Standing Waves with Resonance

First, some interesting sites related to today's discussion:

http://library.thinkquest.org/19537/cgi-bin/showharm.cgi
This site contains a program that allows you to put together harmonics and see what they sound like together.

http://www.pbs.org/wgbh/nova/bridge/meetsusp.html#clips
This site describes one of the most catastrophic applications of resonance, the Tacoma Narrows Bridge collapse.

Now, some solutions:

33. Since the nodes are now at half the distance, and the wave velocity is the same, the frequency must double to 8 Hz. This is beyond the highest frequency of earthquakes.

36. The tube must be closed at one end - look at the ratio of the frequencies to each other, as they are odd fractions. The fundamental frequency is 88 Hz.

37. f = 5v/2L, so v = 247.5 m/s.

38. Open at both ends, 7v/2L = 33o Hz, L = 3.606 m

75. n*lambda/4 = L1, (n+2)*lambda/4 = L2. Subtract the two equations, and you get that lambda = 2(L2 - L1), leaving that f = 630 Hz if the speed of sound is 340 m/s.