Physics109Demonstrations

From Fall 2008 Organized by Pupa Gilbert

Class S1:

• OSCILLATIONS, SHM

• Continuously variable Frequency generator with oscilloscope and speaker: show frequency (pitch), amplitude (loudness)
• Fourier synthesizer to scope and speaker: switch on 3 or 4 harmonics, vary amplitude and phase to change lineshape (timbre)
• Show Pupa’s tone: aaaaaaaa not harmonic. Whistle: harmonic. tuning fork: harmonic. Guitar string: not harmonic. Big bass recorder (Ti or La are good, Sol is not): harmonic
• Mass on a spring
• Pendulum
• Big box stopwatch: use stopwatch t time 5 pendulum oscillations with large amplitude, then 5 oscillations with small amplitude: same time. Repeat for 10 oscillations on the mass on the spring.
• Meter stick clamped to table at one end
• Circular motion: sine wave gizmo with crank and red dots.

Class S2:

• SHM

• Mass on a spring with metric ruler. Add 1kg, see 3.5 cm displacement, add 2 kg, see 7cm displacement, 3kg 10.5cm, 4kg 14cm. Do math on WB, find k=F(N)/x(m)=280N/m. calculate frequency f=1/(2π)√(k/M)=2.66 Hz. Change mass to 2kg, f₂=f₁/√(2)=2.66Hz/1.41=189Hz. Change mass to 3kg, f₃=f₁/√(3)=2.66Hz/1.73=1.54Hz.

• Frequency does not depend on amplitude
• Ping pong ball: non-harmonic: frequency depends on amplitude

  DAMPING AND RESONANCE

• Cart with 2 springs, just to show damping of oscillation depends on friction

• Use frequency generator and speaker right in front of tuning fork box (use C¹ 256), and put microphone almost all the way in.

  • Oscilloscope displays:
    1. tuning fork damping 40ms/div to show that frequency does not change.
    2. Then change scale to 1 sec/div to show envelop of damping.
    3. Oscilloscope single sweep (or seq, or whatever it’s called), hit the tuning fork box with the coated mallet, so it doesn’t bounce. Show damping on oscilloscope single sweep.

• Show that damping time τ and resonance width Δf are quantitatively related: the resonance frequency measured is 248 Hz (instead of the nominal 256 Hz). Tau on setting 3 above gives 25 ms (avoid the initial build up and measure initial amplitude AFTER it, then it works well), thus δf must be 0.4/0.025=16Hz, and it is! Go back to setting 2, with 40ms/div, and show that amplitude is 1/2 at 248±8Hz.

• If there is time, also show the whole thing again with coffee mug, supported on blue foam.

Class S3

• SUPERPOSITION:

• Two pendula on heavy Al stand to visualize concepts of phase shift
• Resonance between two tuning forks: Two forks same frequency but one with added weights: show beats on scope
• 2 oscillators, speaker and frequency display w/switch to show both frequencies, and their beats on the scope. If oscillators are at 440 Hz and 441 Hz, thus period of beats is 1 sec.
• Several tuning forks to demo harmony:

  • C¹(256) & C²(512) — 1:2 is an octave, the most harmonious, consonant, no beats

  • C¹(256) & G¹(384) — 2:3 is a fifth, also very harmonious

  • 3:4 is a fourth, no example with tuning forks?

  • C¹(256) & E¹(320) — 4:5 is a third, considered dissonant 200 years ago, but fairly harmonious now (mostly due to different scale tuning).

• Use 2 A¹(440) forks to demonstrate resonance, which is "sympathetic vibrations" e.g. in a sitar

• Fourier synthesizer → scope and speaker. Show octave (harmonics 1&2), fifth (2&3), dissonance (3&7, non periodic, or very long period: wave form repeats after 7x3=21 peaks)

  WAVES:

• transverse wave, on wave machine 2 section, with one end fixed and damped so it avoids reflection of the wave
• longitudinal wave, on new mini-slinky. Sound is a longitudinal wave because air does not support shear: mime a big block of jello, which I can move longitudinally AND transversally. Air doesn’t do that.

• Send a sinusoidal sound wave of 2000 Hz to speaker - two mikes connected to scope, show both traces simultaneously. Place the two mikes in front of speaker, then move 1 slowly away until it has done an entire period on scope and the two waves are in step again. Measure distance: 17.2 cm. Thus calculate the speed of sound ν=f · λ=2000 · 0.172=344 m/s this worked well in the back room, but awfully in the lecture room, probably dues to ugly room acoustics: the amplitude kept going up and down as I moved the mike.

• interference: two speakers on rotating stand (not used in Fall 08)

Class S4

• STRINGS:

• Speed of sound re-measured with 3 mikes in front of 1 speaker with 3000 Hz: much better! Measured wavelength is 11.5 cm thus speed of sound comes out to be V=λf=345 m/s (higher than 344 m/s at 20°C because air temperature was a bit higher: 0.6 m/s higher every 1°C.)

• wave machine - end clamped (one section).
• string with strobe, string in front of wave machine with black paper behind string
• bring in EL wire
• Set of chords from Steinway grand piano (linear mass greater for bass chord is increased: addtl mass is wrapped around to avoid adding stiffness, and make the tension F be the only restoring force (no elastic force): this gives more harmonic motion, and more pleasant sound. Tension must be max to increase mechanical coupling with soundboard, thus make the piano sound louder.

