Physics of Music 4 Physics 121

Assignment 1
• 1. Express the following quantities in the units specified.
  • 1 inch in cm
  • 3.4 x 10^9 seconds in megaseconds
  • 5.0 x 1^-5 seconds in ms
  • 3.1 x 1^10 ng in grams
  • 4.7 x 1-16 m in fm
• 2. Making your own metronome. You will need a piece of string, a weight, some tape and a watch.
  • a) Cut a piece of string about one meter long.
  • b) Attach a small weight to one end. A paper clip is probably too light. A spoon is too big (it will rotate and twist). A large nut or bolt is just about right.
  • c) Hold the string between your thumb and first finger and start the pendulum swinging. Count the number of periods (complete swings back and forth) in 10 seconds. If this is more than 10, lengthen the string below your fingers. If this is less than 10, shorten the string. Repeat this procedure until you count exactly 10 periods in 10 seconds. Mark this point on the string with a piece of tape.
  • d) Now repeat the procedure, this time getting 10 periods in 20 seconds. Mark this spot with a piece of tape.
  • e) If you imagine hearing a click each time the weight reaches one side or the other of its swing, then you have determined MM60 and MM120 on your metronome (60 and 120 beats per minute).
  • f) For extra credit, determine MM90 and MM180.
  • g) Measure the distance from the center of your weight to the bottom of your tape marks. How do these lengths compare to each other? Does a string that's twice as long oscillate half as fast?