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Exploring Pendulum Vibrations and Wave Concepts

Delve into understanding pendulum vibrations and wave properties through hypothesis testing, experimentation on pendulum mass and string length, and calculations on frequencies and periods. Explore how waves transmit energy through space and time, identifying wave characteristics such as amplitude, frequency, and wavelength.

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Exploring Pendulum Vibrations and Wave Concepts

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  1. Waves transmit energy through space and time.

  2. Focused Learning Target • Given a formulated hypothesis on what affects the pendulum’s vibration, I will be able to prove how the mass of the bob and the length of the string affect the frequency of its vibration by varying the length and mass. • Given a sine wave, I will be able to identify and define period, wavelength, frequency, amplitude, crest and troughs .

  3. Given wave and vibration problems, I will be able to calculate a. frequency b. period c. wave speed Using f = 1/ period or f = 1/T T = 1/f V = λf

  4. Homework : • All odd numbers of Review Questions P 388 #36-41 p 389

  5. CW :PENDULUM 1. HYPOTHESIS : WHAT WILL HAPPEN TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE MASS OF THE PENDULUM INCREASES? ________________ 2. HYPOTHESIS : WHAT WILL HAPPEN TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE STRING OF THE PENDULUM INCREASES? ________________

  6. CW :PendulumPart 1:Half of the String’s Length 3. Length of the String _______cm 4. How many complete cycles in one minute ? Do 3 trials and get the average Cycles = _______ Time = 1 minute 5. Frequency in cycles per minute = ___________ 6.Frequency in cycles per second =_____________

  7. PendulumPart 2 : Double the Length of the String 7. Length of the String _______cm 8. How many complete cycles in one minute ? Do 3 trials and get the average Cycles = ______ Time = 1 minute 9. Frequency in cycles per minute = ___________ 10.Frequency in cycles per second =_____________

  8. PendulumPart 3 : Double the Mass and Use Half of the String’s Length 11. Length of the String _______cm 12. How many complete cycles in one minute ? Do 3 trials and get the average Cycles = ______ Time = 1 minute 13. Frequency in cycles per minute = ___________ 14.Frequency in cycles per second =_____________

  9. Conclusion 15. WHAT HAPPENS TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE STRING OF THE PENDULUM INCREASES? 16. WHAT HAPPENS TO THE NUMBER OF VIBRATIONS OF THE PENDULUM WHEN THE MASS OF THE PENDULUM INCREASES?

  10. Read p 372-373 and Do Vocabulary • What is Vibration? • Describe a Wave. • Give Examples of energy. • What is Period ? • What are the factors affecting Period? 6. What is a simple harmonic motion ?

  11. A repeating back-and-forth motion about an equilibrium position is a vibration. • A disturbance that is transmitted progressively from one place to the next with no actual transport of matter is a wave. • Examples of Waves Light and sound are both forms of energy that move through space as waves.

  12. 25.1Vibration of a Pendulum The period of the pendulum depends only on the length of a pendulum and the acceleration of gravity.

  13. 25.1Vibration of a Pendulum Pendulums swing back and forth with such regularity that they have long been used to control the motion of clocks. 4. The time of a back-and-forth swing of the pendulum is its period. 5. The period of the pendulum depends a. only on the length of a pendulum and b. acceleration of gravity. Galileo discovered that the period of a pendulum depends only on its length—its mass has no effect.

  14. 25.1Vibration of a Pendulum Two pendulums of the same length have the same period regardless of mass.

  15. 25.1Vibration of a Pendulum 6. A long pendulum has a longer period than a shorter pendulum. It swings back and forth more slowly—less frequently—than a short pendulum. Just as a long pendulum has a greater period, a person with long legs tends to have a slower stride than a person with short legs. Giraffes and horses run with a slower gait than do short-legged animals such as hamsters and mice.

  16. 25.1Vibration of a Pendulum What determines the period of a pendulum?

  17. 25.2Wave Description The source of all waves is something that vibrates.

  18. 25.2Wave Description 7. The back-and-forth vibratory motion—called oscillatory motion—of a swinging pendulum is called simple harmonic motion. 8. A sine curve is a pictorial representation of a wave.

  19. 25.2Wave Description Frank Oppenheimer demonstrates that a pendulum swinging back and forth traces out a straight line over a stationary surface, and a sine curve when the surface moves at constant speed.

  20. http://phet.colorado.edu/en/simulations/category/physics/sound-and-waveshttp://phet.colorado.edu/en/simulations/category/physics/sound-and-waves

  21. 25.2Wave Description 9. DRAW : The Parts of a Wave .Color and Label Explain each part by definitions. A weight attached to a spring undergoes simple harmonic motion. A marking pen attached to the bob traces a sine curve on a sheet of paper that is moving horizontally at constant speed. A sine curve is a pictorial representation of a wave.

