Announcements 10/12/12 Prayer Lab 3 due tomorrow, Labs 4 and 5 start tomorrow rob-sheridan.com

From warmup Extra time on? a. a.(nothing in particular) Other comments? a. a.There is a fantastic demo, where a bunsen burner is placed under a big pipe. The air heats, and a note is produced from the pipe. At my highschool, it was done with a cardboard pipe, about 6" diameter, 5' high.

Video Two speaker interference (1:16)

From warmup Give an example of resonance from everyday life. a. a.On one of BYU's organs that I was practicing on in the HFAC, the bench resonated with A flat, so every time I played a low A flat my but would be vibrated with the bench. b. b.I play the violin and if I play a D on the A string, the D string will start to vibrate without me touching it because it is the same note just an octave lower. c. c.A playground swing. You go higher by timing the push to be in phase with the swinging.

Resonance Demo: rubber tubing, one more time Reminder: Swings Video: Bowling ball (0:50) Video: Goblet shattering (1:42) Video: Tacoma Narrows bridge, 1 Jul 1940 – 7 Nov 1940 (2:33) Demo: Trumpet

Standing waves in air: “Open-Open” Quick writing: draw what you think the second and third harmonics should look like For stable patterns: L = _______ What are the frequencies? Relative to the fundamental frequency? Demo: Trumpet, again Open end L =_____ Example: organ pipe

From warmup The boundary conditions for waves on a string with two fixed ends leads to a fundamental mode which looks like half a sine wave, oscillating up and down. But what happens if one end is fixed and the other is free to move? What would the fundamental mode look like for that case? a. a.in this case there would be one end as a node and one end as a anti-node. this would resemble a 1/4 of a sine wave.

Standing waves in air: “Open-Closed” Quick writing: draw what you think the second, third, and fourth harmonics should look like For stable patterns: L = _______ What are the frequencies? Relative to the fundamental frequency? Open end Closed end L =_____

Demo Trumpet

Standing Waves in 2D Advertisement for Physics 318! waves.nb Animations with Mathematica: Fig 18.16

Standing Waves in 3D? From Colton and Wienkes, Rev. Sci. Instr., 2009 a. a.Light waves, frequency = 10 GHz (microwaves) Advertisement for Physics 641! Do they exist? Class poll a = yes b = no

Final Standing Wave Demo Flame standing waves

From warmup In the context of waves, what is "beating" and why does it occur? Explain in your own words, as if to someone who is not familiar with physics. a. a.Beating is a periodic increase/decrease in amplitude of the wave, that occurs (for example) when two instruments that are slightly out of tune play the same note. It happens because the slight change in wavelength causes the maxima/minima to not occur quite together-- they only occur together once every hundred (or so) times. When the maxima do occur together, the volume is increased. Fig 18.17

Beats “beat frequency”: f beat = |f 1 – f 2 | “beat period” (or  beat = |  1 –  2 | )

Beats, cont. Stokes Video (1:33) Tuning fork demo

Beats: Quick Math carrier“envelope” (beat) Wait… is beat frequency 0.5 rad/s or is it 1 rad/s? Class poll a. 0.5 rad/s b. 1 rad/s Can be proved with trig identities

Sine Wave What is its wavelength? What is its location? What is its frequency? When does it occur? Animations courtesy of Dr. Durfee

Beats in Time What is its wavelength? What is its location? What is its frequency? When does it occur?

Localization in Position/Wavenumber What is its wavelength? What is its location? What is its frequency? When does it occur?

Beats in Both...