Chapter 7

1. What is the frequency for these circumstances?

a) A metronome swings back and forth 10 times in 7.6 s.

b) An electron circles the atom 2.5 x 10¹⁰ times in 5.0 s.

c) The period of a sound from a piano is 3.3 X 10^-3 s.

2. Determine the period for these situations.

a) A metronome swings back and forth 20 times in 15 s.

b) An electromagnetic wave has a frequency of 5.0 X 10¹⁴ Hz.

c) The moon travels around the Earth seven times in 191.1 d.

3. A stretched string completes 2048 cycles in 8.0 s. Determine the string's frequency?

4. The tine of a tuning fork vibrates with an amplitude of 0.13 cm. If the frequency of the fork

is 200 Hz, what total distance will the tine travel in 1.00 min?

5. A boat bobs up and down in the water thirty times in 1.00 minutes. Determine the period of the

motion in seconds.

6. A 1.0 kg mass is bouncing up and down on a spring with a force constant of 15 N/m. Calculate

the period of the motion.

7. A helicopter is lifting an object of mass 435 kg. The object is hanging below the helicopter at

the end of a rope that is 4.96 X 10² m long. If the object swings while hanging, what would

be the period of the motion?

8. Determine the necessary location of the center of mass of the pendulum for a pendulum clock,

if the pendulum is to have a period of 1.0s.

9. The amplitude of vibration of an object with mass 2.5 kg is 0.5 m. If the frequency of the

vibration is 1.0 Hz, calculate the restoring force on the object at the ends of the vibrations?

10. As you have learned, a mass bouncing on the end of a spring displays simple harmonic motion.

What will doubling the mass do to the frequency of the motion?

11. A mass of 1.0 kg is hung from a spring with a spring constant of 20 N/m. If the weight is

caused to bounce, what is the period of the motion?

12. Calculate the acceleration due to gravity on a planet if a pendulum of length of 0.50 m has a

period of 1.8 s.

13. When a 0.50 kg mass is hung from a string, the string vibrates with a frequency of 2.2 Hz.

Determine the frequency of vibration of the string when the mass is doubled.

14. A water wave has a wavelength of 1.3 m. If the speed of the wave is 2.5 m/s, what is the

period of the wave?

15. The crest of a water wave travels 19 m in 5.2 s. If a boat in the water bobs up and down 20

times in 17 s, what is the wavelength of the waves?

16. For the following diagram, all of what you see will pass a point in 0.50 s. If this is a full-scale

diagram,

a) determine the wavelength.

b) calculate the frequency.

c) find the velocity of the wave.

17. The lowest sound the average human can hear has a frequency of 20 Hz, and the highest sound

that can be heard on average has a frequency of 20 kHz. What are the wavelengths of these

sounds if the speed of sound is 342 m/s?

18. Two boats in water bob up and down 30 times in 2.0 minutes. The distance between the

boats is 30 m. When one boat is in a trough, the other is on a crest, and there is one crest

between them. Calculate the speed of the waves.

19.

Sketch the shape of the medium when these two pulses overlap, assuming they are traveling

towards each other.

20. Determine the distance between successive nodes in a standing wave if the distance between

the fourth and eighth nodes is 80 cm.

21. The frequency of the source of standing waves has a frequency of 100 Hz. Nine nodes

(including one node at each end) are counted in the standing wave in a distance of 84 cm.

a) Calculate the wavelength of the waves?

b) How fast is the wave moving?

22. Determine the frequencies of the second, third, and fourth harmonics, if the fundamental

frequency for a vibrating string is 400 Hz.

23. Calculate the fundamental frequency if two successive overtones differ by 450 Hz.

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November 21, 2013