Physics 36 /Music 36 Homework Assignments

Assignments will be posted here on the Web site each Thursday, and be due by 5:00 PM the following Thursday (brought to class or placed in the collection box between Physics rooms 140MR and 146). Assignments will be accepted up to one week late, with a 10% deduction in the total score for each day they are late. An extension may be granted by the instructor or a TA in the event of circumstances beyond a student's control.

"Questions" assigned from the textbook are from the "Questions for Thought and Discussion" sections. Answers will be posted in the follow-up section of the course Web site corresponding to the class meeting for which each chapter was assigned reading. Be aware that, even though the edition number hasn't changed, some of the textbook typographical errors pointed out in our answers have been corrected in the latest printing. While posting of answers will be delayed for items chosen for grading, any textbook errors related to those items will be posted immediately.

Teaching Assistants: Josh Albert ( jba10@phy.duke.edu), and Youngmi Cho (youngmi.cho@duke.edu). They are graduate students in Physics and Music, respectively, and both will be working with students enrolled in both Physics 36 and Music 36.

Youngmi has returned from Korea! We welcome her!

Office Hours: Josh Albert, Mondays 1:30-3:30, Room 173 Physics.

Due Thursday March 27:

• Chapter 12: Question 4; Exercise 2. Graded.
• Chapter 17: Exercise 2. Graded.
• Chapter 23: Questions 1 and 2; Exercises 2, 3 and 4. Graded.

Due Thursday March 6:

• Chapter 13: Questions 1 and 3. Graded.
• Chapter 11: Questions 4 and 5; Exercises 1, 2 and 4. Graded.

Due Thursday February 28:

• Chapter 10: Exercises 2, 6, and 7. Graded.
• Chapter 14: Question 4; Exercises 2, 6 and 7. Graded.

Due Thursday February 14:

• Chapter 8: Exercise 6. Graded, except for the response to the final sentence, (about second-order beats).
• Chapter 9: Question 3; Exercises 6 and 7. Graded.

Due Thursday February 7: Note that an addition and two changes occurred in this assignment a day after it first was posted.

• Chapter 5: Exercise 1. Checked for completion but not graded.
• Chapter 6: Exercise 3. Checked for completion but not graded.
• Chapter 7: Questions 4 and 5; Exercises 9 and 10. Graded.

• Additional question: Consider the challenge of tuning a wide range of instruments in an ensemble to the same reference pitch. Within the brass section of the wind symphony, for instance, different instruments may be playing the "same note" in three different octaves. Use figure 7.2 to find the jnd for A2, A3, and A4 (110, 220, and 440 Hz) and compare those results to the frequency differences corresponding to an A-to-A# half step in each of those octaves (6.5, 13.1, and 26.2 Hz, respectively). Comment on the accuracy required for the section to sound "in tune." (Note that, while jnd is defined for sequential pitch comparisons, typical ensemble tuning routines allow at least some simultaneous comparison as well.) Graded. [Note also the Duke Wind Symphony concert at 8 PM in Baldwin on Thursday, Feb. 7!]

Due Thursday January 31:

• Results from Homework Experiments related to topics of the first five class meetings. A summary of what results to turn in can be found at the end of the following detailed instructions for the experiments.

Experiments related to Class 1: Introduction.

• Compare the composition "styles" demonstrated in the "Downloads" section of our course Web site (random pitch and duration changes vs. 1/f-weighted [fractal] ones). Write down any comments that may occur to you, from a musical perspective. We will discuss how these differ in class.

• Play a note on a piano and then sing the same note "into the piano" with the damper pedal held down (the pedal on the right). This works best on a grand piano with the lid raised. [A list of pianos available to the public on campus can be found at http://osaf.studentaffairs.duke.edu/resources/pianos.html You may also be able to find one in a vacant Biddle Building practice room.] Keep the pedal down after you stop singing and listen for a faint "playback" of the spectrum of your voice. Your voice causes the piano sound board to vibrate, which in turn stores energy on all the strings tuned to frequencies that resonate with harmonics of the note you sang. This is a way of listening to the sound spectrum of your (or a friend's) voice in a more neutral, analytic way than you normally hear voices.

• Release the damper pedal and press and hold down the key for the same note, pressing the key so slowly that no sound is made. Sing the note again and listen for a "playback." Now the soundboard can store energy only on the string(s) associated with that one key, since all the other strings remain damped. Experiment with how close the pitch of your voice has to be to the pitch of the note whose key you hold down for the "playback" to occur. [If you have some music background, you may want to go further and compare the "playbacks" for two notes an octave apart with the same key held down. (Notes an octave apart share many of the same harmonics.) Then try singing a note a perfect fifth above the pitch of the note you are holding down. (Not as many, but still a lot of harmonics in common.)]

Experiments related to Class 2: Simple Harmonic Motion, Forces, Energy

• Make a pendulum and play with it. (Tie a compact weight on the end of a piece of light string or thread.) By comparing the number of oscillations in a measured time interval (15 seconds, for instance), describe how the frequency of oscillation depends on the length of a pendulum. (Compare pendulums with lengths differing by a factor of two, for instance. Measure the length from the fixed end of the string to the center of the weight. Write down the two pendulum lengths and the number of oscillations over the same length of time.)

