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A sound wave is vibrating at frequency $50\,Hz$ . What is its time period?

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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Hint: You can easily reach the solution to this question by simply recalling what is frequency, what is time period and how they both are related with each other. Point that should be noted is that vibration of a sound wave is a repeating event and thus, both the frequency and time period exist for it.

Complete step by step answer:
We will be trying to solve this question exactly as we guided in the hint section of the solution. We will first define what is frequency and what is time period, from there we can reach the relation between both of them quite easily.
We will define frequency first:

Frequency: Frequency is the number of times an event is repeated in a single second, that is, frequency is the count of occurrence of an event in a time duration of one second.
Now, let’s define time period:
Time period: Time period is the duration of time of a single cycle of a long, repeating event. In other words, time period is the time duration which a single bit of a repeating even takes to complete.
We can clearly see from the definitions that there is some relation between frequency and time period of an event, in fact, time period and frequency are reciprocal of each other, we can represent this relation mathematically as:
$T\, = \,\dfrac{1}{f}$
Where, $T$ is the time period of the repeating event and,
$f$ is the frequency of the repeating event.
We have been given the value of frequency of the vibration of sound wave as $f\, = \,50\,Hz$
Putting this in the relation of time period and frequency, we get:
$
  T\, = \,\dfrac{1}{{50}}\,\operatorname{s} \\
  T\, = \,0.02\,s \\
 $

Hence, we can say that the time period of the sound wave is $0.02\,s$ .

Note: Many students only try to find the frequency of a sound wave using the wave equation of the sound wave, which is not given here, hence they get stuck. This is the most basic relation that you should remember to score easy and fast marks in any exam.