Frequency and period

The time for one cycle is called the period. The graph below shows position versus time for a mass oscillating up and down on a spring. Notice that one complete cycle occurs from 7 to 14 s; if we start counting the cycle at 7 s, the mass returns to the same position at 14 s. This graph is typical of simple harmonic motion. By simple we mean that there is a single period (or single frequency) that describes the motion. Read the text aloud
Period of an oscillating mass on a spring
The frequency of an oscillator tells you the number of cycles it completes each second. You experience a wide range of frequencies in your environment. A human heartbeat might have a frequency of ⅔ cycle per second when you first awake in the morning, 1–1.5 cycles per second for your normal activity, and 2–3 cycles per second when you are exercising. A plucked rubber band might have a frequency of 50 cycles per second. The sound of the musical note “A” has a frequency of 440 cycles per second. Read the text aloud
The unit of frequency is called the hertz (Hz), where one hertz corresponds to one cycle per second. A frequency of 440 cycles per second is usually written as 440 hertz, or abbreviated 440 Hz. The hertz is a unit that is the same in English and metric measurement systems. Read the text aloud Show FM radio
Frequency and period are the inverse of each other and are related by equation (14.1). A swing with a period of 2.5 s has a frequency of 1 ÷ 2.5 = 0.4 Hz. Large oscillators (such as a swing) tend to have low frequencies. Small or stiff oscillators (such as a guitar string) tend to have higher frequencies. Read the text aloud
(14.1) f= 1 T
f  = frequency (Hz)
T  = period (s)
Frequency and period
A sprinter’s heart beats once every 0.33 s. What is the frequency of her heartbeat?
Asked: frequency f of the heart beat
Given: period of beating heart, T = 0.33 s
Relationships: f = 1/T
Solution: Use the relationship between period and frequency: f= 1 0.33 s =3.0 Hz
Answer: The frequency is 3.0 Hz.
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The swing of a woodcutter’s axe takes 5 s. What is the frequency of his movement?
  1. 0.2 Hz
  2. 0.5 Hz
  3. 5 Hz
  4. 25 Hz

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