Waveform Characteristics

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Contents

Introduction

A wave is a disturbance that moves or propagates in a medium, or even in a vacuum. Despite the diverse nature of the disturbances that might ensue, all waves have a similar behaviour. Sound is a kind of wave that propagates only in the presence of a support means capable of disturbance. The general concepts of waves used to describe sound, but conversely, sound phenomena can better understood by some of the characteristics of wave behaviour.

Characteristics

The ear is able to distinguish one sound from another because it is sensitive to the differences that may exist between them as regards any of the three qualities that characterize all sound, which are amplitude, frequency, and wave form. Even if all of which refer to sound physiological they are related to different properties of the sound waves.

  • The waveform is the feature that allows us to distinguish a note of the same frequency and intensity produced by different instruments. The waveform is determined by the harmonics.
  • Mathematically, the most basic wave is the sine wave (or harmonic wave or sinusoid), with an amplitude described by the equation:


Sinusoidal waves equation.png

Where A = the amplitude of the wave, x = is the space coordinate, t = is the time coordinate, k = is the wavenumber(spatial frequency), ω = is the temporal frequency and φ = is a phase offset


  • Normally, by vibrating a body, you do not get a pure sound, but a sound composed of different frequencies. These are called harmonics. The frequency of the harmonics is always a multiple of the lowest frequency called the fundamental frequency or first harmonic. As the frequencies get higher, the vibrating segments become shorter and the musical tones closer to each other.
  • These harmonics contribute to the auditory perception of sound quality or timbre.

Amplitude

The maximum distance of any particle from its undisturbed position is called the amplitude (A). Amplitude is the degree of movement of air molecules in a wave. This corresponds in musical terms to what we call the intensity. The larger the amplitude of the wave, the harder the molecules collide in the eardrum and the louder the sound is perceived. The amplitude at which a sound is perceived by a person is called the edge of hearing. When the amplitude increases, there comes a time that causes discomfort in the eardrum. This is called the threshold of pain .

Amplitud3.gif

Frequency

Vibration and standing waves in a string, The fundamental and the first 6 overtones

Frequency is the number of oscillations of a wave that takes place at a certain time interval. The number of cycles per second called hertz (Hz) is the unit which measures the frequency. From a musical standpoint, the frequency is related to the height or pitch of the corresponding musical note. The greater the frequency the higher the pitch of a musical note & the sharper the sound. The frequency of a soundwave is the same as that of the vibrating source producing it.

Humans are sensitive to frequencies ranging from 20 Hz to 20,000 Hz. Frequencies below 20 Hz are called infrasound and above, ultrasound. The hearing range of people varies with age and other factors.

If the same note is played on two different musical instruments, it sounds different. The notes are said to have a different quality. An instrument emits a note of a given frequency. It also emits notes which have frequencies that are multiples of that frequency. These higher multiples are called overtones. Different instruments emit different numbers of overtones and overtones of different strengths. It is because of this that the same note played on different instruments sounds different. A tuning fork or a signal generator can emit a note of a pure frequency, i.e. with no overtones present.

A string vibrating with an antinode at its centre and a node at each end (and no other nodes or antinodes) is vibrating at its fundamental frequency.

Wavelength

The frequency, together with the sound propagation speed (v) is related to the wavelength (l), which is the space that a wave travels from the beginning to the end of a full swing. The wavelength increases if the wave speeds up and the wavelength decreases if the waves slow down. Wavelength is measured in metres.

The wavelength is obtained from the formula: space = speed · time. When we speak of a harmonic vibration, wavelength = speed transmission · Period, i.e.

The equation relating v, l, and f is: v = L ° F

Wavelength.jpg

Sound has a speed of 331.5 m / s at a temperature of 0 ° C. Atmospheric pressure is 1 atm (sea level) and presents a relative humidity of 0% (air dry), although it depends very little air pressure.

The speed of sound depends on the type of material. Sound travels faster in solids than in liquids, and in liquids than in gases. This is because the solid particles are closer.

Period

The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. The quantity frequency is often confused with the quantity period. Frequency refers to how often something happens while the period refers to the time it takes something to happen. Period is measured in units of time such as cycles/second.

As Frequency (f) is the number of oscillations per unit time. By definition, the period is the inverse of the frequency:

T = 1 / f

Phase

When waves arrive crest with crest and trough with trough, they are said to be in phase with each other. Phase can also be an expression of relative displacement between or among waves having the same frequency. A complete cycle is defined as 360 degrees of phase as shown in the Illustration:


Phase.gif

  • When the crest of a wave is superimposed on the crest of another, the individual effects join and create a wave with a higher intensity. This phenomenon is called constructive interference, or reinforcement, where the waves are said to be in phase (fig a).
  • When the crest of a wave overlaps with the valley of another, the individual effects are reduced. The upper part of a wave simply fills the lower part of the other. This is called destructive interference, or cancellation, where we say that the waves are out of phase. As a result the sound is louder in some places and softer in others(fig b).

video(a) Constructive.png video(b)

References

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