Question

Define frequency and periodic time. Represent the relation of them by a formula.

Answer 1

Hint: Frequency and periodic time are included among the major attributes of oscillatory motion, where the to and fro motion of a body about a single point is observed. This motion keeps repeating itself and frequency and periodic time are time related properties that exist during the motion.

Complete step by step answer:
Frequency (f) in oscillatory motion can be defined as the number of oscillations or vibrations made by the body or the system in one second.
The S I unit of frequency is Hertz, which is denoted by Hz. In other words, a frequency of one Hertz is equal to one complete oscillation taking place per second.

Time period (T) in oscillatory motion can be defined as the total time taken by the body or the system to complete one oscillation, vibration or a cycle. As the name suggests, the S I unit of time period is Seconds which is denoted by s.
From both the definitions, it is clear that frequency and time period are quantities that are related to time and thus, they are related to one another. In fact, they share an inverse relationship with each other that is, one quantity can be expressed as the reciprocal of the other.

Which implies that
 Time period= $\dfrac{1}{{Frequency}}$ or vice versa.
Hence we have defined frequency and time period. We also generated the relationship between them.

Note:
This relation is to be noted by the students as this is applied in most of the numerical problems. In a given condition or in an experiment, if they wish to increase the frequency, they can decrease the time period of oscillation or vice versa. The relationship of the speed of sound, its frequency, and wavelength is the same as for all waves.