Table of Contents
Dimensions of Frequency: The number of times a repeated occurrence occurs per unit of time is defined as the frequency. It’s also referred to as temporal frequency to distinguish it from spatial frequency, and ordinary frequency to distinguish it from angular frequency.
The greatest energy waves, with the highest frequencies and smallest wavelengths, are gamma rays. Radio waves, on the other hand, are the least energy waves, with the lowest and the longest wavelengths of all electromagnetic radiation.
A Brief Outline
Frequency is measured in hertz (Hz), which corresponds to one (event) per second. The duration is the reciprocal of the frequency since it is the temporal span of one cycle in a repeating occurrence.
Important Concepts
Dimensional Formula of Frequency
The dimensional formula of Frequency is:
[M0 L0 T-1]
M = Mass, L = Length, T = Time
Derivation of dimensions of frequency
Frequency (v) = number of vibrations × sec-1 – 1
The dimensional formula of time = [M0 L0 T1] – 2
On replacing equation (2) in equation (1)
Frequency = number of vibrations × sec-1
v = [M0 L0 T-1]
Hence, frequency is dimensionally embodied as [M0 L0 T-1].
Angular Frequency
The angular frequency is defined as the rate of change of angular displacement, the rate of change of argument of a sine wave, or the rate of change of phase of a sinusoidal waveform. In most cases, the angular frequency is stated in terms of omega (ω).
Spatial Frequency
The spatial frequency and the temporal frequency are similar. However, one or more spatial axes replace the time axis in the temporal frequency.
The rate of oscillation and vibration is described by the frequency parameter. The angular frequency of a sinusoidal wave is defined as the angular displacement of any wave element per unit time or the rate of change of the waveform’s phase.
Instruments for Frequency Measurement
- Stroboscopes were once used to determine the frequency of rotating or vibrating items.
- The high-frequency waves were calculated using electrical equipment known as a frequency counter. The result is displayed in Hertz via the frequency counter.
- The Heterodyne method can be used to determine the frequency of waves that are above the level of a frequency counter.
Significance of dimensions of frequency in IIT JEE exam
It is critical to take a holistic approach to every facet of a subject’s chapter. It will not only adequately prepare you for the exam, but will also clarify your understanding of each topic. It will help you pass the JEE exam’s conceptual problems. The number of questions from the chapter unit and dimensions would be one or two, with a weightage of roughly four marks.
FAQs
A sinusoidal wave's frequency is defined as the number of complete oscillations made by any wave constituent per unit of time.
The time it takes any string element to accomplish an oscillation is defined as the time period of oscillation of a wave.
The change of the waveform phase or the angular position of any element of the wave per time unit is referred to as the angular frequency. Define the term frequency?
Define a time frame?
Define the term Angular Frequency?
