Homework Assignment on Standing Waves
Due Friday 12/14/07 in class
PH308 Bennett
In both problems, be sure to make it clear how you determined the wavelength and frequency of the standing wave – follow the procedure we have used in class.
Bathtub Problem: You are sitting in the middle of a bathtub. If you slosh the water back and forth at the correct frequency, the water makes a standing wave that rises first at one end and then at the other. The length of the tub is 2 meters, and the speed of waves on the water surface in the tub is 4 m/s.
a. Is this a transverse, or longitudinal, standing wave ? Explain how you know.
b. With what frequency must you oscillate in order to produce the standing wave ? Hint #1: Start by deciding where the nodes and antinodes must be for this problem, and draw a snapshot diagram that shows the shape of the standing wave that you must be creating. Hint #2: After doing Hint #1, put yourself on your diagram and make sure that you would want to be sitting at the middle of the bathtub you drew. If not, try a different standing wave pattern !
Human Ear Problem: Do P3 Chapter 15 problem 38; include a snapshot diagram showing air displacement vs position along pipe for the standing wave. Is this a transverse, or longitudinal standing wave ? Explain how you know. Also, find out at what frequency the human ear is most sensitive, and compare your answer with that frequency.