Question

A source produces 60 rarefactions and 60 compressions in$0.6\,{\text{s}}$. Distance between a compression and the next (consecutive) rarefaction is
$150\,{\text{cm}}$.Find the frequency of the wave.
(A) $500\,{\text{Hz}}$
(B) $0.02\,{\text{Hz}}$
(C) $0.01\,{\text{Hz}}$
(D) $100\,{\text{Hz}}$

Answer 1

First of all, we will find out the number of waves that are produced in the given time interval. Then we will find out the number of waves produced in one second. We know the number of vibrations or oscillations produced in one second is the frequency of the wave.

Complete step by step answer:
In the given question, we are supplied with the following data:
The source produces $60$ rarefactions and $60$ compressions.The time required to produce the given number of rarefactions and compressions is $0.6\,{\text{s}}$.The distance between a compression and next rarefaction is $150\,{\text{cm}}$.We are asked to find the frequency of the wave.
To begin with, we know that frequency of a wave is defined as the number of oscillations or vibrations taking place in one second. Frequency is inversely proportional to time. As the frequency increases, the time period decreases. In case of longitudinal waves, there are rarefactions and compressions. In rarefaction, there is reduction in density of air or gas and while in case of compressions there is increase in density of air of gas.
From the given information:
We can say that in a duration of time of $0.6\,{\text{s}}$ , the number of waves which are produced accounts to $60$ .
So, for the duration of time of one second, the number of waves which are produced accounts to:
\dfrac{{60}}{{0.6\,{\text{s}}}} \\\ \Rightarrow\dfrac{{600}}{6}\,{{\text{s}}^{ - 1}} \\\ \Rightarrow100\,{{\text{s}}^{ - 1}} \\\
Again, from the definition of frequency, we know that ${{\text{s}}^{ - 1}}$ is written as hertz $\left( {{\text{Hz}}} \right)$ .
So, the number of waves produced is $100$ .
The number of waves produced in one second is called frequency.
Hence, the frequency is found out to be $100\,{\text{Hz}}$ .

The correct option is D.

Note: While answering this question, most of the students tend to make mistakes while taking the number of waves produced in $0.6\,{\text{s}}$ . They might take the number of waves produced in $0.6\,{\text{s}}$ as $120$ , which is wrong. It is important to remember that a single wave is characterised with a rarefaction and a compression.