Waves & Wave Properties The 4 things that ALL waves do. Sound and Light as examples

λ Physical Waves Need a medium (material) to transmit energy through. Light waves are an exception. They use the space-time fabric itself! NOT position vs. time graphs! Y vs. X (Real Shape frozen in time) 2 Types Travelling Standing λ A photograph, frozen in time, but showing all places, of a travelling water wave.

A Disturbance in the Medium What Makes a Wave? A Disturbance in the Medium What is a Medium? Wave pulse (like Slinkies!) Something that creates a displacement along the medium. An energy input that “wiggles” the medium Has a wave speed due to: v (elasticity/Inertia)^1/2 The medium has to be elastic, like Hooke’s Law. All materials are made of atoms which have “springy” bonds! Space is a medium whose electromagnetic properties are springy. Take AP Physics C to find out more about this. We will; a little.

2 Types of Physical Waves Transverse Longitudinal Energy transfer is 90 degrees to displacement of medium. Makes the SHAPE of a sine/cosine wave. A water wave is an example. Energy transfer is ALONG the direction of displacement of the medium. Think slinky pulse. SOUND is our most well known example. Air molecules don’t exert forces on each other until they bump straight into each other!

2 Types of Transverse Waves Travelling Standing Energy transfers from one place to another via a medium. (TRANSMITS) Energy spreads out in spheres, but are often limited to 1D motion or 2D. Transmit energy at a speed: V=fλ=λ/Τ Energy Reflects at an interface between two media. Frequency of Energy input must match reflected wave. Constructive Interference creates anti-nodes,. Locations of destructive interference are Nodes All other places are in between. Created by Resonance. Microwaves

Standing Wave Terminology

Resonance A condition when the INPUT energy frequency MATCHES the n.r.f. of a system/object, resulting in the greatest efficiency of energy input. THINK “MYTHBUSTERS EARTHQUAKE MACHINE VIDEO” n.r.f. – “natural resonant frequency”. Size (related to mass and density) Shape (Square, Round, linear) Material (as in bonds,IMFs, tension) Density of material (includes size & mass) Creates a standing wave by perfectly timed constructive and destructive interference. (Kid on a swing) If energy input matches energy output (due to friction or heat transfer) then it has a steady Amplitude (Etotal=constant) Amplitude grows over time if more energy goes in than out. Amplitude is “damped” if energy output is greater than input. Damping makes Peak Amplitude decay exponentially. (A(t)=Ae^-kt)

Resonance Graphs

V=fλ v=λ/Τ λ found from y vs. x Τ found from y vs. t Physical Waves and SHM V=fλ v=λ/Τ λ found from y vs. x Τ found from y vs. t

DEMO: Water pendulum Notice something oscillating in SHM like a pendulum can make a real wave (y vs. x). Frequency/Period is determined by equation: The wavelength depends on speed I pull paper!

Applying Wave Equation

Motion Graph (x vs. t)

Speed of Waves Related to the medium they travel through. V water ripples (capillary or “cat’s paw” waves)~1-2 m/s V sound in air = 330 m/s +0.6Tc Depends on Density and “elasticity” “Bulk Modulus” Speed ~ √(Elasticity/Inertia) V sound in steel= 6100 m/s!!! (17x speed of sound in air!) V of light= “c”= 3x10^8 m/s. (Approx. 1 million x faster)

Finding the speed of sound- Reflection from a Wall (ECHO) Speed of sound is constant under constant conditions like temperature and moisture content. Stand a known distance from a wall. Clap hands. Listen for echo, claps hands, listen clap hands listen. Another person clap their hands along with initial clap and echo clap, making a rhythm. This rhythm is related to period. Use a stopwatch to time 10 claps. Divide by 10, now you have Period and distance (2x for echo travel) V=distance over Time.

4 Wave Properties Superposition- overlapping waves add displacements. “Monsterwellen” photo, cargo ships AM radio waves. “Wave Envelope” Reflection- Waves reflect at the interface between 2 boundaries. (Often some of the wave transmits). Refraction- Wave direction changes when passing through a different medium. Interference- Waves overlapping “in-phase nλ”, or “out of phase (λ/2) can double in Amplitude or “cancel”.

Displacements at all x positions add together,. Superposition Displacements at all x positions add together,. Causes a waveform. Vowel Sounds on Oscilloscope A E I O U

Reflection Phet animation. “Waves on a String”http://phet.colorado.edu/en/si mulations/category/physics/sound- and-waves Think “Conservation of Energy”

Refraction The path of a “wavefront” changes when it passes through a different medium with a different wave speed. Snell’s Law “Acrylic Lense Demo w/ Laser” Animation using “Huygen’s Principle”- All waves reform as spheres at boundaries. http://www.walter- fendt.de/ph14e/huygenspr.htm TIR- Total Internal Reflection (Fibre Optics)

Interference When the path length difference between 2 waves is: a WHOLE number mulltiple of a wavelength, then: Constructive interference nl=Dx If the path length difference is a multiple of ½ wavelength then: Destructive Interference. nl/2=Dx Speaker Demo Diffraction Patterns w/ Laser