Question

A tuning fork of frequency \[420{\text{ Hz}}\] completes \[{\text{70}}\] vibrations. Find the distance travelled by sound in air (\[v = 360{\text{ m}}{{\text{s}}^{ - 1}}\]).
A. \[20{\text{ m}}\]
B. \[50{\text{ m}}\]
C. \[60{\text{ m}}\]
D. \[80{\text{ m}}\]

Answer 1

Hint:We are asked to find the distance travelled by sound in air when the tuning fork vibrates \[{\text{70}}\] times. Recall the definition of frequency and calculate the time taken in \[{\text{70}}\] vibrations. Use the formula for distance in terms of speed and time to find the distance travelled by sound in air.

Complete step by step answer:
Given, frequency of tuning fork, \[f = 420{\text{ Hz}}\].Number of vibrations, \[{\text{V}} = {\text{70}}\].Speed of sound in air, \[v = 360{\text{ m}}{{\text{s}}^{ - 1}}\].Frequency can be defined as the number of vibrations per second or number of vibrations in one second.Here, frequency is given to be \[f = 420{\text{ Hz}}\] that means in one second the tuning fork vibrates \[420\] times.So, we can write
For \[420\] vibrations, time taken is \[1{\text{ s}}\].
For \[1\] vibrations, time taken will be, \[\dfrac{1}{{420}}{\text{ s}}\].
For \[{\text{70}}\] vibrations, time taken will be, \[\dfrac{1}{{420}} \times {\text{70 s}} = 0.167{\text{ s}}\]
We have the formula for distance as,
\[{\text{Distance}} = {\text{Speed}} \times {\text{Time}}\] (i)
Here, speed is \[v = 360{\text{ m}}{{\text{s}}^{ - 1}}\] and time is \[0.167{\text{ s}}\]. Putting these values in equation (i) we get distance travelled as,
\[d = 360{\text{ m}}{{\text{s}}^{ - 1}} \times 0.167{\text{ s}}\]
\[ \therefore d = 60{\text{ m}}\]
Therefore, distance travelled by sound in air is \[60{\text{ m}}\].

Hence, the correct answer is option C.

Note:Tuning fork is a device that has two pronged metal forks that forms a U-shape. It is useful to demonstrate how a vibrating object can produce sound. By striking the tuning fork with something we can set vibrations in the tuning fork, this vibrations creates disturbances in the air and this disturbances creates regions of compression and rarefactions which produces sound.