  22. Wave Description • 10. The high points on a wave are called crests. • 11. The low points on a wave are called troughs. • 12. The term amplitude refers to the distance from the midpoint to the crest (or trough) of the wave. • The amplitude is the maximum displacement from equilibrium.

  23. 25.2Wave Description 13. The wavelength of a wave is the distance from the top of one crest to the top of the next one. Equivalently, the wavelength is the distance between successive identical parts of the wave. The wavelengths of waves at the beach are measured in meters, the ripples in a pond in centimeters, of light in billionths of a meter.

  24. 25.2Wave Description Frequency 14. The number of vibrations an object makes in a unit of time is an object’s frequency. The frequency specifies the number of back-and-forth vibrations in a given time (usually one second).

  25. 25.2Wave Description 15. A complete back-and-forth vibration is one cycle. 16. If a vibration occurs in one second, the frequency is one cycle per second; if two vibrations occur in one second, the frequency is two cycles per second. The frequency of the vibrating source and the frequency of the wave it produces are the same.

  26. 25.2Wave Description • 17. The unit of frequency is called the hertz (Hz). • A frequency of one cycle per second is 1 hertz, two cycles per second is 2 hertz, and so on. Higher frequencies are measured in • kilohertz (kHz—thousands of hertz) • megahertz (MHz—millions of hertz) • gigahertz (GHz—billions of hertz)

  27. 25.2Wave Description Electrons in the antenna of an AM radio station at 960 kHz vibrate 960,000 times each second, producing 960-kHz radio waves.

  28. 25.2Wave Description If the frequency of a vibrating object is known, its period can be calculated, and vice versa. Suppose, for example, that a pendulum makes two vibrations in one second. Its frequency is 2 Hz. The time needed to complete one vibration—that is, the period of vibration—is 1/2 second. As you can see below, frequency and period are inverses of each other: 18.

  29. 25.2Questions p 375 Questions 1 and 2 think! 19- Q#1. What is the frequency in vibrations per second of a 100-Hz wave?

  30. 25.2Wave Description think! What is the frequency in vibrations per second of a 100-Hz wave? Answer: A 100-Hz wave vibrates 100 times/s.

  31. 25.2Wave Description think! What is the frequency in vibrations per second of a 100-Hz wave? Answer: A 100-Hz wave vibrates 100 times/s.

  32. 25.3Wave Motion think! 26. The Sears Tower in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration?

  33. 25.3Wave Motion think! 26. The Sears Tower in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? Answer: The period is

  34. CW : Frequency and Period • P 388 • # 21 • # 22

  35. F = 76 heartbeats / min = 1.27 heartbeat /sec = 1.27 hertz T = 1/1.27 = 0.79 sec T = 6.8 sec f = 1/T = 1/6.8 sec = f = 0.15 Hz

  36. 25.2Wave Description What is the source of all waves?

  37. Read p 375 -377 Alternate Reading . 21. What are examples of waves ? 22. Describe how wave travels from source to a receiver. 23. How is a wave produced? 24. What is the speed of sound ? 25. How is speed calculated ? What is the equation for calculating speed ?

  38. 25.3Wave Motion The energy transferred by a wave from a vibrating source to a receiver is carried by a disturbance in a medium.

  39. 25.3Wave Motion How does a wave transfer energy?

  40. 25.4Wave Speed You can calculate the speed of a wave by multiplying the wavelength by the frequency.

  41. 25.4Wave Speed The speed of a wave depends on the medium through which the wave moves. Whatever the medium, the speed, wavelength, and frequency of the wave are related.

  42. 25.4Wave Speed If the wavelength is 1 meter, and one wavelength per second passes the pole, then the speed of the wave is 1 m/s.

  43. 25.4Wave Speed If the wavelength is 3 meters and if two crests pass a stationary point each second, then 3 meters × 2 waves pass by in 1 second. The waves therefore move at 6 meters per second. v =f where v is wave speed,  is wavelength, and f is wave frequency.

  44. 25.4Wave Speed In air, the product of wavelength and frequency is the same for every frequency of sound. That’s why you don’t hear the high notes in a chord before you hear the low notes. The sounds all reach you at the same time. Long wavelengths have low frequencies, and short wavelengths have high frequencies.

  45. 25.4 27. Wave Speed Wavelength and frequency vary inversely to produce the same wave speed for all sounds.

  46. 25.4Wave Speed think! 28. If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed?

  47. 25.4Wave Speed think! 28. If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed? Answer: The frequency of the wave is 2 Hz; its wavelength is 1.5 m; and its wave speed is

  48. 25.4Wave Speed think! 29. What is the wavelength of a 340-Hz sound wave when the speed of sound in air is 340 m/s?

  49. 25.4Wave Speed think! 29. What is the wavelength of a 340-Hz sound wave when the speed of sound in air is 340 m/s? Answer: The wavelength must be 1 m. Then wave speed = (1 m) × (340 Hz) = 340 m/s.

  50. 25.4Wave Speed How do you calculate the speed of a wave?

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