18A Period and Frequency Read: The period of a pendulum is the time it takes to

Question

18A Period and Frequency Read: 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. Finish 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: Frequengy (hertz) Period(seconds)T = Frequency (hertz) Perlod (seconds) Practice: 1. A string vibrates at a frequency of 20 Hz. What is its period? z to Hh 2. A speaker vibrates at a frequency of 200 Hz. What is its period? F: Zoo HE T: ocs 3. A swing has a period of 10 seconds. What is its frequency? f T: OH! 4. A pendulum has a period of 0.3 second. What is its frequency? Tt 33 3536 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? 5. 6. An oscillator makes four vibrations in one second. What is its period and frequency? 18A Period and Frequency

Explanation / Answer

1) Period of 20 Hz string is T = 1/20 = 0.05 s

2) Period of 200 Hz speaker is T = 1/200 = 0.005 s

3) Frequency of the swing is f = 1/T 1/10 = 0.1 Hz

4) Frequency of the pendulum is f = 1/T = 1/0.3 = 3.33 Hz

5) Swing's period is T = 2 seconds

Frequency is f = 1/T =1/2 =0.5 Hz

6) The frequency of the oscillator is f = 4 Hz

The Period of the oscillator is T = 1/f = 1/4 = 0.25 Hz

7) Period of the pendulum is T = 0.5 s

The frequency is f = 1/T = 1/0.5 = 2 Hz

8) The time taken to complete 1 cycle is T = 10/2 = 5 seconds

The period is T = 5 s

The frequency is f = 1/T = 1/5 = 0.2 Hz

9) The number of vibrations in 1 minute is 360/3 = 120

The number of vibrations in 1 second is 120/60 = 2

The period is T = 1/2 = 0.5 s

The frequency is f = 1/T = 2 Hz

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