1. Waves Basics And Mechanical Waves

2. Vibrations and Waves
A wave is a disturbance that carries energy through matter (a medium) or space
The source of all wave motion is a vibration.
Waves transmit energy, not matter.
Some of a wave's energy is always being dissipated as heat. In time, this will reduce the wave's amplitude (displacement).
A wave cannot exist in one place but must extend from one place to another.
Light and sound are both examples of waves.

3. Electromagnetic Waves
A wave is a disturbance that carries energy through matter (a medium) or space:
Electromagnetic Waves
Mechanical Waves
Mechanical waves are waves that must travel through some form of matter to carry their energy.
The matter that carries a wave is called the medium and includes matter such as air, water, rock, metal, etc.
Mechanical waves can be either transverse or longitudinal waves.
In a given medium, the speed of waves is constant. Waves travel very quickly through solids, less quickly through liquids and slowest through gases.
EM waves are waves that can travel through empty space. They do not require a medium.
EM waves are transverse waves.
The EM spectrum consists of waves including gamma rays, x- rays, UV light, visible light, IR waves, microwaves and radio waves.
EM waves travel through space at the speed of light.

4. Transverse Waves Longitudinal Waves
Transverse waves can be modeled by using a sine wave.
Types of transverse waves include EM waves and ocean waves.
Depending on the type of wave, transverse waves may or may not require a medium.
Longitudinal waves can be modeled by using a spring.
Sound waves are longitudinal waves.
Longitudinal waves are mechanical waves – they require a medium.
compression
rarefaction

5. Electromagnetic Waves
Mechanical Waves
do not require a medium
require a medium
transverse wave
transverse wave
longitudinal wave
earthquake
s-waves
Ex: sound
Ex: light
earthquake
p-waves

6. Waves

7. Mechanical Waves
Waves carry energy, not matter. Example: waves form as wind blows across the water's surface, transferring energy to the water. As the energy moves through the water, so do the waves. The water itself stays behind, rising and falling in circular movements.
The speed of a wave depends on the medium.
In a given medium, the speed of waves is constant.
Kinetic theory explains differences in wave speed.
The closer the molecules are, the quicker vibrations are transferred. Therefore, waves travel very quickly through solids, less quickly through liquids and slowest through gases.

8. Transverse Waves
In transverse waves, particles vibrate at right angles to the direction the wave travels.
Transverse waves can be modeled by using a sine wave.
Types of transverse waves include EM waves and ocean waves.
Depending on the type of wave, transverse waves may or may not require a medium.
wavelength
amplitude
trough
crest

9. Longitudinal Waves
In longitudinal waves, particles vibrate back and forth in the same direction that the wave travels.
Longitudinal waves can be modeled by using a spring.
Sound waves are longitudinal waves.
Longitudinal waves are mechanical waves – they require a medium.
compression
rarefaction

10. Longitudinal Waves
Watch the particles carefully – notice that they only vibrate back and forth.
The particles do NOT travel with the wave.

11. Wave Pulses

12. Properties of Waves
Amplitude – Maximum displacement from equilibrium. The larger the amplitude, the more energy the wave carries.
Wavelength – The distance between successive identical parts of a wave. Represented by lambda, .
Crest – The high point of a wave.
Trough – The low point of a wave.
Period – The time needed for a wave to make one complete cycle (wavelength) of motion. Represented by T. Units of seconds.
Frequency – Number of cycles (wavelengths) per unit time. Represented by f. Units of hertz (Hz).
Wavelength
Crest
Amplitude
Equilibrium Position
Trough

13. Period and Frequency
Period is the time needed for a wave to make one complete cycle (wavelength) of motion. Represented by T. Units of seconds.
Frequency is the number of cycles (wavelengths) per unit time. Represented by f. Units of hertz (Hz).
Period and frequency are inverses.
Example: Calculate the frequency of a pendulum that has a period of 1/4 second.
f = 1 / T = 1 / (0.25 s) = 4 Hz

14. Simple Harmonic Motion (SHM)D I C
MOTION
Simple harmonic motion is a type of periodic motion or oscillation motion. It is a repetitive movement back and forth through an equilibrium, or central, position, so that the maximum displacement on one side of this position is equal to the maximum displacement on the other side.
The time interval of each complete vibration is the same, and the force responsible for the motion is always directed toward the equilibrium position and is directly proportional to the distance from it.

