#4 #6 #12 #14 #20 #26 #34 #40 #44 #544. If a pendulum is to the right of vertical, which way does the restoring force on the pendulum bob point?
To the left and down, that is toward the equilibrium position.
6. How can you increase the period of a pendulum?
To increase the period of a pendulum, you would increase the length of the pendulum. The pendulum's period is proportional to the square root of its length.
12. What is the period of the minute hand on a clock?
The definition of a period is the time to make one round-trip. The time it takes for the minute hand to go around once is 60 minutes. Since there are 60 seconds in a minute, the period is 60 minutes or 3600 seconds.
14. Does the natural frequency of a swing depend upon whether you are standing up or sitting down?
Yes. The period of a pendulum is proportional to the square root of the length between the pivot point and the center of mass of the object. Therefore, the natural frequency of the swing is proportional to the reciprocal of the square root of the length between the pivot point and the center of your body mass. The pendulum length is longer when you are sitting down than when you are standing up. So, the natural frequency of the swing will be smaller when you are sitting down than when you are standing up.
20. What actually moves across the surface of a lake when you drop a rock into it?
Energy moves across the lake.
26. What can you do to increase the speed of waves on a rope?
To increase the speed of the waves, you could increase the tension on the rope.
34. Two waves with the same speed have different wavelengths. Which has the higher frequency?
The speed of a wave is its wavelength times its frequency. Therefore, the wave with the shorter wavelength would have the higher frequency.
40. What happens to the wavelength of a periodic wave if the period is doubled while the velocity remains the same?
The speed of the wave is equal to its wavelength times its frequency. Since period is the reciprocal of frequency, the wave's speed is its wavelength divided by its period. So, if the period is doubled, while the speed is constant, the wavelength also doubles.
44. How long does it take a wave to travel a distance equal to its wavelength?
The wave takes a time of one period to travel a distance of one wavelength.
54. What is the wavelength of the fundamental for the aluminum rod in #53 if it is held midway between the center and one end?
The lowest resonant frequency would have a node one-quarter of the rod's length from one end (where the rod is held by your fingers) and antinodes at each of the two free ends. This corresponds to a standing wave whose wavelength is equal to the length of the rod.