Time Period

Time period is the time taken by particles to complete one cycle of vibration or oscillation. The time period is denoted by ‘T’. The unit of the time period is ‘seconds’.

As shown in the above figure, T, the time period is the peak-to-peak value of sinusoidal waves. Time period is the time taken by a vibrating body to complete one oscillation.

In a cosine wave motion, at t= 0 time, the particle is at max positive distance A. The particle oscillates from A to -A and back to A again. The cycle repeats itself again and again. 

The time period is called T, the period of oscillation, or it can be defined as the frequency f-number of oscillations per second.

From the figure, the particle will oscillate about its equilibrium position. That is, x is a function of t that is represented by a sine wave or a cosine wave, so that x may be a function of x (t)= A cos (wt) or x (t)= A sin (wt).

The relationship between time period and frequency is given below formula:

f=1T=w2π

Where f = frequency

            T= time period

            W= angular frequency.

All the waves, whether sound waves or electromagnetic waves, follow the above equation.

A wave is defined through amplitude, frequency, period, phase, angular frequency, and wavelength.

Amplitude

The maximum displacement in either direction of its mean position is called amplitude.

The SI unit of amplitude is metred (m).

An oscillatory motion of a particle can be defined as a sine function or cosine function. It is called the amplitude formula.

The sine or cosine function can be written as:

 x(t)= A sin (wt+¢) or x(t) = Acos (wt+¢)

Where,

 x = displacement of particle

 A =amplitude  

 ¢= phase shift 

 w= angular frequency

 t= time period

Let’s take one example of an amplitude formula to find all parameters to define the vibration or oscillation.

The wave equation is y (t) = 3 sin (6t) and find all the parameters to describe the wave.

When we compare y=3 sin (6t) with standard wave equation y = A sin (wt), we get,

Amplitude A=3

Angular frequency w=6

Phase shift ¢=0

Frequency f=w2π=62π=3π

Time period T=1f=13π=π3

Period

The period of wave time required by a particle for one complete cycle.

The SI unit of the period in seconds (s)

Frequency

The number of cycles or periods per second is called frequency. It is a parameter that describes the rate of vibration or oscillation.

Frequency is represented by f. The relation between frequency and time period is given by below equation:

f=1T=w2π

The SI unit of frequency is hertz (Hz) or s-1.

From the above equation, we can say that if frequency increases, the time period decreases and when frequency decreases, the time period increases.

For example, if a heart beats at a frequency of 120 times a minute (2 hertz), its time period T is the time interval between beats is half (T=1/f = ½ s) a second (60 seconds divided by 120 beats).  

Frequency is an important parameter used in physics and science to specify the rate of oscillation and periodic phenomena, such as mechanical vibrations, sound signals, radio waves, and light.

Angular frequency

The angular displacement of any particle of the wave per unit of time is called angular frequency.

It is also defined as the rate of change in the phase of a waveform. It is represented by w. The below-mentioned formula defines angular frequency:

w=2πT=2πf

The SI unit of angular frequency is rad/s.

Angular frequency is directly proportional to frequency and inversely proportional to time period. 

It means if angular frequency increases, the value of frequency increases and angular frequency decreases, the value of frequency also decreases.

If angular frequency increases, the value of the time period decreases and if the angular frequency decreases, the value of the time period increases.

Phase

The fraction of a period that a particle completes after passing through reference or zero position.

Phase shift 

Two signals are at two different cycle positions in a given time called a phase shift. It is measured as an angle in radians or degrees. It is denoted by ¢. 

Phase shift is more observed in sinusoidal waves in which a single fundamental frequency is present and harmonics are absent.

Wavelength

It is the distance between two consecutive crests or troughs or zero crossing of the wave.

 Wavelength = frequency

From the above relation, we can say that if the wavelength increases, the value of frequency decreases and if the wavelength decreases, the value of frequency increases.

The SI unit of wavelength is metre (m).

Conclusion

You learnt about the time period which is the time taken by a particle for one complete cycle. The one cycle or wave is defined by different amplitude, frequency, and phase shift parameters.