# Difference Between Period vs Frequency

We all deal with time on a daily basis whether it is consciously or unconsciously. It is the continuous and irreversible occurrence of events. Despite being applied generally in all events, this phenomenon is applied a little differently in scientific concepts for a more unique and comprehensive evaluation.

In this post, we will conduct a period vs frequency comparison to understand how these parameters, which fall under the concept of a wave, apply in the world of physics. More importantly, you will learn the distinct difference between the two.

## Definition of Period

A period is defined as a time concept that denotes how much time is required for a subject to complete a cycle or vibration. When an event starts and finishes during a specified time frame, that time frame is what is referred to as the period. It is denoted by the capital letter “T” and is usually measured in seconds, which are denoted by the small letter “s.”

There are many examples of T around us, and they are too numerous to count. Some of them include a rocking chair, a swing in motion, the orbit of earth and other planets around the sun, and even the human heartbeat. Note that the emphasis in this case is the time it takes for the subject to complete a particular round or from start to finish of a particular cycle.

From a similar perspective, some of these motions can be described as oscillations, which are the most basic type of T there is. It is usually demonstrated with the help of a simple harmonic oscillator.

T can be calculated relative to frequency (f) using the following formula.

T = ^{1}/_{f}

This means that period is a reciprocal of frequency. It is important to understand this similarity in order to be able to tell the difference between frequency and period. The former is a factor of rate, while the latter is a factor of time duration.

## Definition of Frequency

Frequency is defined as the number of times a set of similar vibrations or a cycle is completed within a second (unit time). From our earlier definition of period, we explained it is the time it takes for an event to complete a single cycle or vibration.

When this particular event keeps repeating itself in cycles in a certain amount of time, it is said to be frequent. The measure of how many cycles take place within a certain amount of time is what is known as the frequency, which is usually denoted with a small letter “f.”

Take a rocking chair, for instance. It moves back and forth when set in motion and is able to complete several cycles within a time frame. The number of cycles it is able to complete within a second is what is referred to as its frequency. Other examples include a water wave, a vibrating tuning fork, a bouncing ball, a swing in motion, and so on.

From what we have shared so far, it is safe to conclude that f is pretty much dependent on T. This goes to show the difference between period and frequency. Since T is a reciprocal of f, this means that f is inversely proportional to T.

f = ^{1}/_{T}

## Main Differences Between Period vs Frequency

This table below is a summary of how these two concepts of time are different from one another, despite having some similarities.

Basis of Comparison | Period | Frequency |

Definition | A time concept that denotes how much time is required for a subject to complete a cycle or vibration | The number of times a set of similar vibrations or cycle is completed within a second (unit time) |

Denotations | Capital letter T | Small letter f |

Formula | T = ^{1}/_{f} | f = ^{1}/_{T} |

Units | Seconds per cycle | Cycles per second or hertz |

Relationship to duration | The longer the T, the lower the f | The higher the f, the shorter the T |

## Difference Between Period and Frequency: Conclusion

To conclude the frequency vs period comparison, one can say that the latter is how long it takes for a cycle or vibration to be finished while the former is how many vibration cycles occur in a given time. T and f are inversely related to one another because one increases when the other decreases.