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| Intensity and Loudness of Sound |
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| Physically, a wave involves the propagation of energy. This transfer of energy by a
traveling wave is expressed in terms of the intensity I. Intensity of sound waves is defined as the average energy transported per second per unit area perpendicular to the direction of propagation. It is measured in Js-1m-2 or Wm-2. |
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As seen from equation (1-14), the intensity of sound in air depends on the square of the frequency and the square of the amplitude. Thus, for a given frequency, the amplitude is an important factor in deciding the intensity. If P is the acoustic power of a point source and there are no intervening losses, then at a distance of r
meters from the source
energy passes through the surface area  of a sphere of radius r around the source. Then, intensity at a distance r is  For
a given source, P is a constant. |
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i.e., the intensity of sound varies inversely as the square of the distance from the source and the point where its effect is considered. Intensity of sound involves purely objective considerations with respect to the source of sound and is independent of the observer. In other words, intensity will have to be measured using instruments. |
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| For a person with normal hearing, the minimum intensity of sound (at a frequency of 1000 Hz) that can cause the sensation of hearing is 10-12Wm-2. The amplitude of the sound waves at this threshold has been estimated to be about 1 x 10-10m. This is about the diameter of a hydrogen atom and gives some idea of the enormous sensitivity of the human ear. When sound becomes so intense that it is painful to the ear, the amplitude is of the order of 1-2mm. |
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| The loudness of sound is defined as the degree of sensation of sound produced in the ear. The loudness of sound depends on its intensity but the relationship is not linear. It obeys an approximate law of psychology which states that - the magnitude of any sensation is proportional to the logarithm of the physical stimulus which produces it. This is called the Weber-Fechner law. It does not exactly represent the relationship between loudness and intensity but is a fair approximation for pure tones at most frequencies. For complex tones, however, there is no simple relationship. Thus, according to this law, |
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| l = K log I ----------- (1-32) |
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| Where l is the loudness, I is the intensity and K is a constant of proportionality. As already mentioned, the minimum intensity of sound required to produce aural sensation is 10-12Wm-2. Let this be denoted by I0. Let the loudness corresponding to this threshold of audibility be l0. Then equation (1-32) can be written as |
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| l0 = K log I0 ---------- (1-33) |
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| Subtracting equation (1-33) from equation (1-32), we get |
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| l - l0= K log I - K log I0 |
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| = K (log I - log I0) |
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| (l - l0) indicates as to how much the loudness of a given sound is above the minimum value for hearing. Therefore, it is called the intensity level L. |
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| If the value of the constant K is chosen to be 1, then L is measured in a unit called bel (in
honor of Alexander Graham Bell). |
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| Hence, the intensity level of a sound is said to be 1 bel, if its intensity is ten times the threshold intensity. |
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If the value of the constant K is chosen to be 10, then L is measured  |
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| If I = 10I0, then L = 10 dB. Hence, the intensity level of a sound is said to be 10 dB, if its intensity is ten times the threshold intensity. |
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| Hence, the intensity level of a sound is said to be 1dB, if its intensity is 1.26 times the threshold intensity. |
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| Thus, a change in intensity by 26% corresponds to a change in the intensity level by 1dB. |
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| The following table gives the relation between the intensity ratio and the intensity level in decibels. |
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| In the above table, each number in the left column is higher than its previous number by about 26%. |
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