15. SHM and Periodic Motion
Periodic Motion any motion in which the path of the object repeats itself in equal time intervals. The simple pendulum is a great example of this type of motion

16. SHM and Oscillatory Motion
Another example of simple harmonic motion is the oscillation of a mass on a spring.
Simple harmonic motion is typified by this motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law, F = −kx, where k is the spring constant and x is the displacement of the spring.
The spring constant, k, is representative of how stiff the spring is. Stiffer (more difficult to stretch) springs have higher spring constants.

17. Period
The period, T, of a simple pendulum (time needed for one complete cycle) is approximated by the equation:
The period, T, of an oscillating mass on a spring (time needed for one complete oscillation) is approximated by the equation:
where l is the length of the pendulum and g is the acceleration of gravity.
where m is the mass and k is the spring constant.

18. Characteristics of Periodic Motion
All objects that are in periodic motion have three similar characteristics: velocity, period, and amplitude.
Velocity - They all have a velocity. You can measure the velocity of a bouncing ball, the weight on a pendulum, or such.
Period - is the time the object takes to go back and forth. If you spin a weight on a string, you can measure the time it takes to go 1 revolution. Drop a ball and measure the time it takes until it bounces back up. That is its period.
Amplitude - The amplitude is 1/2 the distance the object goes before it changes from one side of the period to the other. For an object in rotation, the amplitude is the radius of the circle (1/2 the diameter).

19. Other Examples of Periodic Motion
Vibrating spring - If you start a spring vibrating, it will continue to move back-and-forth for a long time. Internal friction slows it down or dampens its vibrations.
Bouncing ball - If you drop a ball, it will start to bounce in a regular fashion. A good rubber ball or a super-ball will keep bouncing for a long time. Because of internal friction and air resistance, the ball bounces less and less each time, until it finally stops. A perfect ball—without friction—would bounce forever.
Tuning fork - You strike a tuning fork, and you can see the ends vibrate back and forth. The vibrations cause the air to vibrate, resulting in sound or a musical note.
Circular motion - Spin a weight on a string around in circles. This is a periodic motion that repeats itself every rotation. The Earth rotates around the Sun in a periodic circular motion.

20. Check Question
Given the equation for the speed of waves: v = λ f Does this mean, for example, that high frequency sounds (high pitches), travel faster than low frequency sounds? NO!!! Wavelength and frequency vary inversely to produce the same speed of all sounds. So when one goes up, the other goes down.

21. Amplitude Indicates Energy
A tsunami is basically an ocean wave with a large amplitude. It carries considerable destructive energy.
Photo from:

22. Check for Understanding
How are the frequency and period related to each other?
What indicates how much power a wave has?
What is the speed of a wave with a frequency of 620 Hz and a wavelength of 10.5 m?

23. Earthquakes
Vibrations provide the energy for waves. The bigger the vibrations, the bigger the waves they create.
The vibrations from earthquakes can cause waves in the ocean and in the ground.
Tsunamis are giant ocean waves caused by undersea earthquakes.
Earthquakes cause waves in the ground called seismic waves. Different types of seismic waves travel at different speeds:
P-waves are longitudinal waves; they travel the fastest.
S-waves are transverse waves.

24. Earthquake monitoring station
Earthquake Waves
Earthquakes release energy that travels through and around the Earth in seismic waves.
The two main types of seismic waves are body waves and surface waves.
Body waves can travel through Earth’s inner layers.
Surface waves move only along the surface.
Earthquake location
Earth
Body wave path
Earthquake monitoring station
Surface wave path

25. Earthquake monitoring station
Earthquake Waves
The two types of body waves are primary (P) waves and secondary (S) waves.
P waves vibrate parallel to the direction they are traveling in a push-pull motion. P waves travel at a velocity of 4 to 6 km/s.
S waves vibrate perpendicular to their direction of travel. S waves travel at a velocity of 3 to 4 km/s.
The two types of surface waves are the Love wave and the Rayleigh wave.
Love waves move the surface of the ground from side to side.
Rayleigh waves roll along the surface in a circular motion, like an ocean wave. Most of the shaking felt from an earthquake is caused by Rayleigh waves.
Earthquake location
Earth
Body wave path
Earthquake monitoring station
Surface wave path
The Love wave is slightly faster than the Rayleigh wave, but both move at about 4 km/s.

