Amplitude Frequency Period Sound

What Is Amplitude?

You may have observed the waves of sound traveling in air, and waves of ripples in water. If you touch the tip of your pencil or pen to the still water of a container, you will notice that the water surface gets disturbed and produces ripples or waves.

Electromagnetic waves like light waves, microwaves, radio waves and x-ray do not require any medium for their propagation. These waves cannot be seen or heard, but these waves exist in nature and are used in many ways, in day-to-day life.

Every type of wave has some amplitude. Amplitude is the maximum displacement of the wave about its mean position. It is the degree or intensity of change in wave position. This maximum displacement or amplitude of a wave is measured in terms of the mean position or equilibrium position of the wave.

The diagram below represents the amplitude and wavelength of a wave. Wavelength is the distance between two consecutive crests or two consecutive troughs of a wave. The uppermost or highest position of a wave is called a crest, and the lowermost position of a wave is called a trough. Wavelength is also defined as the time required completing one full cycle of the wave.

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What Is Amplitude Formula?

The formula to calculate amplitude is mentioned below:

x = A sin(ωt+ϕ)


●        x = displacement of wave, in metres.

●        A = amplitude of wave, in metres.

●        ω = angular frequency of wave, in radians.

●        t = time, in seconds.

●        ϕ = phase shift, in radians.

Amplitude And Frequency

Frequency is defined as the number of wave cycles which passes a point per second. It is the number of oscillations that occurs in a wave per second. Frequency is inversely proportional to wavelength. So, the higher the frequency, lower will be the wavelength and vice versa.

Wavelength and frequency are related to each other, but amplitude and frequency are completely independent features of a wave. Both amplitude and frequency can be changed, but a change in one parameter doesn't affect the other. A change in frequency doesn't change the amplitude of the wave, and a change in amplitude doesn't change the frequency of the wave. 

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The amplitude of a wave cannot be determined by knowing the value of frequency of the wave. Also, the frequency of a wave cannot be determined by knowing the amplitude of the wave.

Amplitude And Frequency Of A Ferris Wheel

The oscillatory motion (height of a passenger in this case) in a Ferris wheel, relative to the center of Ferris wheel, given by the function:

F(t) = Asin(ωt+ϕ) + B,

The time period of this cycle is: 2/

The phase shift of this cycle is given by:


A = amplitude

B = vertical shift

Amplitude of Sound

Sound is a form of energy by which we can hear. If you strike a bell, it produces sound. You can feel the vibration of the bell, if you touch it. You can notice that the bell is shaking. This to and fro motion of the bell is called vibration.

The amplitude of a wave, (like that of a sound wave) is the measure of the displacement from the mean position. The amplitude of a sound wave is defined as the maximum displacement of the wave from the equilibrium position. It is also defined as the loudness of sound after it is produced.

Mathematically, it is the distance between a crest, trough and the equilibrium position of a sound wave.

The sine wave is given by the equation:

y = A sin ω t


 A = amplitude of the wave,

ω = angular frequency of the wave,

t = time period of one oscillation.

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The amplitude of the wave will change depending upon its oscillation. The loudness of a sound wave varies directly in relation to its amplitude. Higher is the amplitude, higher will be the sound. If the amplitude is low, the sound produced will also be less.

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Time Period In Sound

An event is said to be periodic if it occurs repeatedly. The time taken by a sound wave to complete one cycle is called its time period. The time period is inversely proportional to frequency, and is given by:

Period = 1/Frequency 

Frequency In Sound

The number of oscillations made by the sound wave per second is called its frequency. The SI unit of frequency is Hertz, and is denoted by Hz. Frequency describes how many times a particle vibrates when the wave travels through a medium.

Frequency = 1/Period

FAQ (Frequently Asked Questions)

1. Do Sound Waves Differ Only In Frequency (And Amplitude)?

Sound waves are described by their frequency and amplitude. The pure tone of a sound wave is a sine wave. You should note that the sound produced by a musical instrument is not a pure tone. A sound wave is usually described by its phase. If two sound waves traveling in the same direction, and having the same frequency and phase coincide with each other, they produce a new sound wave of higher amplitude. If two sound waves having a phase difference of 180° coincide, they cancel out.

Let us consider a long hollow tube (like that of a musical instrument) in which sound waves are formed. The wavelength of sound formed in this tube is the submultiples and multiples of the length of the tube.

2. What Is The Difference Between Amplitude And Frequency?

The major differences between amplitude and frequency of sound are mentioned below:

● Amplitude is the maximum displacement of the particles of a sound wave. Frequency is the number of vibrations made by a sound wave per second.

● Amplitude describes the size of sound waves. Frequency describes the number of waves per second.

● Amplitude is measured in metre Frequency is measured in Hertz.

● Amplitude measures the loudness of sound. Frequency measures the shrillness of sound.

● Higher the amplitude louder will be the sound. Higher the frequency, shriller will be the sound.

3. How Do Frequency, Amplitude, And Wavelengths Affect Sound?

●   Short wavelength gives rise to high frequency with higher pitch, and faster cycles.

●   Long wavelength gives rise to low frequency with lower pitch and slower cycles.

Amplitude determines the volume of a sound wave. It is not related with frequency. Thus, it is possible to have a loud sound wave of low frequency, or a quiet sound wave of high frequency.

4. What Are The Characteristics of Sound Waves?

  • Unlike light waves, sound waves cannot travel through vacuum. 

  • Sound waves are longitudinal waves, whereas light waves are transverse waves.