Question

A tuning fork has the frequency of vibration 200Hz. If the velocity of sound in air is 330m/s, then how far the sound has traversed while turning the fork completes 20 vibrations.
(A)24 m
(B)57 m
(C)42 m
(D)33 m

Answer 1

The frequency is the characteristic of the source and it does not change. The velocity of the sound is dependent upon the medium as it is a longitudinal wave. Here we can exploit the relationship between frequency, velocity and Time period.

Complete step by step answer:
Frequency=200Hz
Speed of sound =330m/s
Number of vibrations=20
We know the relationship between the frequency $\nu$and time period, T is given by $\nu T=1$
200 $\times$ T = 1
which gives T=0.005 s.
Also, Total time= Time period $\times$ number of vibrations
Total time = 0.005 $\times$20
Total time = 0.1 s
Now,
Distance travelled= Speed $\times$time
= 330$\times$0.1 = 33m

So, the correct answer is “Option D”.

Additional Information:
The vibrating object is the source of the disturbance that moves through the medium and when such a body vibrates which is to and fro motion it happens at a particular frequency.

Note:
When dealing with such problems we always get confused between time period and normal time. Time period in simple language can be defined as the time taken by the object to come back to its initial position or in terms of uniform circular motion the time taken to complete one revolution. Frequency and time period are inverse of one another. The time period is to be taken in seconds and frequency in the inverse of the second commonly called hertz.