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Which of the following sounds is not audible?
A) A tuning fork vibrating $400$ times in $2s$
B) A tuning fork vibrating $3600$ times in $60s$
C) A tuning fork vibrating $1$ time in $1s$
D) A tuning fork vibrating $900$ time $2s$

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Last updated date: 17th Apr 2024
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Answer
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Hint: Frequency of a wave is the no of complete oscillations per unit time. The more is the number of oscillations the more will be the frequency. We have to calculate the respective frequencies for each option. Humans have a range of audibleness from $20Hz$ to $20kHz$. Any frequency falling in this range should be audible.

Formula Used: $f = \dfrac{n}{T}$
Where,
$f$ is the frequency of the tuning-fork
$n$ is the number of oscillation
$T$ is the time period for oscillation

Complete step by step answer:
A vibrating tuning fork oscillates at a specific rate in a specific time period. Frequency can be calculated by the above formula by calculating the ratio of the number of oscillations and its time period.
Human ears are sensitive to a frequency range of $20Hz$ to $20000Hz$. If a sound wave falls inside this range, it should be audible to us.
Let’s analyse every option now.
For option A, number of oscillations is $400$ and time period is $2s$.
Substituting these values in the formula we get,
$f = \dfrac{{400}}{2} = 200Hz$
This frequency is audible.
For option B, number of oscillations is $3600$ and time period is $60s$
Substituting these values in the formula we get,
$f = \dfrac{{3600}}{{60}} = 60Hz$q
This frequency is also audible.
For option C, number of oscillations is $1$ and time period is $1s$
Thus frequency becomes, $f = \dfrac{1}{1} = 1Hz$
This frequency is less than the minimum frequency is not audible.
Again, if we analyse option D, number of oscillations is $900$ for a time period $2s$, which means,
Frequency will be, $f = \dfrac{{900}}{2} = 450Hz$
This is an audible frequency.

Thus the correct answer is option C, a tuning-fork vibrating $1$ time in $1s$is not audible by human ears.

Note: Humans have a smaller range of frequencies compared to many animals, dogs can hear in a range of $50 - 50kHz$ and bats can even hear up to $100kHz$. These easy problems are a treat for the eye of the student, but watch for the system of units. Sometimes the examiner asks in a different system of unit and students tend to overlook.