater amplitude

17. Constructive Interference
Two pulses are traveling in opposite directions
The net displacement when they overlap is the sum of the displacements of the pulses
Note that the pulses are unchanged after the interference

18. Constructive Interference
When two waves momentarily overlap and combine to form a larger wave.
To create constructive interference, a crest must meet a crest or a trough must meet and trough.

19. Destructive Interference
Two waves, a and b, have the same amplitude and frequency
out of phase
When they combine, the waveforms cancel

20. Destructive Interference
Two pulses are traveling in opposite directions
The net displacement when they overlap is decreased since the displacements of the pulses subtract
Note that the pulses are unchanged after the interference

21. Destructive Interference
When two waves momentarily overlap and combine to partially or totally cancel each other
To create destructive interference, a crest must meet a trough

22. Ruben’s Tube Sound Intro
Visual Representation of a Sound wave involving FIRE

23. Producing a Sound Wave
Sound waves are longitudinal waves traveling through a medium
A tuning fork can be used as an example of producing a sound wave

24. Pitch
Pitch is related mainly, although not completely, to the frequency of the sound
Pitch is not a physical property of the sound
Frequency is the stimulus and pitch is the response
It is a psychological reaction that allows humans to place the sound on a scale

25. Using a Tuning Fork A tuning fork will produce a pure musical note
As the tines vibrate, they disturb the air near them
As the tine swings to the right, it forces the air molecules near it closer together
This produces a high density area in the air
This is an area of compression

26. Using a Tuning Fork, continued
As the tine moves toward the left, the air molecules to the right of the tine spread out
This produces an area of low density
This area is called a rarefaction

28. Categories of Sound Waves
Audible waves
Lay within the normal range of hearing of the human ear
Normally between 20 Hz to 20,000 Hz
Infrasonic waves
Frequencies are below the audible range
Earthquakes are an example
Ultrasonic waves
Frequencies are above the audible range
Dog whistles are an example

29. Applications of Ultrasound
Ultrasonic Waves – can be used to create images of very tiny objects.
Most commonly used as a diagnostic and treatment tool in medicine.

30. The Doppler Effect
A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer.
When the source and the observer are moving toward each other, the observer hears a higher frequency
When the source and the observer are moving away from each other, the observer hears a lower frequency

31. The Doppler Effect
Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves
Assumptions:
The air is stationary
All speed measurements are made relative to the stationary medium

32. Forced Vibrations
A system with a driving force will force a vibration at its frequency
When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance

33. An Example of Resonance
Pendulum A is set in motion
The others begin to vibrate due to the vibrations in the flexible beam
Pendulum C oscillates at the greatest amplitude since its length, and therefore frequency, matches that of A

34. Other Examples of Resonance
Child being pushed on a swing
Shattering glasses
Tacoma Narrows Bridge collapse due to oscillations by the wind
Upper deck of the Nimitz Freeway collapse due to the Loma Prieta earthquake

35. Tacoma Narrows

36. Characteristics of Light
What your eye recognizes as “white” light is actually light that can be separated into six elementary colors of the visible spectrum: red, orange, yellow, green, blue and violet
However, not all light is visible to the human eye
The spectrum includes MORE than just visible light

37. The Nature of Light
Light can be described as both a wave and a particle
Experiments can be devised that will display either the wave nature or the particle nature of light
In some experiments light acts as a wave and in others it acts as a particle
Particles of light are called “photons”

38. The Electromagnetic Spectrum
Light can be found in a variety of forms including radiation
Examples include: X Rays, microwaves, radio waves which all have similar properties to visible light
These are considered examples of electromagnetic waves.

39. The Electromagnetic Spectrum
Electromagnetic waves vary based upon frequency and wavelength.
Although specific ranges for frequency and wavelength are indicated on the table, in reality, the spectrum is continuous
Meaning, there is no definite division between types of waves and even some ranges actually overlap with one another.

40. c = 3.0 x 108 m/s Using the Spectrum
All electromagnetic waves move at the speed of light
We will denote the speed of light with the letter, c.
c = 3.0 x 108 m/s

41. Fundamental Wave Equation for Light Waves
The fundamental wave equation discussed previously relating speed, frequency and wavelength can be re-written to be specific for electromagnetic waves.
c= fλ

42. Example pg. 522 Sample 14A
The AM radio band extends from 5.4 x 105 Hz to 1.7 x 106 Hz. What are the longest and shortest wavelengths in this frequency range?

43. Brightness
Brightness decreases by the square of the distance from the source.
The further you get from a light source, the less bright the light appears to be.
The further away from the light source, the more spread out the light gets.

44. Reflection of Light
The texture of a surface affects how it reflects light
When light is reflected, the angle of incidence an the angle of reflection are equal to each other.

45. Law of Reflection The normal is a line perpendicular to the surface
It is at the point where the incident ray strikes the surface
The incident ray makes an angle of θi with the normal
The reflected ray makes an angle of θr with the normal
θi = θr

46. Refraction
When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium
The ray that enters the second medium is bent at the boundary
This bending of the ray is called refraction

47. Refraction of Light
The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane
The angle of refraction, θ2, depends on the properties of the medium

48. Refraction Light may refract into a material where its speed is lower
The angle of refraction is less than the angle of incidence
The ray bends toward the normal

49. Refraction Light may refract into a material where its speed is higher
The angle of refraction is greater than the angle of incidence
The ray bends away from the normal

50. Index of Refraction
When light passes from one medium to another, it is refracted because the speed of light is different in the two media
The index of refraction, n, of a medium can be defined

51. Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2
θ1 is the angle of incidence
30.0° in this diagram
θ2 is the angle of refraction

52. Total Internal Reflection
Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction
Ray 5 shows internal reflection

53. Critical Angle
A particular angle of incidence will result in an angle of refraction of 90°
This angle of incidence is called the critical angle