Homework 4 -- due Oct. 8

1. Text, Chapter 3, problem 3

2.

  1. In a Kundt's tube the nodes and antinodes of air vibration are made visible. How?

  2. In such a tube the distance between the "last" node and the tube end is measured. The distance of the the right end to the node closest is found to be larger than the corresponding distance for the left end. Which end (L or R or both) is open?

3. Text, Chapter 3, problem 7

4. Text, Chapter 3, problem 9

5. Text, Chapter 3, problem 12

6.

  1. A violinist plays on the "A" string -- this means that fundamental frequerncy of the full length, "open" string is A440 (f = 440 Hz). She holds her finger lightly at a place 1/3 of the length of the string from the "nut*", creating a node at her finger. Sketch the mode of vibration of the string, indicating where the bridge, the finger, and the frog is located. (See p. 318 for a diagram of a violin. The bow that excites the string would be between the bridge and the fingerboard. The nut is the right end of the string.)
  2. At what harmonic will the string vibrate when it is bowed near the bridge? What is the frequency and the note on the musical scale? (For the musical scale see p. 359; use letter with frequency closest to what you calculate. If you are beyond the range of the table, divide frequency by 2, thereby going down one octave.)
  3. She now presses the finger down on the fingerboard, making the vibrating part of the string end at her finger (rather than the nut). What is the new frequency and note?

*mistakenly called "frog" in an earlier version of this homework. (The frog is actually a part of the violin bow.) We thank one of the students for pointing this out and apologize for any confusion that this may have caused