Class Exam II, no demos needed

Class S5

• STRINGS:

• Slinky: ask a student to hold one end very steady, as I hold the other, with quite a bit of tension. Make a fast, small pulse go through the length and back, count 1 aloud, to and fro 2, to and fro 3, 4… about 5 reflections of the same pulse can be counted, with decreasing amplitude but same period T. No need for stop watch, just count by voice and get in step with the counting rate. Maintain the same rate, and now move one end up and down, with harmonic SMALL motion of the my hand. 1, 2, 3, 4….. moving the hand and counting at the same rate, the fundamental mode is excited. Doubling the rate the second mode is excited, at 3x the rate the 3^rd mode is excited.

• The vibrating part of the string is the between the nut and the bridge. Beyond the nut are the tuning pegs, to adjust the tension while tuning.
• “Playing natural harmonics”: On the guitar, play last or second to last string, and touch for a split second the string on the fret immediately right of the double dots (center of string). This damps the fundamental, and all the odd partials. The difference is quite audible!

• “Playing a fifth” on a violin: pluck a string, then pluck it again at 2/3 the length. Is this a fifth up or down? UP, because you cannot make the string longer, you can only make it shorter. f₁/f₂=L₁/L₂ thus L₂=(2/3)L₁. No need to know the frequency, the tension, the speed of propagation, just change the length! Measure guitar string length, then show on the white board, and demo on the guitar.

• To change f on string: tension F, linear density ρ, length L. The only practical parameter to change while playing is the length L. The tension F is changed when tuning.

• What are frets? Why frets on the guitar or the viola fingerboard? Violin has no frets, thus it requires much greater accuracy and experience to play.

• Sonometer with pickup (as in electric guitar) → to sound system and to scope. Mention that multiple modes play simultaneously. They change with time, and the frequencies shift continuously like a worm: the partials on an electric guitar are slightly anharmonic.

• Fourier synthesizer scope, speaker, to hear the sound of different partials.

Class S6

• PIPES:

• Open and closed pipe with mike inside - the 1.25 m long pipe
• organ pipe with air and helium

• helium and SF₆ to breathe

• swing corrugated pipe
• flute
• large slinky in stand

Class S7

• PIPES:

• Rubens tube with gas and flames, driven by speaker, and frequency generator. Use large frequency display
• organ pipe open and closed

• organ pipe with air, helium, SF₆

• helium and SF₆ to breathe

• oboe (double-reed instr. Conical pipe ⇒ f=ν/(2L) thus higher f than clarinet with approximately the same length), clarinet (single-reed, cylindrical, closed pipe ⇒ f=ν/(4L) so the frequency is lower than clarinet by a factor of 2, despite the same length.

• other instruments: flute (huge mouth hole makes it an open pipe), trombone with slide: most obviously changing length, French horn, trumpet: each valve opens an additional length of pipe. One is one is 1/2 tone, one is 1 full tone, one is 1.5 tones. There is also a disk thing to tune the trumper at the beginning, and a sliding part, which the player slides with the left thumb while playing, to adjust for the non-exact tones resulting from having just 3 valves.

Class S8

• FOURIER ANALYSIS:

• Fourier synthesizer to same mixer (something new to try - called "fusion of partials")
• Fourier analyzer: with wavetek pulse generator (to speakers) and with mike on stand
• Various musical instruments and their harmonics (violin, guitar, recorder, voice, tuning fork)

Class S9

• SCALES:

• keyboard from 109 lab, tuned to Just scale, with frequency counter and scope
• two oscillators + mixer + scope
• aluminum bars with scales marked: show how to compose the just scale on the white board, first drawing the intervals for the major triad C-E-G, then the same shifted so it starts from G: G-B-D, then the same so it ends on the next C: F-A-C

• transposition: fra martino campanaro, do-re-mi-do or fa-sol-la-fa or mi-fa^#-sol^# (use garage band on my mac to show this, as it has the tempered scale tuning)

• show difference between the just and tempered tuning: major triad: F-A-C

  	F	A	C
  Just	640	800	960Hz play the 3 notes in sequence and simultaneously
  Tempered	641	807	960Hz re-tune A to 807 during demo, and play the 3 notes in sequence and simultaneously. They sound different, but not that much. As we are all used to the tempered scale nowadays we prefer the sound of the tempered triad.

• major scale: do-re-mi-fa-sol-la-si-do (C-D-E-F-G-A-B-C) (sounds happier)
• minor scale: la-si-do-re-mi-fa-sol-la (A-B-C-D-E-F-G-A) (sounds sadder)

Class S10

• SCALES:

• some of the demos, whatever I did not do yet

Class S11

• Jack Fry’s movie
• No demos needed

Class No class

Class S12

• SCALES:

• some of the demos, whatever I did not do yet

Class S13

• Teaching evaluations and pencils

  MUSICAL INSTRUMENTS:

• vocevista Fourier analyzer
• Sonometer with METAL HAMMER - to SPEAKERS (NO scope)
• Piano Action from 109 lab
• Piano Strings
• Wind Instruments
• Guitar

Class Exam III, no demos needed