• Find a location (preferably outdoors) where a flat sound reflecting wall returns a distinct echo when you clap your hands. Here are maps of parts of East and West campuses with red lines showing where some such walls can be found.

• Find distances from the wall for which the echoes provide offbeats for various tempos (the echoes being heard exactly half way between claps).

• Select some convenient distance from the wall, measure it, and count the hadclaps per minute for which that distance provides offbeats. [Distances from the wall just southeast of the Bryan Center can be measured using multiples of the length of the walkway paving stones there. Reasonablly accurate estimates of such distances can be obtained by calibrating your normal walking stride. Many city sidewalks have expansion joint lines every five feet along their length, providng a handy way of setting up a calibrated distance of 50 to 100 feet. Walk that distance several times, trying to walk "normally" and average the number of steps required. Dividing the calibrated distance by your average number of steps gives you a distance-per-step calibration that you can use to measure distances from a sound reflecting wall.]

• Calculate the speed of sound in air from the distance and clapping rate you measured.

Experiments related to Class 3: Waves, Resonance

• Find the minimum distance from your sound reflecting wall at which you can hear a distinct echo. Using the speed of sound, calculate the corresponding time delay between hand clap and echo.

• Have a friend hold two pencils in one hand, like chopsticks, with the pencil points separated by various distances. While you look away, have the friend touch your skin lightly either with one pencil point or with both simultaneously. Tell your friend whether you felt one or two. Find out how far apart the pencil points have to be for you to know that there are two. (Have your friend hold the "chopsticks" over a millimeter rular to measure the separation of the points. If you don't have such a rular, use one of the scales in Figure 1.3 of the textbook.) The result should depend on the density of tactile nerve endings in the region of skin involved. Compare, for instance, the back of a forearm and the tip of a finger.

• Have your friend hold a single pencil and touch your skin with it twice, either in the same place or at slightly different places. Find out how far apart the touches have to be for you to know that they were at different places. (Again, the result will be different for areas of skin with different densities of tactile nerve endings. Your friend can hold the rular or other scale just above the skin to guide the separations.)

• For the same area of skin (finger tip or back of forearm) is it the sequential or the simultaneous touches that have to be further apart for you to know two different locations are involved?

Experiments related to Class 4: Hearing

• Using the Pitch Matching utility from the Downloads section of the course Web site, see how big a difference in frequency is required between two simultaneously sounded notes (pure tones, fundamentals only) for you to hear two distinct pitches

• Using the Pitch Comparison utility from the Downloads section of the course Web site, see how big a difference in frequency is required between two sequentially sounded notes for you to hear two distinct pitches (best done with a friend, with one person controlling the frequencies and the other responding "same" or "different")

Experiments related to Class 5: Sound Pressure, Loudness, et c.

• Using the Pitch Comparison utility from the Downloads section of the course Web site, see how big a difference in amplitude level is required for you to hear a distinct difference (best done with a friend, with one person controlling the levels and the other responding "same" or "different")

Summary of Homework Experiment results to turn in

1. Pendulum: for each of two different pendulum lengths, report (a) the length of the pendulum, (b) the length of time over which you counted its oscillations, (c) the number of oscillations counted and (d) the corresponding frequency in oscillations per minute. Compare the ratio of the two pendulum lengths with the ratio of the squares of the two frequencies and comment.

2. Speed of Sound in Air: report (a) the distance to the wall and how you determined it; (b) report the clapping rate (claps per minute) for which you heard offbeat echoes; calculate (c) the distance the sound traveled between successive claps and then calculate (d) the speed of sound.

3. Minimum Delay Required for a Distinct Echo: report (a) the minimum distance from the wall and calculate (b) the corresponding time delay between hand clap and heard echo.

4. Discriminating Simultaneous Touches ("chopsticks"): report the minimum separation required to feel two touches (a) on finger tip, and (b) on back of forearm. Discriminating Sequential Touches: report the minimum separation required to tell that different points were touched, (c) on finger tip and (d) on back of forearm. (e) Commment on any difference you observe between the simultaneous and sequential cases.

5. Discriminating Pitch Differences between Simultaneous and Sequential pure tones: Report (a) the frequency you held constant, (b) the minimum difference in frequency required to hear two distinct pitches when the two pure tones were played simultaneously, and (c) the minimum difference required when they were played sequentially. (d) Comment on any difference you observe between the simultaneous and sequential cases.

6. Discriminating Sound Level Differences: Report (a) the minimum level difference (in decibels, dB) required for you to identify a difference in loudness. Describe (b) the other attributes of the sounds you were comparing (fundamental frequency, harmonics included).

You may have felt the need to develop an experimental method to improve accuracy while obtaining some of the information requested above, and/or you may have had some concerns about possible sources of variation. If so, feel free to describe them in your report.

Due Thursday January 24:

• Chapter 1: Question 3; Exercises 4, and 12. Checked for completion, but not graded.
• Chapter 2: Question 2; Exercises 1, 2, 3, and 5. Checked for completion, but not graded..
• Chapter 3: Question 3; Exercises 2, 3, 5, and 9. Graded.
• Chapter 4: Exercises 3 and 8. Graded.