Unit of Frequency

Introduction

Wave is the disturbance in the medium to transfer energy without the transfer of mass. Waves are usually in a periodic motion like a simple harmonic oscillator. They have crests and troughs.

The amplitude of the wave is the height of the wave. The distance covered between two consecutive crests is called the wavelength of the wave. The number of waves passed per second is called the frequency of the wave. Phase is not the property of waves. But it gives the relation between two signals with the same frequency.

Now, we are going to discuss about the waves, low and high frequency waves and their units.

What is the Frequency?

The number of waves that pass through a point at a particular time is denoted as frequency. It is also denoted as the number of vibrations or the number of cycles per unit of time. If an object is in a periodic motion it completes a complete event and returns to its original position. The frequency of the wave is the reciprocal of the time interval taken for the complete cycle.

The arms of the tuning fork vibrate back and forth with a specific frequency. Frequency is generally related to the processes such as vibration, oscillation, and rotation. The frequency is denoted by f. frequency is an important element in audio signals, mechanical vibrations, light, and radio waves.

Unit of frequency

The unit for frequency is Hertz. One vibration or oscillation per second is denoted as one Hertz. The sound wave that passes through the air makes a change in air pressure. This air pressure is detected by the human and living things' ears to catch the sound. Generally, the audible range of frequency of the sound wave by the human is between 20Hz and 20000 Hz.

Infrasound waves have a frequency less than the frequency of the audible range of humans. That is less than 20 Hz. Ultrasound waves have a frequency greater than the frequency of the audible range of humans. That is greater than 20000 Hz. The sensation that is caused by the frequency is called the pitch. If the frequency of the sound wave is high then the pitch is also high and vice versa.

$$\mathrm{1\:Hertz=1\:Vibration\:second^{−1}}$$

One KiloHertz is equal to 1000 Hz, 1 MHz is equal to 106 Hz and 1 GHz is equal to 10⁹ Hz. In spectroscopy, the frequency is measured as a wave number. The number of waves per unit distance is denoted as wavenumber. In mechanical devices, it is calculated as rotation per minute (rpm).

$$\mathrm{1\:Hertz = 60\:rpm}$$

The frequency is classified into two according to the periodic motion of the particle. They are spatial frequency and angular frequency.

Spatial Frequency

Spatial frequency of the particle is governed by the spatial coordinates. Spatial frequency is the characteristic of any periodic structure. The spatial frequency of the particle inversely depends upon the wavelength of the vibrating particle. Measurement of spatial radiation is done as radian per meter.

Angular Frequency

The particle that undergoes rotational motion is associated with the angular frequency. It is defined by the number of revolutions that are done by the particle at a particular time. The unit for angular frequency is also Hertz. Angular frequency is denoted by $\mathrm{\omega}$. The frequency and the angular frequency are denoted by,

$$\mathrm{f=\frac{\omega}{2\pi}}$$

$\mathrm{\omega}$ denotes the angular frequency of the particle.

Thus the angular frequency is given by,

$$\mathrm{\omega=2\pi f}$$

Formula for Frequency

Depending on the known quantities the formula for calculating frequency is classified as three.

Formula-1

The frequency of the particle is the reciprocal of the period of oscillation of the particle and it is denoted as

$$\mathrm{f=\frac{1}{T}}$$

Here f denotes the frequency of the particle.

Here T denotes the time taken by the particle for a complete cycle.

Formula-2

Frequency is also referred to as the ratio between the velocity and the wavelength of the wave and it is given by,

$$\mathrm{f=\frac{velocity}{wavelength}}$$

$$\mathrm{f=\frac{
u}{\lambda}}$$

Here v denotes the velocity of the wave

Here $\mathrm{\lambda}$ denotes the wavelength of the wave.

Formula-3

Frequency is also calculated by the angular velocity of the particle which undergoes rotational motion and it is given by,

$$\mathrm{f=\frac{\omega}{2\pi}}$$

Solved Examples

1. What is the frequency of the light wave whose wavelength is 400 nm?

Given:

$$\mathrm{Wavelength= \lambda=400 \times 10^{−9}m}$$

$$\mathrm{Velocity\:of\:light\:c=3 \times 10^{8}\: m/s}$$

Frequency of the light wave $\mathrm{= f=\frac{c}{\lambda}}$

$$\mathrm{f=\frac{3 \times 10^{8}}{400 \times 10^{−9}}}$$

$$\mathrm{f=\frac{3}{400}\times 10^{8}\times 10^{9}}$$

$$\mathrm{f=0.75\times 10^{−2}\times 10^{8}\times 10^{9}}$$

$$\mathrm{f=0.75 \times 10^{15}}$$

$$\mathrm{f=7.5 \times 10^{14}\:Hz}$$

Thus the frequency of the light wave is $\mathrm{f=7.5\times\:10^{14}\:Hz}$

2. Calculate the frequency of the pendulum which takes 5 sec to complete one cycle.

Given: Time taken = T =5 sec

The frequency of the pendulum is $\mathrm{f=\frac{1}{T}}$

$$\mathrm{f=\frac{1}{5}}$$

$$\mathrm{f=0.2\:Hz}$$

The frequency of the pendulum is 0.2 Hz.

Conclusion

In this tutorial, the facts about the frequency, unit of frequency and angular frequency are discussed. The formula for frequency and some solved examples are also discussed.

FAQs

Q1. What is frequency modulation?

Ans. There is a change in the frequency of the carrier wave if the instantaneous signal voltage changes. It is known as frequency modulation. So amplitude and phase of the carrier wave are not changing.

Q2. Give the application of FM modulation

Ans. Frequency modulation is applied in radar and EEG monitoring circuits. It is mainly used in FM broadcasting. It is also applied in magnetic tape recording systems. It has a wide range of applications in satellite and microwave communication, cellular radio communication, and TV sound transmission.

Q3. What are the applications of frequency modulation?

Ans. Frequency modulation is used in the study of oscillatory phenomena, vibrating phenomena of the audio waves, radio waves, and light waves. The frequency formula is used to measure the wavelength, frequency, wave speed, period, and some other related formulas.

Q4. What are the differences between amplitude modulation and frequency modulation?

Ans.

Amplitude Modulation	Frequency Modulation
Variation in amplitude following carrier signal	Variation of the frequency following carrier signal
Frequency and phase kept constant	Amplitude and phase kept constant
Poor sound quality	Better sound quality
It is less complex compared to FM	It is more complex.
Bandwidth is less	Bandwidth is large
Power is wasted during transmission	It is highly efficient as all power is utilized.

Q5. How to measure frequency?

Ans. There are two types of instruments used to measure the frequency such as a tachometer and an oscillator. Fullarton tachometer and Frahm tachometer are the types of tachometers used to measure frequency. Quartz oscillators, Rubidium oscillators, and Cesium oscillators are the types of oscillators. In a normal electrical circuit, the frequency is measured by a digital multimeter, power analyzers, and oscilloscope.