26. Earthquake Check Question
A surface wave generated by an earthquake was recorded at Seismic Station 1. Forty seconds later the same wave was recorded at Seismic Station 2. What accounts for the time difference?
The origin of the wave is closer to Seismic Station 1.
The speed of the wave decreases with distance.
The wavelength is longer at Seismic Station 2.
The wave frequency increases when the wave passes through soil.

27. Check for Understanding
What is the speed of a wave with a frequency of 620 Hz and a wavelength of 10 m?

28. Wave Interactions Reflection Absorption Refraction Diffraction
Law of Reflection
Total Internal Reflection
Absorption
Refraction
Diffraction
Interference
Constructive
Destructive
Standing Waves
Polarization
Resonance

29. Wave Interactions

30. Anechoic Chamber
An anechoic chamber ("an-echoic" meaning non-reflective, non-echoing or echo-free) is a room designed to completely absorb reflections of either sound or electromagnetic waves. They are also insulated from exterior sources of noise.

31. Wave Interactions
The law of reflection states that the angle of incidence is equal to the angle of reflection.

32. Wave Interactions

33. Check for Understanding
What is the difference between reflection and refraction?
Provide an example of each.

34. Wave Interactions

35. Wave Interactions – Interference
When two or more waves are at the same place at the same time, the resulting effect is called interference.
Waves overlap to form an interference pattern.
The waves combine to form a single wave.
Constructive interference - when the crest of one wave overlaps the crest of another, their individual effects add together. The result is a wave of increased amplitude.
Destructive interference – when the crest of one wave overlaps the trough of another, their individual effects are reduced. The result is a wave of decreased amplitude.

36. Check for Understanding
What is interference?
Is interference always a bad thing?

37. Polarization Polarization is the alignment of transverse waves.
Longitudinal waves, such as sound, cannot be polarized.
Polarizing light filters affect light waves the way the fence affects the waves in the rope.

38. Standing Waves
Although waves usually travel, it is possible to make a wave stay in one place. A wave that is trapped in one spot is called a standing wave.
Standing waves are the result of interference. The resultant wave is created by the interference of two waves traveling at the same frequency, amplitude and wavelength but in opposite directions.
In a standing wave, the nodes remain stationary. This is where you can touch a standing wave on a rope without disturbing the wave.
The positions on a standing wave with the largest amplitudes are know as antinodes. Antinodes occur halfway between nodes.
Standing waves can be set up on the strings of musical instruments, in organ pipes, and by blowing across the top of a soda bottle.

39. Sound Waves Sound waves are caused by vibrations of material objects.
Sound waves are longitudinal waves.
Sound waves require a medium. Sound cannot travel through a vacuum.
Any matter will transmit sound.
Sound travels fastest through solids, less fast through liquids and slowest through gasses.
The subjective impression about the frequency of sound is pitch.
high pitched – high frequency
low pitched – low frequency

40. Frequency Ranges
The frequency range for normal human hearing is between 20 Hz and 20,000 Hz. As a person ages, the range will shrink, especially at the high frequency end.
Infrasonic (subsonic) sounds have frequencies below 20 Hz.
Ultrasonic sounds have frequencies above 20,000 Hz.

41. Animation courtesy of Dr. Dan Russell,
Sound in Air
Compression waves travel through air or along springs.
These waves travel with areas of compressions and rarefactions.
Sound is a mechanical wave – remember that it is not the medium that travels from one place to another, but the pulse that travels.
Animation courtesy of Dr. Dan Russell,
Kettering University

42. Speed of Sound
The speed of sound in a material depends not on the material’s density, but on its elasticity.
Elasticity is the ability of a material to change shape in response to an applied force, and then resume its initial shape once the distorting force is removed.
Steel is elastic, putty is inelastic.
In elastic materials, the atoms are relatively close together and respond quickly to each other’s motions, transmitting energy with little loss.
Sound travels about fifteen times faster in steel than in air, and about four times faster in water than in air.

43. Speed of Sound 340 m/sec x 3 sec = 1020 meters
The speed of sound in dry air at 0C is about 330 meters per second.
For each degree above 0C the speed of sound increases by 0.60 meters per second.
The speed of sound in air at normal room temperature (~20C) is about 340 meters per second. Use this number in calculations if no other information is provided.
Check: How far away is a storm if you note a 3 second delay between a lightning flash and the sound of the thunder?
340 m/sec x 3 sec = meters

44. Sonar

45. Loudness
The intensity of a sound is proportional to the square of the amplitude of a sound wave. . (i = ka2)
Sound intensity is objective and is measured by instruments such as an oscilloscope.
Loudness is a physiological sensation sensed by the brain. It is subjective but related to sound intensity.
The unit of intensity for sound in the decibel (dB).
Loudness varies nearly as the logarithm of intensity (powers of 10).

