Chapter 12 Review Waves

1. What is simple harmonic motion?

Motion when an object is disturbed and the restoring force follows the formula F = -kx.

2. Which of these are examples of simple harmonic motion?   A. a pendulum B. a weight on a spring C. a “plucked” guitar string D. a weightlifter doing five repetitions E. an oboe player tapping her foot F. a bouncing ball

2. Which of these are examples of simple harmonic motion?   A. a pendulum B. a weight on a spring C. a “plucked” guitar string D. a weightlifter doing five repetitions E. an oboe player tapping her foot F. a bouncing ball

3a. A mass on a spring is oscillating 3a. A mass on a spring is oscillating. Describe the net force, acceleration, and velocity of the mass when it crosses the equilibrium position.

The net force is and acceleration are zero The net force is and acceleration are zero. The velocity is at its maximum.

3b. Describe the net force, acceleration, and velocity of the mass when it is at the point of maximum displacement.

The net force and the acceleration are at their maximum The net force and the acceleration are at their maximum. The velocity is at zero.

4. What is the spring constant of a spring if a force of 100 N stretches the spring 20 cm?

F = kx 100 N = k(.2 m) k= 500 N/m

5. A spring is compressed 10 cm 5. A spring is compressed 10 cm. If the restoring force is 200 N, what is the spring constant?

F = kx 200 = k(0.1 m) 2000 N/m = k

6. A weight oscillating on a spring is held next to a meter stick 6. A weight oscillating on a spring is held next to a meter stick. If the center of mass of the weight oscillates from the 10 cm point to the 40 cm point, what is the amplitude of the oscillation?

The distance of oscillation from maximum displacement to maximum displacement is 30 cm. The equilibrium position is halfway between. Since amplitude is from equilibrium position to maximum displacement, the amplitude is 15 cm.

7. A pendulum swings through a total angle of 38° 7. A pendulum swings through a total angle of 38°. What is the angle of amplitude?

Half the total, 19°.

8. How does period relate to frequency?

T = 1/f or f = 1/T

9. How does period relate to amplitude?

Period and amplitude are NOT related to each other.

10. If the frequency of an oscillator is 20 Hz, what is the period?

T = 1/f T = 1/20 T = 0.05 s

11. How should you change the length of a pendulum to double the period?

T = 2π√(l/g) If I want the period T to double, the √(l/g) must be 2 times as much, therefore the length l must be increased to four times the length, because the √4 is 2.

12. What is the period of a 2 kg mass in simple harmonic motion with an amplitude of 20 cm if the spring constant is 400 N/m? What is the frequency?

T = 2π√(m/k) T = 2π√(2/400) T = 0.44 s f = 1/T = 1/0.44 f = 2.25 Hz

13. How would the period in problem 12 change if the amplitude were 40 cm?

None, amplitude doesn’t affect period or frequency.

14. What is the period of a 2 m pendulum?

T = 2π√(l/g) T = 2π√(2/10) T = 2.8 s

15. What would be the period of the same 2 m pendulum on the moon where g is 1/6th as much?

T = 2π√(l/g) T = 2π√[2/(10/6)] T = 6.9 s

16. Describe the motion of a single particle in a transverse wave.

In a transverse wave the particles move perpendicular to the direction of the wave.

17. Describe the motion of a single particle in a longitudinal wave.

In a longitudinal wave the particles move parallel to the direction of the wave.

18. Which type of wave are sound waves?

Sound waves are longitudinal.

19. What is the speed of a sound wave if the frequency is 512 Hz and the wavelength is 0.7 m?

v = f l v = 512 x 0.7 v = 358 m/s

20. If a wave travels 14 m/s and a floating duck bobs up and down once every 3 seconds, what is the wavelength of the wave?

3 seconds is the period, T = 1/f, so the frequency is 1/3 Hz v = f l 14 = 1/3 x l l = 42 m

21. What is the difference in constructive and destructive interference?

In constructive interference the amplitude is increased; in destructive interference the amplitude is decreased.

22. Which of these are examples of constructive interference and which of these are examples of destructive interference?   A. noise-canceling headphones B. a “dead spot” in a movie theater C. an earthquake causes a building to fall D. a singer breaks a glass with his voice

22. Which of these are examples of constructive interference and which of these are examples of destructive interference?   D A. noise-canceling headphones D B. a “dead spot” in a movie theater C C. an earthquake causes a building to fall C D. a singer breaks a glass with his voice

23. What are fixed-end termination and free-end termination?

Fixed-end there is a change in phase at reflection Fixed-end there is a change in phase at reflection. Free-end there is no change in phase at reflection.

24. What is a standing wave?

When two waves of the same amplitude and frequency cross over each other and produce pattern of loops and nodes.

25. Draw a string vibrating at the 3rd harmonic 25. Draw a string vibrating at the 3rd harmonic. How many nodes are present? How many antinodes are present? How many loops are present?

Three loops and antinodes (same thing), four nodes.

26. Draw a transverse wave. Label the crest, trough, wavelength, and amplitude.

Crests are the high points, troughs are the low points.