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Waves
Waves
• Waves are everywhere. Sound waves, light waves, water waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of waves.
• Waves transport energy from one location to another.• Waves are caused by vibrations • Vibration (or oscillation) -- back-and-forth or up-and-down
motion; a wiggle in time.• Wave -- a disturbance that travels from one location to
another; a wiggle in space and time.• The medium is a substance or material that carries the wave.
Anatomy of a Sine Wave• The parts of a wave include crest, trough,
wavelength, amplitude, frequency and period
The points A and F are called the CRESTS of the wave.
crest
This is the point where the wave exhibits the maximum amount of positive or upwards displacement
trough
The points D and I are called the TROUGHS of the wave.These are the points where the wave exhibits its maximum negative or downward displacement.
Anatomy of a Sine Wave• The distance between the rest position (shown by the dashed
line) and point A is called the amplitude of the wave.• The amplitude is the maximum displacement that the wave
moves away from its equilibrium (dashed line).• The distance between two consecutive similar points (in this
case two crests) is called the wavelength.• The wavelength is also the length of the wave pulse.
Amplitude
Wavelength
Wavelength
Wavelength
Comparison of Characteristics of Waves
• These two waves have the same
frequency but different amplitudes. • These two waves have the same amplitude but different frequencies.
Frequency
• Hertz- a unit of frequency (named after Heinrich Hertz). 1 Hz = 1 vibration per second. Ex. 10 hertz means 10 vibrations per second. Radio stations operate on hertz frequencies.
• Pitch is the frequency of sound.• Our limitations of hearing- 20 Hz to 20,000 Hz.
– Ultrasonic (sound to hi frequency for us to hear)– Infrasonic (sound too low frequency for us to hear)
Wave Frequency and Period• Frequency measures how often something
happens over a certain amount of time (# of waves/second). It is the number of complete waves that pass a point in a given period of time (usually a second).
• We can measure how many times a pulse passes a fixed point over a given amount of time. This will give us the frequency.
The Period of a Pendulum• Period – time it takes for 1 complete wave to pass a point. Measured in sec.• The motion of a pendulum and the motion of a mass on a spring can be
described using a wave.• The period of a pendulum is the time is takes for one full back and forth
motion.
Wave Frequency and Period
• The period is also is the reciprocal of the frequency.• Period = 1/ frequency T = 1 / f• Frequency = 1/ period f = 1 / T
Wave Speed• Wave speed is the distance the disturbance travels in a fixed
amount of time. • Wave speed can be determined from the product of the
wavelength and the frequency• velocity = wavelength x frequency
• v = f• All waves traveling thru the same medium do so at the same
speed!
Factors Affecting Speed• Electromagnetic (light/radiant) waves travel at 3.0 x
108 m/s in air while sound travels in air at 3.0 x 102 m/s. 186,000 mi/s vs. 0.21 mi/s.
• Three factors that affect the speed of the wave in transferring energy are:– 1. Type of medium– 2. Temperature of medium– 3. State of matter of medium (solid, liquid, gas)
WaveTypes• Waves which require a medium are
mechanical waves, also known as compressional or longitudinal waves.
• Waves which do not require a medium are transverse waves, commonly electromagnetic waves.
Wave Motion• Most waves we see travel through some
substance or matter (medium), but weirdly enough, the medium doesn’t really travel just the energy.
• Examples of Mediums-1. Air2. Water3. All phases of matter (s,l,g)**Not all waves require a medium though!**
Types of Waves
• Transverse wave - oscillations are transverse (perpendicular) (at right angles to) to the direction of motion
• Longitudinal (or Compression) wave - oscillations are in the direction of motion, or parallel to the direction of motion.
Transverse Waves
• Electromagnetic waves (light waves) are transverse.
• This is the same for stringed instruments.
Electromagnetic Waves
Visible Spectrum
Longitudinal Waves• Also known as compressional waves or
mechanical waves• Medium compres-
ses together orspreads out to formcompressions andrarefactions
Longitudinal Waves
•Sound waves are longitudinal waves. They are produced by the vibrating air molecules.
Uses of Longitudinal Waves
Interference and the Superposition Principle• Suppose two waves pass through the same medium. What
happens?• Wave interference is the phenomenon which occurs when
two or more waves meet while traveling along the same medium.
• The superposition principle tells us how waves interact.• The principle of superposition is sometimes stated as follows:
When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
Algebraic sum of two waves
Interference
• There are 2 types of interference: destructive and constructive.
• Destructive interference- this occurs when the crest of one wave overlaps the trough of another. This cancels the waves out.
• Constructive interference- occurs when the crests of two waves overlap causing them to join, this increases the amplitude.
Constructive Interference• Constructive interference is a type of interference which occurs
at any location along the medium where the two interfering waves have a displacement in the same direction. The resulting displacement is greater than the displacement of the two interfering pulses alone.
Destructive Interference• Destructive interference is a type of interference which
occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. The resulting displacement is less than the displacement of the two interfering pulses alone.
Wave Addition
Interference
• Beats – periodic changes in intensity of sound• Inference in light produces light and dark
patterns
Two Opposite Waves• When the two opposite waves arrive at the same
location, they cancel, destructively.
Interference• Water waves from two oscillating sources show
interference. Note light and dark areas where difference amounts of light pass thru the water.
