# Relation between amplitude and frequency

## Introduction

The aspects of amplitude and frequency are associated with the waveforms. Amplitude is depicted when a wave shows a greater deviation from zero. On the other hand, the total number of waves or oscillations passing through a particular point in a second is termed frequency. Amplitude, as well as frequency, is inversely proportional to each other. That is with the decrease in frequency, the amplitude of the wave increases and vice versa.

## Amplitude and frequency: Definition

Amplitude in the case of sound waves measures the wave height. As opined by He et al. (2021), amplitude of sound wave is the loudness or is depicted as maximum displacement of vibrating particle of any medium from its mean position during sound production. Distance existing between trough or crest is denoted as amplitude of sound waves.

Figure 1: Amplitude of Sound

In terms of a vibrating body, it can be established that amplitude denotes the maximum amount of displacement or distance covered by any object from its equilibrium position. This aspect is half the length of the path of vibration. The amplitude of a wave is noted by the formula

$$x = A \:sin \:(\omega t + \phi)$$

Here, x = displacement of the wave in metres;

A = amplitude of waves; \omega is the angular frequency of the waves, measured in radians,

t = time period, measured in seconds and $\varphi$ is the phase shift, measured in radians.

Frequency on the other hand is defined by the number of occurrences of the wave associated with a repeating event in a particular unit of time. Frequency is mainly of two types, namely angular and spatial frequency.

The frequency of any given object is measured in Hertz and it is symbolized by Hz(openstax, 2022).

Hertz is defined as the repetition of a particular event occurring per second, in such case, the period is associated with the duration of time of a particular cycle in a repeating course of event such that the period is the reciprocal of the frequency and the unit of its measurement is in seconds or s.

## Amplitude and Frequency: relation

The relationship between the amplitude and frequency can be established in such a manner that a particular uniform motion will have an angular velocity that is uniform in nature. To establish the relation further, certain functions are taken into consideration, Function such as the amplitude modulation or AM is capable of having double periods. These period functions are furthermore hidden in other period functions in existence (weebly, 2022).

The inverse of the frequency of a periodic motion gives away the time which is determined in seconds. According to Tao et al. (2019), these periodic motions are further classified into two sub-parts simple harmonic motion and damped harmonic motion.

Time difference between two similar events or occurrences helps in obtaining the frequency of recurring periodic motion.

The frequency of a simple pendulum is dependent on the length of the pendulum and the associated gravitational acceleration, which are vibrations.

Figure 2: Amplitude

## Amplitude and frequency of sound

The highest amount of displacement of vibrating particles of a particular medium from their mean location is characterized by the loudness of the sound wave.

This loudness of the sound is associated with the amplitude of the sound wave (Weebly, 2022).

Therefore, it can be established that it is the distance between the troughs and crests of a particular wave regarding its mean position. The amplitude of sound further enhances the loudness of the sound that is the biggest displacement of sound wave from its equilibrium location.

The frequency of the sound wave is the number of times it repeats itself per second, the fewer the oscillations the lower the frequency of the sound. For example, the frequency of drumbeats is lower than blowing the whistle. The oscillations of the sound wave are more common in higher frequencies. The frequency is measured in Hertz.

According to Peña et al. (2021), the frequency of the sound between 20Hz to 20,000 Hz is audible to the human ear, beyond 20,000Hz the sound is classified as Ultrasound. A short-wavelength produces a higher amount of frequency that comes along with a higher pitch and faster cycles and a short wavelength produces a very high amount of frequency with a higher pitch and faster cycles.

Figure 3: Amplitude and frequency of sound

## Conclusion

The amplitude and frequency are generally associated with waveforms of sound. The frequency aligns with the crest and troughs of the travelling wave in every unit of time that is measured in seconds. The amplitude is associated with the maximum displacement of a wave measured from the position of its equilibrium, simply the number of waves passing through a particular point in a given amount of time; it is the number of the completed wave cycles per given second.

## FAQs

Q1. Which wave functions determines the loudness and pitch of the sound?

The amplitude is associated with the loudness of the sound both these aspects are directly related to one another. That is, louder sounds are associated with higher amplitude and the pitch of the sound is directly proportional to its frequency. That is higher pitch means a higher frequency of sound.

Q2. What are the amplitude and frequency of the sound waves?

The number of oscillations per second defines the frequency. It is measured in Hertz and the amplitude is defined b the maximum height attained by the troughs and crests of the sound wave.

Q3. What are sound waves?

The sound wave is fiend by the sequence of disturbance that is generated by the flow of energy as it travels away from the source of the sound across various forms of medium. A source of a sound wave is an object that produces vibration.

Q4. Do amplitude and frequency are dependent on each other?

No, the aspect of amplitude and frequency are independent of one another. The first depends on the total amount of energy existing in a particular system and the frequency depends on the oscillator’s properties. The amplitude of a source can be altered but the frequency can't be changed.

## References

### Journals

He, J. H., Hou, W. F., Qie, N., Gepreel, K. A., Shirazi, A. H., & Mohammad-Sedighi, H. (2021). Hamiltonian-based frequency-amplitude formulation for nonlinear oscillators.Facta Universitatis, Series: Mechanical Engineering,19(2), 199-208. Retrived from: http://casopisi.junis.ni.ac.rs

Peña, E., Pelot, N. A., & Grill, W. M. (2021). Non-monotonic kilohertz frequency neural block thresholds arise from amplitude-and frequency-dependent charge imbalance.Scientific reports,11(1), 1-17. Retrieved from: https://www.nature.com/articles/s41598-021-84503-3

Tao, Z. L., Chen, G. H., & Xian Bai, K. (2019). Approximate frequency–amplitude relationship for a singular oscillator.Journal of Low Frequency Noise, Vibration and Active Control,38(3-4), 1036-1040.Retrieved from: https://journals.sagepub.com/doi/full/10.1177/1461348419828880

### Websites

Openstax (2022). About 13.2 Wave Properties: Speed, Amplitude, Frequency, and Period. Retrieved from:https://openstax.org/books/physics/pages/13-2-wave-properties-speed-amplitude-frequency-and-period [Retrieved on: June 11, 2022]