Waves 1 The Transfer of Energy

The Basics: A λ d(m) (#λ or m) d = displacement Amplitude = max displacement from origin λ = wavelength (in m) f = frequency = oscillations per second = Hz = s -1 = 1/s T = period = time per oscillation (in seconds) V = velocity = λ /T or λf (in m/s) f (units = 1/s) so f = 1/T

Wave types Longitudinal wave = motion of particle in same direction as motion of energy ( ) Sound waves – Transverse wave = motion of particle is perpendicular to motion of the energy ( ) Slinky, light -

Standing waves 2 waves moving in opposite directions have interference that results in a stationary wave pattern – no net propagation of energy! (demo) Note: wave can appear and disappear in same spot – no forward propagation! Also happens when medium is moving in opposite direction as wave (standing wave in river) Show Waimea river standing wave Making standing waves 30s – 1:30s

Mode (n) = basic unit of oscillation: L of the wave =( n/2)(λ) node anti-node Fundamental (f 0 ) 1 st mode Lowest f of periodic waveform: L =n/2 λ = ½ λ 2 nd mode (3 nodes): L = n/2 λ = 2/2 λ = 1λ 3 rd mode (4 nodes) L = 3/2λ 4 th mode (5 nodes) L = 4/2λ = 2λ

Sound waves Longitudinal waves = particle motion in same direction as energy motion Hearing ~ 20 to 20,000 Hz Loudness = amplitude Pitch = frequency Strings: v = Ft m/l length density

Diffraction Apparent bending of waves around obstacles and spreading out of waves past an opening.

Refraction (into higher density)

Refraction (into/out of water)

Refraction – consider angles

Wave interference

Constructive and destructive interference

Superposition Waves in a medium pass each other without being disturbed Graphic at: uperposition/superposition.html

Multiple frequency interference (music when a mathematical relationship is present)

BEATS Periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of similar frequencies interfere with each other.

The beat frequency = the difference in the frequency of the two notes. Ex: 2 sound waves with 256 and 254 Hz are played at the same time, a beat frequency of 2 Hz will be detected.

Standing Waves in Pipe

Last part of lab ¼ λ 1λ Tuning fork you

Resonance Small periodic oscillations produce large amplitude oscillations Tacoma narrows bridge example Swing example – add E at just the right time = larger amplitude oscillations

Reflection For all waves θ i θ r θ i = θ r Why???? Conservation of momentum In coming ray has x and y components Y component changes direction

Electromagnetic waves

The speed of light c = 3.0 x 10 8 m/s In a vacuum Slower through dense materials