Question

What is the time period of a wave having a frequency of 50Hz?
A.\[0.02\,{\text{s}}\]
B. \[0.20\,{\text{s}}\]
C. \[2.0\,{\text{s}}\]
D. \[20\,{\text{s}}\]

Answer 1

Hint: Use the formula for the time period of a wave. This formula gives the relation between the time period of the wave and frequency of the wave. From this formula, one can conclude that the time period of the wave is reciprocal of the frequency of the wave.

Formula used:
The time period of a wave is given by
\[T = \dfrac{1}{f}\] …… (1)
Here, \[T\] is the time period of the wave and \[f\] is the frequency of the wave.

Complete step by step answer:
We have given that the frequency of a wave is \[50\,{\text{Hz}}\].
\[f = 50\,{\text{Hz}}\]
We can determine the time period of the wave using equation (1).
Substitute \[50\,{\text{Hz}}\] for \[f\] in equation (1).
\[T = \dfrac{1}{{50\,{\text{Hz}}}}\]
\[ \therefore T = 0.02\,{\text{s}}\]

Therefore, the time period of the given wave is \[0.02\,{\text{s}}\].Hence, the correct option is A.

Additional information:
Any wave has four characteristic properties: wavelength, amplitude, time period and frequency.The time period of a wave is the time required for a wave to complete its one cycle.The unit of time period in the SI system of units is second.The frequency of a wave is the number of cycles of the wave passing in one second.The unit of frequency of a wave in the SI system of units is hertz. The frequency of the music or beating of the heart is also measured in beats.

Note:While solving such types of problems, the students should carefully check whether the given frequency of the wave is linear frequency or angular frequency of the wave. The equation (1) is applicable only for the linear frequency of the wave. For determining the time period from the angular frequency of the wave, the formula is \[T = \dfrac{{2\pi }}{\omega }\].