

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 it was enough energy that 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.
Amplitude and Frequency
Do you know what amplitude is? Well! Amplitude is something similar to the height of a string that 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 complete waves, i.e., a crest and a trough are made, the higher is the frequency. Definition of amplitude: We define the amplitude of a periodic variable is a measure of its change/variation in a given period such as time or spatial period. 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 between 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.
Amplitude Formula
The following formula is used to compute amplitude:
x = A sin(ωt+ϕ)
Where,
x = displacement of the wave, in metres.
A = amplitude of the wave, in metres.
ω = angular frequency of the wave, in radians.
t = time, in seconds.
ϕ = phase shift, in radians.
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 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; hence, 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. For example,
A planet orbiting around the sun is in 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 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).
Amplitude of Sound
We can hear sound because it is a kind of energy. When you ring a bell, it makes a sound. The vibrations may be felt if you touch the bell. The bell is ringing, as you can see. The bell's to-and-fro motion is referred to as vibration. A sound wave's amplitude is a measure of the wave's height. The largest displacement of vibrating particles of the medium from their mean location at the moment the sound is emitted may be characterized as the loudness of a sound wave. It is the distance between the crest or trough of a wave and its mean position. The loudness of a sound is related to its amplitude. The amplitude of a sound wave enhances the loudness of the sound. If the amplitude is little, the sound will be weak. The greatest displacement of a sound wave from its equilibrium location is defined as its amplitude. It's also known as the loudness of a sound after it's been created.
The sine wave is given by the equation:
y = A sin ω t
Where,
A = amplitude of the wave,
ω = angular frequency of the wave,
t = period of one oscillation.
Depending on how the wave oscillates, the amplitude will fluctuate. A sound wave's amplitude and loudness are proportional. The sound will be louder if the amplitude is greater. The sound generated will be smaller if the amplitude is little.
Frequency of Sound
A sound pressure wave's frequency is the number of times it repeats itself per second. The frequency of a drumbeat is significantly lower than that of a whistle, while the frequency of a bullfrog cry is much lower than that of a cricket. The fewer the oscillations, the lower the frequency. Oscillations are more common at higher frequencies. The frequency units are called hertz (Hz). Sounds between 20 Hz and 20,000 Hz can be heard by those with normal hearing. Ultrasound is defined as frequencies greater than 20,000 Hz.
Effect of frequency and amplitude on sound
A short-wavelength produces a high frequency with a higher pitch and quicker cycles.
A short-wavelength produces a high frequency with a higher pitch and quicker cycles.
Does Amplitude affect Frequency?
The relationship between the wave's amplitude and frequency is such that it is inversely proportional to the frequency. The amplitude decreases as the frequency increases. The amplitude increases as the frequency decreases.
FAQs on Relation Between Amplitude and Frequency
1. What is the fundamental relationship between amplitude and frequency in a simple wave?
For a simple wave or oscillation, amplitude and frequency are fundamentally independent properties. This means changing the amplitude does not change the frequency, and vice versa. Amplitude is determined by the initial energy given to the system, while frequency is an intrinsic property determined by the physical characteristics of the system (like the mass and spring constant for a spring, or the length of a pendulum).
2. How are amplitude and frequency defined in physics?
In the context of waves and oscillations, the definitions are as follows:
- Amplitude (A): It is the maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position. It relates to the wave's intensity or energy.
- Frequency (f): It is the number of complete oscillations or cycles that occur in a unit of time. It is measured in Hertz (Hz), where 1 Hz is one cycle per second. Frequency determines the pitch of a sound or the colour of light.
3. In a sound wave, what do amplitude and frequency represent in the real world?
In sound waves, these two properties correspond to distinct perceptual qualities:
- Amplitude determines the loudness of the sound. A sound wave with a larger amplitude carries more energy and is perceived as louder. A smaller amplitude results in a quieter sound.
- Frequency determines the pitch of the sound. A high-frequency sound wave results in a high-pitched sound (like a whistle), while a low-frequency wave produces a low-pitched sound (like a bass drum).
4. Why are amplitude and frequency considered independent in simple harmonic motion (SHM)?
In simple harmonic motion (SHM), the frequency of oscillation depends only on the system's inherent properties, such as mass (m) and the spring constant (k). The formula for angular frequency is ω = √(k/m). Notice that amplitude (A) is not a variable in this equation. The amplitude is determined by the initial conditions—how far you initially stretch or compress the spring. Therefore, you can start the oscillation with a large or small amplitude, but the frequency at which the system oscillates will remain the same.
5. How does the total energy of an oscillating system relate to its amplitude?
The total energy of an oscillating system is directly proportional to the square of its amplitude (E ∝ A²). This is a crucial relationship. It means if you double the amplitude of an oscillation, you quadruple its total energy. The energy does not depend on the frequency in this direct way for a mechanical oscillator. This explains why a wave with a larger amplitude is more intense and can do more work.
6. What is the difference between frequency, period, and amplitude?
These are three distinct parameters of a wave:
- Amplitude is a measure of displacement (how far the medium moves from equilibrium).
- Frequency is a measure of time (how often a cycle repeats per second).
- Period (T) is also a measure of time (how long it takes for one full cycle). Frequency and period are reciprocals of each other (f = 1/T).
7. Is there a formula to convert amplitude directly to frequency?
No, there is no formula to convert amplitude to frequency because they measure different, independent physical quantities. Amplitude measures maximum displacement (a unit of distance, like metres), while frequency measures cycles per unit time (a unit of inverse time, Hz). Attempting to convert one to the other would be like trying to convert kilograms to seconds; they represent fundamentally different aspects of a physical system.

















