1) Given a pipe with one end closed. Where would you put a piece of gauze in order to damp out the second mode but not the first?
2) Figure 1 shows the nodes of the first 6 modes of a drum head. Where would you lightly rest your finger(s) to damp out the first mode . Where to damp out the third but not the second (could you damp out only the third mode and none of the others?)
=5in
3)How many ocataves and semitones are the two notes with frequency 150Hz and 800Hz apart?
4)A baritone sings two notes a perfect fourth apart. What is the difference in frequency between the two notes if the lower one is sung at 220Hz.
5)Which modes of a xylophone bar remain undamped if you held the bar in its middle? Where would you remove material from the bar if you wanted to lower its frequency?
6)Which would ring for a longer time, a bar with a frequency of 3000Hz and a Q of 2000 or a bar with a frequency of 200 Hz and a Q of 200? Why?
7) The statement has been made (in many undergraduate physics text books) that the Tacoma Narrows bridge fell due to resonance. The bridge, built just south of Seattle in the late '30s fell in a wind storm (40 mph winds), and its amplitude of vibration was over 100 times its amplitude in lower winds (the bridge deck tilted back and forth by over 40 degrees from the horizontal). Do you find this explanation convincing? Why (or why not)? (Hints: What would the Q of the bridge have to be? What would the frequency of pushing of the wind on the bridge have to be?)
8) A small lump of tape is placed on a guitar string exactly at a point 1/3 of the length from the end of the string. What effect would this have on the frequencies of the various modes of the string? (Consider the lowest 4 modes).