After reading this article you will learn about: 1. Meaning of Sound Wave 2. Amplitude and Intensity of Sound 3. The Decibel Scale of Sound.
Meaning of Sound Wave:
A sound wave, is a one-dimensional pressure wave that is propagated through a medium, usually air. When the wave enters the ear, it causes the eardrum to vibrate. This in turn causes the three tiny bones in the inner ear—incus, malleus and stapes—to vibrate. This vibration is passed on to the brain, which, in turn, hears these vibrations as sound.
The ear is a very sensitive and flexible device and the frequency range that it can hear is 20 Hz to 20,000 Hz. The amplitude—or intensity—of the sound range that it can hear is logarithmically expressed because of this huge range.
The limits of this audibility varies from the sound of a mosquito buzzing at a distance of three metres as the lower limit to the sound of a train horn at a distance of one metre (which can puncture the ear drum) or the sound of a civil defence siren at a distance of thirty metres (which may be called the threshold of pain).
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The amplitude (or intensity) of sound is usually expressed as a ratio in decibels. For these ratios, the lower limit of audible sound is assumed to be that of a mosquito buzzing at a distance of three metres (about 10 feet) and is assumed to be equal to 0 decibel.
However, in order to understand the decibel notation, one has to understand the concept of the terms amplitude and intensity in sound waves.
Amplitude and Intensity of Sound:
The equilibrium value of pressure represented by the evenly spaced lines in the figure marked A in Fig. 11.1, is equal to the atmospheric pressure that would prevail in the absence of the sound wave. With passage of the compressions that constitute the sound wave, there would occur fluctuations above and below atmospheric pressure.
The lines show these in part A of Fig. 11.1. The magnitude of this fluctuation from equilibrium is known as the amplitude of the sound wave and is measured in pascals or newton’s/square metre. The wave shape can be seen in part C of Fig. 11.1.
The amplitude of the sound wave given by C in Fig. 11.1 above is expressed in pascals or newton’s per square metre is described by the letter A in the Fig. 11.1 and the wavelength is given by the term A in the Fig. 11.1. Mathematically, the above wave can be described by the equation
The above equation implies that the size of the disturbance y at time t, x distance away from the source of the sound, is equal to the amplitude A times the sine of 2r times a quantity equal to the frequency times the elapsed time (that is ft.) minus the distance from the origin (x) divided by the wavelength (A).
The amplitude of the sine wave specifies the intensity of the sine wave and is perceived by the ear as loudness. The acoustic intensity is defined as the average rate at which energy is transmitted per unit area perpendicular to the direction of wave propagation. The relationship between acoustic intensity I and the amplitude A is given by the equation
where p is the equilibrium density of the air (measured in kilograms per cubic metre) and 5 is the speed of sound (in metres per second).
The intensity I is measured in watts per metre squared. The value of atmospheric pressure under standard atmospheric conditions is assumed to be 105 pascals or 105 newton’s per metre squared. The minimum amplitude of pressure variation that can be sensed by the human ear is about 10-5 pascals.
The pressure amplitude at the threshold of pain is about 10 pascals, so the pressure variation in sound waves is not very large compared with the pressure of the atmosphere. Under these conditions sound waves propagate linearly, that is, they continue to propagate through the air without any (or very little) loss.
Therefore, there is very little dispersion or change of shape. However, when the amplitude of the wave reaches about 100 pascals (approximately 1/1000 the pressure of the atmosphere) definite nonlinearities develop in the propagation of the wave. The reason for this non- linearity apparently is the sinusoidal displacements of air molecules and their effect on the air pressure.
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When the vibratory motion that constitutes the wave is small, the increase and decrease of air pressure are also small and are in fact nearly equal. But when the motion of the wave is large, each compression generates an excess pressure of greater amplitude than the decrease in pressure caused by the reverse.
This can be predicted by the ideal gas law according to which “increasing the volume of a gas by one half decreases the pressure by only one-third, while decreasing its volume by one half increases the pressure by a factor of two”. This results in a net excess in pressure. This phenomenon is significant only for waves with amplitudes in excess of about 100 pascals.
The Decibel Scale of Sound:
The decibel scale (expressed as dB) is a measure of the ratio between two quantities and is used in a wide variety of measurements in acoustics as well as in physics and electronics. It was conceived by engineers of the Bell Telephone Laboratory to express the reduction in the audio level over a 1-mile length of telephone cable and was originally called a transmission unit or TU.
But it was later renamed in 1923 in honour of the telecommunications pioneer Alexander Graham Bell as ‘bel’ (B). The bel, however, was too large for everyday use so the decibel (dB) equal to 0.1 bel became more commonly used, while the bel is still used to represent noise power levels in hard drive specifications.
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These, however, are logarithmic scales. A decibel is defined in two common ways and, as we shall see shortly, these two definitions do cause considerable confusion. When referring to measurements of power XDB is given by
But when referring to measurements of voltage it is
where X0 is a specified reference against which the specified value of X is to be compared. Which of the two above is used depends upon the context (and convention), but it is obvious that it will cause confusion. An intensity or power can be expressed in decibels by the standard equation
where IO and P0 are levels of intensity and power that have been specified earlier. Thus, if lob is greater than I0DB by 10 Db then the former is 10 times greater than the latter.