Question

How is the frequency of a wave related to its time period?

A. $\upsilon =\dfrac{1}{T}$
B. $T=\dfrac{1}{\upsilon }$
C. $\upsilon T=1$
D. All the above

Answer 1

The frequency and the time period are inversely related to each other, as the frequency represents the cycles completed per second, while the time period represents the time taken to complete the cycles. Frequency is the cycles/second. The time period is the seconds/cycle.

Formula used:
$\upsilon =\dfrac{1}{T}$

Complete step by step answer:
Frequency:
The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. The frequency is represented by the small letter “f” and a Greek letter “v” pronounced as ‘nu’. The units like vibrations/second, cycles/second and waves/second, are used to represent the rate quantity, that is, the frequency. The most commonly used unit for frequency is the Hertz(abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second.
Time period:

The period of a wave is the time for a particle on a medium to make one complete one cycle. The units like years, hours, minutes and seconds are used to represent the time quantity, that is, the period.

Mathematically, the frequency is the reciprocal of the time period and vice – versa.
In terms of the equation, the relation between the frequency and the time period can be expressed as,
$\upsilon =\dfrac{1}{T}$

Where $\upsilon$ is the frequency and T is the time period.
As the frequency is inversely related to the time period, the options, A. $\upsilon =\dfrac{1}{T}$,B. $T=\dfrac{1}{\upsilon }$ and C. $\upsilon T=1$ represent the correct relation, thus, option (D) All the above is correct.

Note:
The things to be on your finger-tips for further information on solving these types of problems are: Some of the time, the unit of the frequency will be given as per second, so there the confusion may occur regarding the units of the parameter.