H133: 1094 Session 1

Write your name and answers on this sheet and hand it in at the end.

1. Q1: Group Problems [15 min.]

1. Introduce yourself to the other students at your table.
2. Problem Q1B.8: Draw pictures of waves to illustrate your answer.
   
   
   
   
   
3. Problem Q1S.5 (Note: The pitch of a sound you hear is determined by its frequency):
   
   
   
   
4. Hint: you might find the animated images of colliding and reflecting pulses on the H133 webpage of use!

2. Fourier Transforms and Guitar Physics [15 min.]

Start up the PhET applet "Fourier: Making Waves" (Start->Programs->PhET, choose "Sound & Waves" from the left menu, and click once on the Fourier icon).

• You can set the amplitudes of sine wave to add together by dragging the bars with the mouse or changing the numbers under A1, A2, etc. The "Sum" graph shows the net result. Try some different amplitudes to get a feel how the waves combine.
• Now reset A1 = 1 and figure out the coefficients needed to build up a square wave according to equation (Q1.14). What values did you set for A2 and A3?
  
  The Fourier transform theorem says that these coefficients are unique! You only have low frequencies available; what parts of the square wave are not well reproduced?
  
  
• Try the "Wave Game" (middle tab). Start at Level 1, where you have one amplitude to adjust. Then try one at Level 4. (And then move on!)

The sound from a plucked guitar string results from a superposition of the fundamental vibration and various harmonics. The relative weighting of these vibrations determines the tonal "color" of the note, and is fixed by how you pluck the string. Support your answers to the following questions with an observation from a demo in class, a Q1 discussion or homework problem, or the PhET simulation.

1. The strings on a guitar are all the same length. Why do they play different notes?
   
   
   
   
   
2. If you want a sound with more high-frequency harmonics, should you pluck the string so that it initially has a sharp or rounded bend? Should you pluck it in the middle or toward one end?
   
   
   
   
   
3. Invent a way to start a string vibrating at only the fundamental frequency.
   
   
   
   

3. Q2: Wave Interference and Diffraction [15 min.]

Start up the "Wave Interference" PhET applet (also under "Sound & Waves") and switch to the "Light" tab. The simulation shows a light wave. Click on "Show Screen" and "Intensity Graph". You have control of the wavelength and amplitude of the wave, and of one or two slits.

1. With No Barrier, what does the intensity graph show?
   
   
2. Now select "One Slit". Compare the simulation to Figures Q2.1 and Figure Q2.10. What is the width of the intensity plot? Predict what will happen if you decrease the wavelength. What actually happens if you change to purple light?
   
   
   
3. Now switch to "Two Slits" and answer two-minute problem Q2T.2 using your observations of the applet (i.e., play with the controls!).
   
   
   
   
4. At Prof. Furnstahl's house, his small stereo speakers ("tweeters") are carefully positioned but the big subwoofer is hidden behind the couch. How can he get away with that?