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Question: A tuning fork of frequency \[420{\text{ Hz}}\] completes \[{\text{70}}\] vibrations. Find the distan...

A tuning fork of frequency 420 Hz420{\text{ Hz}} completes 70{\text{70}} vibrations. Find the distance travelled by sound in air (v=360 ms−1v = 360{\text{ m}}{{\text{s}}^{ - 1}}).
A. 20 m20{\text{ m}}
B. 50 m50{\text{ m}}
C. 60 m60{\text{ m}}
D. 80 m80{\text{ m}}

Explanation

Solution

We are asked to find the distance travelled by sound in air when the tuning fork vibrates 70{\text{70}} times. Recall the definition of frequency and calculate the time taken in 70{\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 Hzf = 420{\text{ Hz}}.Number of vibrations, V=70{\text{V}} = {\text{70}}.Speed of sound in air, v=360 ms−1v = 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 Hzf = 420{\text{ Hz}} that means in one second the tuning fork vibrates 420420 times.So, we can write
For 420420 vibrations, time taken is 1 s1{\text{ s}}.
For 11 vibrations, time taken will be, 1420 s\dfrac{1}{{420}}{\text{ s}}.
For 70{\text{70}} vibrations, time taken will be, 1420×70 s=0.167 s\dfrac{1}{{420}} \times {\text{70 s}} = 0.167{\text{ s}}
We have the formula for distance as,
Distance=Speed×Time{\text{Distance}} = {\text{Speed}} \times {\text{Time}} (i)
Here, speed is v=360 ms−1v = 360{\text{ m}}{{\text{s}}^{ - 1}} and time is 0.167 s0.167{\text{ s}}. Putting these values in equation (i) we get distance travelled as,
d=360 ms−1×0.167 sd = 360{\text{ m}}{{\text{s}}^{ - 1}} \times 0.167{\text{ s}}
∴d=60 m\therefore d = 60{\text{ m}}
Therefore, distance travelled by sound in air is 60 m60{\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.