Explanation on Period and Frequency

In physics, frequency refers to the number of waves that pass a given point in one unit of time. It is also defined as the number of cycles or vibrations that a body in periodic motion undergoes in one unit of time. After travelling through a series of events or positions and returning to its original state, a body in motion is said to have completed one cycle or one vibration.

Definition of a time period

A period can be defined as the amount of time that passes among subsequent instances of the same condition in an oscillation or cyclical phenomena, such as mechanical motion, AC voltage, or a magnetic field.

The length of time it takes to perform an activity is called a time period, and intermittent refers to an occurrence that occurs on a regular basis. The length of time it takes for the seasonal phenomena to repeat itself is referred to as the cycle. A particle’s time span determines how long it will take to finish a vibration cycle.

The time period of a simple pendulum 

Generally, a pendulum consists of a mass suspended from a light wire or thread with a small mass attached to it. We may identify the conditions under which the simple pendulum performs simple harmonic motion and get an equation for its period.

F = -mgΘ

For small angles 

Θ= S/l

F= -mgS/l

F = -Kx

So K = mg/l

Where m is the mass of the pendulum,

g is the acceleration due to gravity,

Θ is the angular displacement,

K is the force constant

L is the length of the pendulum.

We know that 

T=2π√m/k=2π√m/mg/L=2π√L/g

A basic pendulum’s period is determined solely by its length as well as its acceleration owing to gravity. Other elements, such as mass, have no bearing on the period. The period T of a pendulum, like that of simple harmonic oscillators, is nearly independent of amplitude, especially if it is smaller than roughly 15°.

Frequency

The number of wave cycles that pass through a point every second are termed frequency. It is the number of oscillations per second that happen inside a wave. Wavelength and frequency are inversely related. The SI unit of frequency hertz is its measure scale. The smaller the wavelength, the stronger the frequency; conversely, the longer the wavelength, the lower the frequency. Moreover, the frequency of anybody does not rely on the amplitude of the body, and both are independent mechanisms. 

If the time necessary to finish one cycle or vibration is 1/2 second, the frequency is 2 per second. If the amount is 1/100 of an hour, the frequency is 100 per hour. The frequency is the reciprocal of the time period. Thus, frequency = 1/period = 1/ (time interval).

Amplitude 

A sound wave’s amplitude is a measurement of the wave’s height. The maximum displacement of vibrating particles in a medium from their mean location when the sound is emitted is known as the amplitude of a sound wave. The frequency of the largest disruption of particles in the medium on each side of the mean value is the wave’s amplitude.

Frequency of periodic motion 

The frequency of periodic motion can be defined as the time in which an object’s motion repeats itself over and over again, such as travelling back and forth or in a circular orbit. Consider a thread that is strewn over the floor at random. An insect is travelling at a constant pace throughout the thread though it is moving over a fixed area of the thread regularly.

Properties of periodic motion

Periodic motion has three attributes: the object’s velocity, period, and amplitude. Periodic motion can be seen in a variety of waveforms and is commonly employed in clocks and other electronic equipment. The time taken by a particle in periodic motion to pass a specific point from a specific direction at regular intervals is referred to as a time period. A periodic motion might follow a circular, elliptical, linear, or more complicated path.

Conclusion

Periodic motion is an oscillation that takes place repeatedly in an amount of time. On the other hand, frequency is the number of times an instance occurs within any specific time period. It is measured on the scale of hertz per second.