Question

A tuning fork of frequency 480Hz 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, ${l_1}$ =30cm and ${l_2}$ =70cm. Then v is equal to:
A. $\eqalign{ & 332m{s^{ - 1}} \cr} $
B. $\eqalign{ & 379m{s^{ - 1}} \cr} $
C. $\eqalign{ & 384m{s^{ - 1}} \cr} $
D. $\eqalign{ & 338m{s^{ - 1}} \cr} $

Answer 1

Hint: Since we know that vibration produces sound. Here, we will use the expression which relates the speed of sound, frequency and the two successive lengths of air column used in the experiment. Using the given values will give us the required result.

Formula used: $v = 2f({l_2} - {l_{1}})$

Complete step by step answer:
We know that a tuning fork is used in experiment and it serves as a useful illustration of how a vibrating object can produce sound.
The fork consists of a handle and two tines. When this tuning fork is hit with a rubber hammer, the tunes start to vibrate and so, the back and forth vibration of the tunes produce disturbances of surrounding air molecules. This disturbance produces sound.
The relation between the speed of sound v, frequency of tuning fork and the two successive lengths of the air column ${l_1}$ and ${l_2}$ is given by:
$v = 2f({l_2} - {l_{1}}) $
Putting the values, we get:
$ \eqalign{
 & v = 2 \times 480 \times (70 - 30) \times {10^{ - 2}} \cr
  & \Rightarrow v = 960 \times 40 \times {10^{ - 2}} \cr
  & \Rightarrow v = 38400 \times {10^{ - 2}}m/s \cr
  & \therefore v = 384m/s \cr} $

So, the correct answer is “Option C”.

Additional Information: The speed of sound is defined as the distance travelled per unit of time, as it propagates through any medium.
Also, At $20$ degree Celsius, the speed of sound in air is around 343 meters per second or one kilometer in 2.9 sec or one mile in 4.7 sec. Further we know that the speed of sound depends strongly on temperature as well as on the medium through which it is propagating.
Frequency is defined as the number of occurrences of a periodic event per unit time and is measured in cycles/second or Hertz.

Note: Vibration produces sound. The range of frequency that is audible to human ranges from 20Hz to 20kHz. Below this range humans cannot hear any sound and the sound above this range damages the ear. These frequency ranges are different for different animals and birds.