46. Common Levels of Sound SOURCE OF SOUND LEVEL (dB)
Jet Engine, at 30 m 140
Threshold of pain 120
Loud rock music 115
Old subway train 100
Average factory 90
Busy street traffic 70
Normal speech 60
Library
Close Whisper 20
Normal breathing 10
Hearing threshold 0

47. Sound Waves and Forced Vibrations
Resonance is a natural amplification of sound.
All objects have their own natural frequencies at which they are likely to vibrate.
Vibrations can also be forced. When the frequency of a forced vibration matches the natural frequencies of an object, resonance occurs.
Sounding boards are used to augment (increase) the volume (amplitude) of a vibrating object (like a string or tuning fork).
Sounding boards can be forced into vibrations.
Sounding boards are important in all stringed musical instruments.

48. Natural Frequency
Everything vibrates, from planets and stars to atoms and almost everything in between.
A natural frequency is one at which minimum energy is required to produce forced vibrations.
It is also the frequency that requires the least amount of energy to continue this vibration.
Natural frequencies depend on factors such as the elasticity and shape of the object.

49. Resonance
Every object vibrates at a characteristic frequency – this is its resonant, or natural, frequency.
Resonance is a condition that exists when the frequency of a force applied to a system matches the natural frequency of the system.
Examples of resonance are:
Pushing a swing
Tuning a radio station
Voice-shattered glass.
Tacoma Narrows Bridge Collapse in 1940.—High winds set up standing waves in the bridge, causing the bridge to oscillate at one of its natural frequencies.

50. Resonance
When the frequency of a forced vibration on an object matches the object’s natural frequency, a dramatic increase in amplitude occurs. This is called resonance.
For example, a swing, or the hollow box parts of musical instruments are designed to work best with resonance.
In order to resonate, an object must be elastic enough to return to its original position and have enough force applied to keep it moving (vibrating).

51. Sound and Resonance
Sound travels fastest through solids, less fast through liquids and slowest through gasses.
Resonance is a natural amplification of sounds or vibrations.
All objects have their own natural frequencies at which they are likely to vibrate.
Vibrations can also be forced. When the frequency of a forced vibration matches the natural frequencies of an object, resonance occurs.
You can’t easily hear an electric guitar unless it is plugged in, but you can easily hear a classical guitar because the body of the electric guitar will not resonate while the hollow body of a classical guitar will resonate.
Resonance can be positive, such as hearing a guitar or other wood instrument, or it can be destructive. View these videos to see the destructive force of resonance:

52. Interference
Sound waves interfere with each other in the same way as all waves.
Constructive interference - augmentation
Destructive interference - cancellation

53. The Doppler Effect
The Doppler effect is the change in observed frequency due to the motion of the source or observer.
The Doppler effect is the frequency shift that is the result of relative motion between the source of waves and an observer.
Higher frequency: Object approaching
Lower frequency: Object receding
Example: As the sound of a car's horn passes and recedes from you, the pitch of the horn seems to decrease.
Some application:
Echolocation (e.g., Submarines, Dolphins, Bats, etc.)
Police Radar
Weather Tracking

54. The Doppler Effect
STATIONARY
SOUND-GENERATING OBJECT
MOVING
SOUND-GENERATING OBJECT
Velocity, v A B
Waves are created at point source and radiate outward creating a wave front with the same frequency as that of the source.
Although the frequency of the sound generating object remains constant, wave fronts reach the observer at Point B more frequently than Point A.

55. Ultrasound
Ultrasound is cyclic high frequency sound wave beyond the upper limit of human hearing.
Ultrasound waves can be bounced off of tissues using special devices. The echoes are then converted into a picture called a sonogram.
Ultrasound imaging (ultrasonography) allows physicians and patients to get an inside view of soft tissues, organs, body cavities, etc., with real time images and without using invasive techniques.
The most well known application of ultrasound is to examine a fetus during pregnancy.
Ultrasound has been used to image the human body for at least 50 years. It is one of the most widely used diagnostic tools in modern medicine.
As currently applied in the medical environment, ultrasound poses no known risks to the patient and there is no convincing evidence for any danger from ultrasound during pregnancy.