The sound from a mosquito is produced when it vibrates its wings at an average rate of $500$ vibrations per second. What is the time period of the vibration?
A) $0.001$
B) $0.002$
C) $0.003$
D) $0.004$

Hint: Frequency is the number of oscillations of a vibrating body per second. The time period is the inverse, or the reciprocal of frequency of oscillation.

Complete step by step answer:
Frequency is the number of waves, which go through a given point per second or the number of oscillations of a vibrating body per second. It can also be the number of cycles per second.
And, the time period is defined as the time required to complete one oscillation. The time period is also defined as the inverse of the frequency of oscillation.
Now, assume that the frequency of oscillation is $f$.
In this question, it is given that the mosquito vibrates its wings at an average rate of $500$ vibrations per second. Therefore, the frequency of oscillation or the frequency of the sound is $500$ Hz and as the time period of the waves is the reciprocal of the frequency of the wave the time period is $T = \dfrac{1}{f} = \dfrac{1}{{500}} = 0.002$ seconds.
Hence, the time period of the vibration produced by the wings of the mosquito is $0.002$ seconds.

Note: If the effect of forces other than the restoring force is negligible on a vibrating body, its motion is called a free or natural vibration.
A body undergoing free vibration has a definite frequency, i.e., the body executes a fixed number of vibrations in unit time. It is called its natural frequency. This natural frequency depends on the density, shape, and elasticity, etc. of the vibrating body.