Final answer:
The period is the time it takes for one complete cycle of an oscillation, while frequency is the number of cycles per second. They are inversely proportional, where frequency equals the reciprocal of the period, and computing one allows for the determination of the other.
Step-by-step explanation:
Period and Frequency in Oscillations
The period (T) of a vibration or a wave is the time it takes to complete one cycle. On the other hand, the frequency (f) of the vibration or wave is the number of complete cycles that occur in a specific period of time. Since the period is the time for one complete cycle, the frequency is the number of these cycles that happen per second.
The relationship between period and frequency is inversely proportional. Mathematically, we can express this relationship as f = 1/T or equivalently T = 1/f. Therefore, if you increase the frequency, the period decreases correspondingly, and vice versa.
To compute the frequency and period of an oscillation, like observing the vibrations of a guitar string, you would count the number of complete vibrations (cycles) in a second (for frequency) or measure the time it takes for one complete vibration (for period).
To determine the frequency of oscillations, you can look at a graphical representation of a wave, where the horizontal axis typically represents time and the vertical axis represents the displacement. One complete wave cycle on this graph corresponds to the period, and by taking its reciprocal, you can find the frequency.