Question

The relation between frequency (f) and time period (T) is given by
A) ${\rm{f}} = {\rm{T}}$
B) ${\rm{f}} = \dfrac{1}{{\rm{T}}}$
C) ${\rm{T}} = {{\rm{f}}^{\rm{2}}}$
D) ${\rm{T}} = {{\rm{f}}^3}$

Answer 1

Hint: The frequency is the number of occurrences of a repeating event per unit of time. The frequency is used to measure in terms of Hertz. The value of one Hertz equals the one occurrence of a repeating event per second.

Complete step by step answer:
In the given question, we are talking about the periodic phenomenon. Here the frequency is the number of times it repeats itself, and the period is the amount of time it takes to repeat itself.
We know that frequency and time period are the inversely proportional quantities form the definition of the frequency and time period.
${\rm{f}} = \dfrac{1}{{\rm{T}}}$
Here, the time period is ${\rm{T}}$ and the frequency is ${\rm{f}}$.
In the derived relation, the unit for time is second, and the unit for frequency is Hertz (periods per second or cycle per second).
The frequency and period are inverse functions because when the frequency is high, then the time period is low, or when the time period is low, then the frequency is increased.

Thus, the relation between frequency ($f$) and time period ($T$) is given by ${\rm{f}} = \dfrac{1}{{\rm{T}}}$. Hence, from the given options, only option B is correct.

Note:
The time period is defined as the time taken to complete a cycle of the given function. The SI unit of the time period is second. On the other hand, the frequency is defined as the number of cycles of the given function completed in the unit time. The SI unit for frequency is $sec^{-1}$