6. An oscillator makes four vibrations in one second. What is its period and frequency?
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1 Period and Frequency 19.1 The period of a pendulum is the time it takes to move through one cycle. As the ball on the string is pulled to one side and then let go, the ball moves to the side opposite the starting place and then returns to the start. This entire motion equals one cycle. Frequency is a term that refers to how many cycles can occur in one second. For example, the frequency of the sound wave that corresponds to the musical note A is 440 cycles per second or 440 hertz. The unit hertz (Hz) is defined as the number of cycles per second. The terms period and frequency are related by the following equation: 1. A string vibrates at a frequency of 20 Hz. What is its period? 2. A speaker vibrates at a frequency of 200 Hz. What is its period? 3. A swing has a period of 10 seconds. What is its frequency? 4. A pendulum has a period of 0.3 second. What is its frequency? 5. You want to describe the harmonic motion of a swing. You find out that it take 2 seconds for the swing to complete one cycle. What is the swing s period and frequency? 6. An oscillator makes four vibrations in one second. What is its period and frequency? 7. A pendulum takes 0.5 second to complete one cycle. What is the pendulum s period and frequency? 8. A pendulum takes 10 seconds to swing through 2 complete cycles. a. How long does it take to complete one cycle? b. What is its period? c. What is its frequency? 9. An oscillator makes 360 vibrations in 3 minutes. a. How many vibrations does it make in one minute? b. How many vibrations does it make in one second? c. What is its period in seconds? d. What is its frequency in hertz?
2 Harmonic Motion Graphs 19.2 A graph can be used to show the amplitude and period of an object in harmonic motion. An example of a graph of a pendulum s motion is shown below. The distance to which the pendulum moves away from this center point is call the amplitude. The amplitude of a pendulum can be measured in units of length (centimeters or meters) or in degrees. On a graph, the amplitude is the distance from the x-axis to the highest point of the graph. The pendulum shown above moves 20 cm to each side of its center position, so its amplitude is 20 cm. The period is the time for the pendulum to make one complete cycle. It is the time from one peak to the next on the graph. On the graph above, one peak occurs at 1.5 seconds, and the next peak occurs at 3.0 seconds. The period is = 1.5 seconds. 1. Use the graphs to answer the following questions a. What is the amplitude of each vibration? b. What is the period of each vibration?
3 Page 2 of 2 2. Use the grids below to draw the following harmonic motion graphs. Be sure to label the y-axis to indicate the measurement scale. a. A pendulum with an amplitude of 2 cm and a period of 1 second b. A pendulum with an amplitude of 5 degrees and a period of 4 seconds.
4 Waves 20.1 A wave is a traveling oscillator that carries energy from one place to another. A high point of a wave is called a crest. A low point is called a trough. The amplitude of a wave is half the distance from a crest to a trough. The distance from one crest to the next is called the wavelength. Wavelength can also be measured from trough to trough or from any point on the wave to the next place where that point occurs. The frequency of a wave is 40 Hz and its speed is 100 meters per second. What is the wavelength of this wave? Given Frequency = 40 Hz; Speed = 100 m/sec Looking for The wavelength Relationships Speed = Frequency Wavelength, therefore Speed Frequency = Wavelength Solution m/sec 40 Hz = m/sec = Wavelength 40 cycles/sec 2.5 meters = Wavelength The wavelength of this wave is 2.5 meters. 1. On the graphic at right label the following parts of a wave: one wavelength, half of a wavelength, the amplitude, a crest, and a trough. a. How many wavelengths are represented in the wave above? b. What is the amplitude of the wave shown above?
5 Page 2 of 2 2. Use the grids below to draw the following waves. Be sure to label the y-axis to indicate the measurement scale. a. A wave with an amplitude of 1 cm and a wavelength of 2 cm 20.1 b. A wave with an amplitude of 1.5 cm and a wavelength of 3 cm 3. A water wave has a frequency of 2 hertz and a wavelength of 5 meters. Calculate its speed. 4. A wave has a speed of 50 m/sec and a frequency of 10 Hz. Calculate its wavelength. 5. A wave has a speed of 30 m/sec and a wavelength of 3 meters. Calculate its frequency. 6. A wave has a period of 2 seconds and a wavelength of 4 meters.calculate its frequency and speed. Note: Recall that the frequency of a wave equals 1/period and the period of a wave equals 1/frequency. 7. A sound wave travels at 330 m/sec and has a wavelength of 2 meters. Calculate its frequency and period. 8. The frequency of wave A is 250 hertz and the wavelength is 30 centimeters. The frequency of wave B is 260 hertz and the wavelength is 25 centimeters. Which is the faster wave? 9. The period of a wave is equal to the time it takes for one wavelength to pass by a fixed point. You stand on a pier watching water waves and see 10 wavelengths pass by in a time of 40 seconds. a. What is the period of the water waves? b. What is the frequency of the water waves? c. If the wavelength is 3 meters, what is the wave speed?
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