Ripple Tank
Boundary Behavior of Waves• The behavior of a wave when it reaches the end of its
medium is called the wave’s boundary behavior.• When one medium ends and another begins, that is called a
boundary.• One type of boundary that a wave may encounter is that it
may be attached to a fixed end.
The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse.
Standing Waves• When a reflected wave interferes with an incident
wave, a standing wave can form.
Nodes are points of no motion
Anti-nodes are points of maximum motion
Wave Reflection
Wave Behavior• Now the we know the parts of a wave and how we
describe and analyze them, we can look at wave behavior
• In the next section we will look at interference, the boundary behavior of waves, standing waves and the Doppler Effect.
The Doppler Effect
The Doppler Effect• The Doppler Effect is the apparent change in frequency of a wave due to
relative motion between source and observer.• As the sound move toward the observer, the apparent frequency
decreases, the waves get compressed.• As the sound moves away from the observer, the apparent frequency
increases, the waves get “stretched out”• A sound wave frequency change is noticed as a change in pitch.
Doppler Shift for
Light
Doppler and Line of Sight
We are only sensitive to motion between source and observerALONG the line of sight.
Shock Waves
• When speed of objectgenerating waves
surpasses speed of waves in thatmedium, shock waveresults
Shock Waves
• The more the sourceexceeds the wave speedthe narrower the V
Wave Reflection
• Normal line (perpendicular to plane surface ) bisects incoming and outgoing ray to determine angle of incidence or angle of reflection
Wave Reflection
• Law of reflection – angle of incidence = angle of reflection
Wave Reflection
• From a single point
Wave Reflection
• From a concave surface
Wave Reflection
Acoustics of room design is very interesting. Need some reflections to “liven” the room. Too many reflections and the sound gets mushy. Look in a concert hall or auditorium to see the different sound treatments
Wave Behavior- Refraction• Refraction- the bending of waves in various
angles as it goes from 1 medium to another.
Refraction
• Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance).
Refraction
Wave BehaviorDiffraction
• Diffraction -- object causes a wave to change direction and bend around it.
• The amount of bending depends on the size of the obstacle and the wavelength of the wave.
• If an obstacle is larger than the wavelength , the waves do not diffract much.
Natural Frequencies
• Objects have “natural” frequencies based on their size and structure
• Guitar strings are an example• Timpani heads• Air columns
Forced Vibrations
• Can externally impose a vibration on an object• Guitars and violins and pianos• Set the wood into motion at the frequency of
the string• This provides a larger surface to interact with
the air• Harp vs. Piano
Resonance
• When the forced vibration matches a natural frequency we get a “resonance” condition
• Think about a swing on a playground• You go high when you pump the swing at its
natural vibration frequency• Other examples:
– Sympathetic vibrations in tuning forks– Famous Tacoma Narrows bridge collapse
Resonance
Swinging a child in a playground swing is an easy job because you are helped by its natural frequency.
But can you swing it at some other frequency?
Opaque, Transparent, Translucent
• Wave behaviors cause objects to appear differently.
Reflection and Refraction
Harmonics• There are a variety of patterns by which the guitar
string could naturally vibrate; each pattern is associated with one of the natural frequencies of the guitar strings.
Sources
• Conceptual Physics by Paul Hewitt• www.physicsclassroom.com• pls.atu.edu/physci/physics/people/robertson/courses/
phsc1013/PHSC1013-Waves.ppt –• Waves and Vibrations -Physics: Mr. Maloney• www.drake.edu/artsci/physics/Lecture_14_3-4-2004.ppt• https://bba-physics.wikispaces.com/file/view/Waves2.ppt• www.knott.k12.ky.us/schools/teachers/nritchie/waves
%20good%20copy.ppt
Characteristics of ALL waves!• Crest
(compression)• Trough
(Rarefactions)• Wavelength• Amplitude• Frequency• Wave Speed- V=f
Sound in warm air near the ground doesn’t seem to carry well because the warm air causes the sound to bend away from the ground. This is just the opposite for cool air.
Wave Questions1) Rhonda sends a pulse along a rope. How does the position of a point on
the rope, before the pulse comes, compare to the position after the pulse has passed?
2) Why don't incoming ocean waves bring more water on to the shore until the beach is completely submerged?
3) In order for a medium to be able to support a wave, the particles in the wave must bea) frictionless.b) isolated from one another. c) able to interact. d) very light.
4) A transverse wave is transporting energy from east to west. How will the particles of the medium will move?
5) A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a _______________.
More Wave Questions
6) In the diagram above, the wavelength is given by what letter?7) In the diagram above, the amplitude is given by what letter?8) A wave has an amplitude of 2 cm and a frequency of 12 Hz, and the
distance from a crest to the nearest trough is measured to be 5 cm. Determine the period of such a wave.
9) A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is ________.
10) A pendulum makes 40 vibrations in 20 seconds. Calculate its period?11) Mac and Tosh are resting on top of the water near the end of the pool
when Mac creates a surface wave. The wave travels the length of the pool and back in 25 seconds. The pool is 25 meters long. Determine the speed of the wave.
12) A marine weather station reports waves along the shore that are 2 meters high, 8 meters long, and reach the station 8 seconds apart. Determine the frequency and the speed of these waves.