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 -

Waves investigation A Discuss your observations as a class when finished….

Waves on a string calculations L in m Ft in N Mass in kg velocity in m/s Strings: v = Ft m/l (length density)

Waves on a string question 1 1) A guitar string has a length of 70cm, a mass of 1.5g, and is strung to a tension of 100N. (a) At what speed do waves travel in the string when it is plucked? This type of question will be on the quiz!

Waves on a string question 2 If the density of a violin string is 7.8 x 10-4 kg/m, then if a wave on the string has a frequency of 440 Hz, and a wavelength of 65 cm, then what is the tension in the string?  

Key

Follow up questions: 1) Violin string L = .9m, mass = 2g., Ft = 80N What is the velocity of the wave on the string? 2) String density = 4.6 x 10-3 kg/m, f of wave = 300 1/s, wavelength = 80cm What is the force of tension on the string?

Key 1) 190 m/s = v 2) 265 N = Ft

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

Superposition Waves in a medium pass each other without being disturbed http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

Constructive and destructive interference

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 https://www.youtube.com/watch?v=18BL7MKjtZM Making standing waves 30s – 1:30s https://www.youtube.com/watch?v=NpEevfOU4Z8

Conduct investigation B here

Follow up questions Orville and Wilber are standing 3 meters apart with a spring that has a total of 5 nodes (including the ends) when it has a frequency of 3 cycles/second. A. What is the wavelength of the wave on the spring? What is the velocity of the wave on the spring?

λ = 1.5m V = 4.5 m/s

Quiz Waves on a string here

Sound waves Longitudinal waves = particle motion in same direction as energy motion Hearing ~ 20 to 20,000 Hz (sound generator) http://plasticity.szynalski.com/tone-generator.htm Loudness = amplitude Pitch = frequency Rubens tube: tone generator and “the lion sleeps tonight”

Closed tube waves 1st mode = ¼ λ node at closed end anti node at open end antinode 1st harmonic (overtone) L = ¼ λ 2nd harmonic L = ¾ λ 3rd harmonic L = 5/4 λ

Odd series of #s math relationship L = (2n – 1) /4 λ λ = v/f So the L = (2n – 1) / 4 v/f

Investigation C here

Sound videos https://www.youtube.com/watch?v=Ude8pPjawKI https://www.youtube.com/watch?v=MwsGULCvMBk https://www.youtube.com/watch?v=cK2-6cgqgYA

Acoustics https://www.youtube.com/watch?v=JPYt10zrclQ

Follow up questions A) A Rubens tube filled with propane gas has a measured λ of 1.81m when a tone of 246 Hz is used. What is the speed of the sound wave in the propane? B) The first fundamental frequency is produced in a tube with a measured length of 0.32m and a diameter of 11cm using a 247 Hz tone. What is velocity of the wave in the tube? (do not forget the correction factor!!!)

The answers A) 445 m/s B) 359.6 m/s

More fun questions A) If the temperature of a room filled with air is 32OC (at one atmosphere of pressure), what is the velocity of a sound wave in the room? The answer: 350.2 m/s

Doppler effect here

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

Sinθi Vi λi nr Sinθr = vr = λr = ni

Wave interference

Graphic at: http://www.youtube.com/watch?v=CAe3lkYNKt8

Destructive interference = 1 peak1 + trough2 = cancel out = 0 amplitude = no sound 2 Constructive interference = peak1 + peak2 = double amplitude = double the sound (also with trough and trough)

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 Tuning fork you ¼ λ 1λ

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

Electromagnetic waves Y E X Z B Transverse wave: Both E and B are to the direction of travel of the wave. = particle motion perpendicular to energy flow

The speed of light c = 3.0 x 108 m/s In a vacuum Slower through dense materials