Waves

Waves Waves are everywhere. Sound, light, water, stadium waves, earthquake waves, waves on a string, and slinky waves are just a few examples 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 -- disturbance that travels from one location to another; wiggle in space and time Medium -- substance or material that carries wave

Anatomy of a Sine Wave Parts of wave include crest, trough, wavelength, amplitude, frequency, period crest trough Points A and F are CRESTS of wave. P point where wave exhibits maximum amount of positive or upwards displacement Points D and I are TROUGHS of wave. Points where wave exhibits maximum negative or downward displacement

Anatomy of Sine Wave Distance between rest position (shown by dashed line) and point A is called amplitude of wave Amplitude is maximum displacement the wave moves away from equilibrium (dashed line) Distance between two consecutive similar points (in this case two crests) is wavelength Wavelength is also length of wave pulse Wavelength Wavelength Amplitude 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- unit of frequency (named after Heinrich Hertz). 1 Hz = 1 vibration per second. Example: 10 hertz means 10 vibrations per second. Radio stations operate on hertz frequencies Pitch is frequency of sound. Human limitations of hearing- 20 Hz to 20,000 Hz. Ultrasonic (sound too hi frequency for us to hear) Infrasonic (sound too low frequency for us to hear) The human ear can hear pitches 20 go 20,000 hertz.

Wave Frequency and Period Frequency l measures how often something happens over some amount of time (# of waves/second). It is 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 fixed point over a period of time. This will be frequency

The Period of a Pendulum Period – time it takes for 1 complete wave to pass a point. Measured in sec. Motion of pendulum and motion of mass on a spring can be described using a wave Period of pendulum is time is takes for one full back and forth motion

Wave Frequency and Period Period is also reciprocal of frequency. Period (time in sec) = 1/ frequency T = 1 / f Frequency = 1/ period f = 1 / T

Wave Speed Wave speed is distance a disturbance travels in a fixed amount of time Wave speed can be determined by multiplying wavelength times 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 affect the speed of waves in transferring energy: 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 energy travels Examples of Mediums- Air Water 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 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 Same for stringed instruments

Electromagnetic Waves

Visible Spectrum

Longitudinal Waves Also known as compressional waves or mechanical waves Medium compres- ses together or spreads out to form compressions and rarefactions

Longitudinal Waves Sound waves are longitudinal waves. Produced by vibrating air molecules

Uses of Longitudinal Waves

Interference and Superposition Principle Suppose two waves pass through the same medium. What happens when they meet? Wave interference is phenomenon which occurs when two or more waves meet while traveling along same medium Superposition principle tells us how waves interact 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 2 types of interference: destructive and constructive Destructive interference- occurs when crest of one wave overlaps trough of another. Cancels waves’ displacement from equilibrium Constructive interference- occurs when crests of two waves overlap causing them to join. Increases amplitude

Constructive Interference Constructive interference -- type of interference which occurs at any location along a medium where two interfering waves have displacement in the same direction. Resulting displacement is greater than displacement of two interfering pulses alone.

Destructive Interference Destructive interference -- type of interference which occurs at any location along the medium where two interfering waves have displacement in opposite directions. Resulting displacement is less than displacement of either of the interfering pulses alone

Wave Addition

Interference Beats – periodic changes in intensity of sound Inference in light produces light and dark patterns Occurs when frequencies are close, but not identical

Two Opposite Waves When two opposite waves arrive at 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 water Ripple Tank

Boundary Behavior of Waves Behavior of wave when it reaches 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 a wave may encounter is if its is attached to a fixed end Reflected pulse has same speed, wavelength, and amplitude as incident pulse.

Standing Waves When reflected wave interferes with an incident wave, a standing wave can form Nodes are points of no motion (rest position, or equilibrium) 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

Doppler Effect The Doppler Effect is the apparent change in frequency of a wave due to relative motion between source and observer As a sound wave moves toward observer, the apparent frequency increases, and waves get compressed As sound moves away from the observer, the apparent frequency decreases, the waves get “stretched out” Sound wave frequency change is noticed as change in pitch Light waves exhibit changes in frequency (color). Known as red shift (moving away) or blue shift (moving toward)

Doppler Shift for Light

Doppler and Line of Sight We are only sensitive to motion between source and observer ALONG the line of sight

Shock Waves When speed of object generating waves surpasses speed of waves in that medium, shock wave results

Shock Waves The more the source exceeds the wave speed the 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 Reflection from single point

Wave Reflection 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 sound gets mushy. Look in concert hall or auditorium to see different sound treatments

Wave Behavior- Refraction Refraction -- bending of waves in various angles as it goes from 1 medium to another

Refraction Waves traveling from deep end to shallow end of water body can be seen to refract (i.e., bend), decrease wavelength (wave fronts get closer together), and slow down (take longer to travel the same distance) Refraction direction dependent on density, temperature

Refraction Sound in warm air near the ground doesn’t seem to carry well because warm air causes sound to bend away from the ground. This is just the opposite for cool air.

Wave Behavior Diffraction Diffraction -- object causes wave to change direction and bend around it Amount of bending depends on size of obstacle and wavelength of wave If obstacle is larger than wavelength ,waves do not diffract much

Natural Frequencies Objects have “natural” frequencies based on their size and structure Guitar strings, timpani heads, air columns are examples

Forced Vibrations We can externally impose vibration on an object Examples: Guitars, violins, pianos Waves set wood into motion at the frequency at which string vibrates Provides a larger surface to interact with air Compare sound intensity of harp vs. piano

Resonance When forced vibration matches a natural frequency, get “resonance” condition Think about swings on a playground Go high when pump the swing at its natural vibration frequency Other examples: Sympathetic vibrations in tuning forks Tacoma Narrows bridge collapse

Resonance Swinging a child on playground swing is easy because you are helped by its natural frequency Can you swing at some other frequency?

Opaque, Transparent, Translucent Wave behaviors cause objects to appear differently

Reflection and Refraction

Harmonics Variety of patterns by which guitar string could naturally vibrate; each pattern associated with one of natural frequencies of 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=lf

Wave Questions 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? Why don't incoming ocean waves bring more water on to the shore until the beach is completely submerged? In order for a medium to be able to support a wave, the particles in the wave must be a) frictionless. b) isolated from one another. c) able to interact. d) very light. A transverse wave is transporting energy from east to west. How will the particles of the medium will move? 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.