1. The fundamental frequency of a vibrating guitar string is modeled by the following equation:
f=12LTgμ
Where:
f = vibration frequency in Hertz
L = length of string in meters
T = string tension in Newtons
μ = string density
Determine the appropriate unit for μ if the preceding equation is to be homogeneous in units?
2. The strength of a tree branch is approximately proportional to its cross-sectional area while its weight is proportional to its volume. If you scale up a branch by a factor two (i.e., double all of its linear dimensions), determine (a) by what factor its strength increased and (b) by what factor its weight increased.
3. The speed of sound in air is approximately 340 m/s. The speed of sound in steel is approximately 5900 m/s. If your friend strikes one end of a steel pipe with a hammer while you listen at the other end, you will hear two distinct sounds: one traveling through the air and the other traveling through the steel pipe. If the pipe is 1.94 seconds elapses between the two distinct sound, how long is the steel pipe.
4. A "teeter-totter" (or "see-saw" if you prefer) has a 50lb child sitting at one end, 10ft from the center pivot point (fulcrum). How far from the center point should a 125lb adult sit in order to balance the teeter-totter?