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A tuning fork of frequency $480\;{\text{Hz}}$ is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, ${{\text{l}}_1} = 30\;{\text{cm}}$ and ${{\text{l}}_2} = 70\;{\text{cm}}.$ Then ${\text{v}}$ is equal to:
(A) $332\;{\text{m}}{{\text{s}}^{ - 1}}$
(B) $379\;{\text{m}}{{\text{s}}^{ - 1}}$
(C) $384\;{\text{m}}{{\text{s}}^{ - 1}}$
(D) $338\;{\text{m}}{{\text{s}}^{ - 1}}$

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Last updated date: 16th Jun 2024
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Answer
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Hint: Since we know that sound is produced by vibration. Here, we will use the phrase that refers to the speed of sound, frequency and the two successive air column lengths used in the experiment. Using the values given will give us the result required.
Formula Used: We will be using the following formula,
$v = 2f\left( {{l_2} - {l_1}} \right)$
Where
$v$ is the velocity of sound
$f$ is the frequency of the tuning fork
${l_1}$ and ${l_2}$ are the two successive lengths of the air column

Complete Step-by-Step solution :
We know that an experimental tuning fork is used and it acts as an effective explanation of how sound can be produced by a vibrating object.
A handle and two bones constitute the fork. The tunes begin to vibrate when this tuning fork is hit with a rubber hammer, and so the tune’s back and forth vibration produces disturbances of surrounding air molecules. This disruption creates sound.
Now, let us use our formula to get the final result
$v = 2f\left( {{l_2} - {l_1}} \right)$
Upon substituting the values, we get
$v = 2 \times 480 \times (70 - 30) \times {10^{ - 2}}$
$ \Rightarrow v = 960 \times 40 \times {10^{ - 2}}$
Upon further solving, we get
$ \Rightarrow v = 38400 \times {10^{ - 2}}\;{\text{m}}/{\text{s}}$
Rewriting it further,
$\therefore v = 384\;{\text{m}}/{\text{s}}$

Hence, the correct option is (C.)

Additional Information: A tuning fork is made of a steel, nickel and chromium alloy, called elinvar. It is a material for which there is no change in elasticity. Humans can hear sound with a range of \[20 - 20,000Hz\]. Humans cannot hear any sound below this range and the sound above this range damages the ear.

Note: Vibration is a mechanical effect that happens around an equilibrium point through oscillations. The oscillations may be periodic, such as a pendulum's motion, or random, such as a tire's movement on a gravel road.