Relation Between Amplitude and Frequency

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Relationship Between Amplitude and Frequency

Let’s suppose that you are climbing high mountains and your friend is observing you and climbing the small mountains. Here, your friend took time and could not complete the climbing task, while you were able to complete your journey, as the height was less, so is enough energy you had to accomplish the task. 

Here, you both had to cover the same distance; however, the amplitude of your friend was high, but the frequency was low, while in your case, it was just the reverse. 

So, there is an inverse relationship between amplitude and frequency.

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Amplitude and Frequency 

Do you know what amplitude is?

Well! Amplitude is something similar to the height of a string is hurled while skipping. Whenever the height is greater, we can say that is the amplitude of that instant hurl. 

Similarly, when you and your partner keep on hurling the string, the more number of complete waves, i.e., a crest and a trough is made, the higher is the frequency.

Definition of amplitude: We define the amplitude of a periodic variable as a measure of its change/variation in a given period such as time or spatial period of time. There is another definition and that is the phase of a periodic function.

Definition of frequency: We define frequency as the number of occurrences of a repeating event in a unit of time. We often refer to frequency as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. 

We measure the frequency in Hertz, which is symbolized as Hz. Hertz is defined as one occurrence of a repeating event per second, where the period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency and its unit is seconds or s.


Importance of Frequency 

For example, if a newborn baby girl's heart beats at a frequency of 180 times a minute (3 hertz), its period, T, i.e., the time interval between beats, i.e., is one-third a second (60 seconds divided by 180 beats). 

We consider frequency as a significant parameter/function of time that is used in science and engineering to specify/understand the rate of oscillatory and vibratory phenomena such as mechanical vibrations, audio signals or a sound, radio waves, and light, etc.


Difference Between Amplitude and Frequency 

Amplitude

Amplitude is also a very important concept in a periodic motion. To understand this we need to have a crystal clear understanding of harmonic motions. 

A simple harmonic motion or SHM is a motion that describes the relationship between the displacement and the velocity in the form of a = -2x, where “” is the angular velocity and “x” is the displacement. 

Acceleration and displacement are nonparallel, which means that the net force on the object is also in the direction of the acceleration. This relationship describes a motion where the object oscillates about a central point. We know that when the displacement is zero the net force on the object is also zero, and this is the equilibrium point of the oscillation. 

We also know that the maximum displacement of the object from its equilibrium point is known as the amplitude of the oscillation. The amplitude of a simple harmonic oscillation entirely relies on the total mechanical energy of the system. 

For a spring-mass system, the total internal energy is E, the amplitude is equal to 2E/k, where k is the spring constant/force constant of the spring. At this amplitude, the instantaneous velocity is zero; whereby, the kinetic energy is also zero, which means the total energy of the system is in the form of potential energy.; however, at the equilibrium point, the potential energy becomes zero.


Frequency

Frequency is a concept that is discussed in the periodic motions of objects. 

To understand the logic behind the term frequency, a proper understanding of periodic motions is required. 

A periodic motion is a motion that repeats itself in a fixed period of time. 

For example, a planet orbiting around the sun is a periodic motion. 

A satellite revolving around the earth is a periodic motion.

The movement or the motion of a balanced football set is a periodic motion. 

We must note that most of the periodic motions that we encounter are circular, linear or semi-circular. 

A periodic motion has a frequency. The frequency means how “frequent” the event is or how often an event occurs. 

For our understanding, we take frequency as the events per second; however, periodic motions can either be uniform or non-uniform. 


Amplitude and Frequency Relation

In the above context, we understood the amplitude and frequency relationship.

A uniform motion can have a uniform angular velocity. Functions such as amplitude modulation or AM can have double periods; they are periodic functions encapsulated/hidden in other periodic functions. 

The inverse of the frequency of the periodic motion gives time for a period of seconds. 

Simple harmonic motions and damped harmonic motions; are also considered periodic motions. Since the frequency of a periodic motion can also be obtained using the time difference between two similar occurrences/events. The frequency of a simple pendulum only depends on the length of the pendulum and the gravitational acceleration for small oscillations (vibrations).


FAQ (Frequently Asked Questions)

1. Does amplitude depend on frequency?

No.


Amplitude depends on the total energy of the system, whereas the frequency of an oscillation depends on the properties of the oscillator itself. For a given system, the amplitude can be changed but we cannot change the frequency.


For example, if you are going up the tall building through big stairs, and your friend through the small stairs, though the room number is the same; however,  if you have the energy you can reach that room, maybe your friend cannot but to reach that room, you both will have to climb the same number of stairs.

2. What does an amplitude specify?

An amplitude refers to maximum displacement from the equilibrium that an object in periodic motion shows.


For example, a pendulum swings through its equilibrium point and then swing to a maximum distance away from that equilibrium point. Therefore, the distance of the far distance from the centre is A.

3. How is amplitude measured in a longitudinal wave?

For a longitudinal wave, such as a sound wave, we measure the amplitude in terms of the maximum displacement of a particle from its position/point of equilibrium or mean position. The amplitude of a wave steadily pr slowly reduces when it loses its energy or say, it becomes damped.