[Physics Class Notes] on Relation Between Amplitude and Frequency Pdf for Exam

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 amplitu
de. 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

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.