Musical Acoustics Final Exam Review, Fall 2000

Exam Schedule
The exam will take place in Carnegie 204 at 10:30 a.m. on Wednesday, December 13. Please bring only a writing implement and calculator into the room with you. You may not leave the room until you hand in the exam, so please plan accordingly.

Exam Basics

The exam will focus on the later material in the class, presented between October 31 and December 7, that is, Chapters 9-13. This includes the acoustics of percussion instruments, string instruments, the piano, and wind instruments. Twenty questions will comprise the exam, each worth 5 points for a total of 100 points. Equations will be provided on a separate sheet. Also included will be material from the last three labs of the semester, i.e. bar vibrations, the guitar and the recorder.

You should base your study on the following areas:

Sample Review Questions - a list of review questions follows. This is not meant to be exhaustive, i.e. to indicate the entire range of material covered on the final exam, but just to provide sample questions to help in your review.

1. A thin bar oscillates in its fundamental transverse mode with a frequency of 750 Hz. Calculate the resonant frequency of two additional transverse modes.
2. The speed of waves in an aluminum bar is around 5150 m/s. Calculate the frequencies of the first two longitudinal modes for a 0.45 m long bar.
3. Sketch patterns that illustrate the first three transverse standing waves of a thin bar.
4. Are the modes of a thin bar harmonic? Why or why not?
5. Describe two differences between a glockenspiel bar and a marimba bar.
6. Sketch several vibration patterns for a circular membrane, and label them by their nodal structure using a pair of numbers for each mode.
7. Are the resonant frequencies of a kettledrum the same as those of the top drumhead alone? Explain why or why not.
8. Suppose a thin bar, free at both ends,  is resonating at 3 kHz. Describe some ways you could learn about the standing wave pattern that corresponds to this resonant frequency.
9.What are Chladni patterns? How are they created, and what do they indicate?
10. Describe how you could play a series of pitches that correspond to the frequencies of a  harmonic series on one string of a guitar.
11. A guitar string is lightly touched at a distance of L/3 from one end, where L is the string length, while being struck at L/5 from the end. Describe the harmonic spectrum that results.
12. The highest pitched guitar string should be tuned to about 328 Hz. If it's found to be at 164 Hz, by what factor must the string tension be increased in order to bring the string into tune?
13. Describe some characteristics of the piano sound that result from its particular acoustics.
14. Why do some piano keys strike pairs or triplets of strings?
15. What is the result of inharmonicity in piano strings?
16. Explain how the stick/slip mechanism of a bowed string works, discussing concepts such as the traveling kink and friction.
17. Suppose a violin is producing a pitch of 440 Hz, and bowed in such a way that the spectrum is that of a sawtooth wave, with even and odd harmonics having amplitudes proportional to 1/n. Further suppose that in the instruments response curve, the response at 880 Hz is 10 dB greater than at 440 Hz. Which harmonic will be stronger in the radiated sound, n=1 or n=2, and by how much?
18. Describe how different radiation patterns arise for an instrument such as the guitar.
19. Calculate the first three harmonics of a 0.6 m long tube that is (a) closed (b) open.
20. Describe three mechanisms for generating standing wave patterns in wind instruments.
21. What musical interval separates the lowest two registers of a recorder?
22. What musical intervals separate the three registers of the clarinet?
23. Describe the function of tone holes in wind instruments.
24. The oboe's lowest note is B3 flat at 233 Hz. What is its effective length? Why is this greater than the actual length of the instrument?
25. What mechanism is used to excite the resonances of the recorder? Provide a rough sketch indicating how this works. How does overblowing affect the musical notes generated, and why?
26. What is the importance of the cutoff frequency in wind instruments?
27. Describe what is meant by the term impedance. How is this term relevant to the production of sound in the piano or the guitar?
28. Start with a harmonic series of frequencies built on a fundamental of 100 Hz, i.e. 100 Hz, 200 Hz, 300 Hz., etc. What pitch frequency would be heard if the following subsets of harmonics of the original series were resonating (all numbers are frequencies, in Hz):