Dimensional Formula of Frequency

Technically, the definition of frequency can be given as the number of waves that pass through a fixed point in the unit time. The unit through which we measure frequency is hertz, and one hertz can be defined as one cycle per second. It can be generally expressed as the reciprocal of the time interval or period. The wavenumber is also sometimes used as a unit of frequency specially in spectroscopy.

Frequency of the periodic motion

A periodic motion repeats after a fixed time interval. If the motion repeats itself for a long time, it has a frequency. So, the frequency is the number of times the motion repeats itself in unit time. You can say that one complete motion is equal to one frequency; the number of times one complete motion is repeated in a given period is its frequency.

The letter f depicts the frequency of the periodic motion. ‘Hertz’ or Hz is the unit used to measure the frequency of a periodic motion.

Frequency (f) = 1/T. This formula is explained in detail in the next part.

The formula of a frequency of periodic motion

The time period, T, is the time required by the motion to repeat itself. The standard unit to measure the time period is seconds. 

Frequency (f) is the number of times a motion repeats itself in unit time. Hertz (Hz) is used to measure the frequency.

There exists an inverse relationship between time period and frequency. Mathematically, it can be depicted as follows:

      f = 1/T

Equation (1) is the formula of periodic motion. 

Dimensional Formula of Frequency

Frequency = 1T

                              = [M0L0T-1]

Since frequency is the reciprocal of time interval, so only time is included in the dimensional formula of frequency.

Importance of Frequency

• Frequency is extremely important in the world of music, because every instrument has its own frequency and because of which we get to hear such wonderful sounds.
• It plays a very important role in power transmission systems as well.                       

Dimensional formula of frequency importance

• The dimensional formula of frequency helps us to understand the physical correctness of any equation involving force in it.
• It helps us to  understand relationship between different physical quantities involving Gravitational energy
• It helps us in converting units from one physical quantity to another
• In any relationship, the constant dimensions can be found using this analysis.

Dimensional Formula

The dimensions can be written as the powers of the fundamental units of length, mass, and time. It depicts their nature and does not show their magnitude. 

Example to write dimensions

Let’s take the formula of the area of the rectangle

Area of the rectangle = length x breadth

= [L1] X [L1]    ( where breadth is also showing the length of the side)

= [L2]

 Here, we can see the length to the power of 2 and we cannot find the dimension of mass and time.

Hence, the dimension of the area of a rectangle is written as [M0 L2 T0]

Dimensional formula dimensional equation

The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity, along with the powers.

Example

Let’s take the formula of speed

Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [ M0 L1 T-1]

Hence, we can conclude that the speed is dependent on only length and time, not mass.

Dimensional equation

The physical quantity is equated with the dimensional formula, to get the dimensional equation. 

Example

Velocity =  [ M0 L1 T-1]

Here, velocity is the physical quantity, which is equated to the dimensional formula.

Application of dimensional analysis 

In real-life physics, dimensional analysis is a crucial part of the measurement. We use dimensional analysis for three main reasons:

• To ensure that a dimensional equation is consistent.
• Determining the relationship between physical quantities in physical phenomena
• To switch from one system to another’s units
• Development of a fluid phenomena equation
• The number of variables necessary in an equation is reduced.

Conclusion

This article briefly acts as a dimensional formula of Frequency notes. Includes basic definitions of frequency and all the terms related to it. Also the dimensional formula of Frequency and its importance. The dimension is the property of units and measurements, which is used for many applications like correction, comparison, and derivation of the physical quantity. The dimensional formula has the basic terms of length, mass, and time. The equation of physical quantity and dimension is called the dimensional equation. Frequency can be defined as the number of times something repeats itself frequently. Frequency plays a really important role in the music industry and in power transmission systems too. The units used in expressing frequency are hertz and wave number.