Question

What is the frequency of a vibrating body whose time-period is 0.05 second?
A) $10Hz$
B) $20Hz$
C) $40Hz$
D) none

Answer 1

In this question, we can use the relation between frequency and time period. The frequency is always reciprocal of the time period i.e. $f = \dfrac{1}{T}$of a vibrating body. The reciprocal of the second is Hz.

Complete step by step answer:
We know that if the frequency of the vibrating body is $f$ and the time-period of the vibrating body is $T$. We know that frequency is directly proportional to the time period i.e.
$f = \dfrac{1}{T}$
According to the question, we have the time period of the vibrating body$T = 0.05\sec$. So, substituting the value of time-period in the above equation, we have-
$\Rightarrow f = \dfrac{1}{{0.05}} \\\ \Rightarrow f = \dfrac{{100}}{5} \\\ \Rightarrow f = 20Hz \\\$

Hence, the frequency of a vibrating body is $20Hz$ whose time-period is $0.05$ second. Therefore, option B is correct.

Additional Information:
Frequency- This is a number of occurrences of a periodic event per unit time. In general this is also the number of repetition of the event per unit time. Its unit is cycle/second. It is a rate quantity.
Time period- It is time which is taken in completing a cycle. In general, time taken to complete a cycle is known as time period. Its unit is second. It is a time quantity.

Note:
In this question, we have to remember that frequency is reciprocal of the time period. Frequency is not inversely proportional to the time period because there must be a constant added in the equation after removing the proportionality. We have to keep in mind that the unit of time period is second while the unit of frequency is Hz.