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10.2 The relationship between loudness and intensity

The loudness of an auditory stimulus is a psychological, not physical attribute of the stimulus. The physical attribute of sound that is most closely correlated with loudness is intensity. So loudness is the listener's subjective description of the intensity of the stimulus. As you know, we are not equally sensitive to sounds of all frequencies so perceived loudness of a tone in fact depends on frequency as well as intensity. Two sounds can have the same physical sound pressure levels but if they are of different frequencies, they are often perceived as having different loudness.

How do we measure loudness? To do so, we have to relate a subjective quality such as loudness to a physical quantity such as sound pressure level. One way of doing this is to generate a plot of equal loudness contours. A 1000 Hz tone is set to some specific intensity and then the sound levels of other tones of different frequency that are equal in loudness to the 1000 Hz tone, are determined. For example, a subject may be presented with a 1000 Hz standard tone at 60 dB SPL and then asked to manipulate the intensity of a 2000 Hz tone until it matches the loudness of the 1000 Hz tone. The same 1000 Hz tone would then be compared with a 3000 Hz tone and the intensity manipulated till it matched the 1000 Hz tone in loudness. In this way, the intensity of tones at a variety of frequencies could be obtained so that all tones matched the loudness of the 60 dB SPL, 1000 Hz tone. These intensities are then plotted as a function of frequency to generate equal loudness contours as shown in Figure 35. The term that is used to describe or measure the loudness of a signal is known as a phon. The loudness in phons is the level in dB SPL of an equally loud 1000 Hz tone. So all tones judged equal in loudness to a 40 dB SPL, 1000 Hz tone have a loudness of 40 phons. The tones presented at levels such that they are equal in loudness to a 70 dB SPL, 1000 Hz tone all have loudness levels of 70 phons, and so on. The equal loudness contours in Figure 35 form the phon scale. Look at the contour labelled 30 in Figure 35. Any sound whose frequency and intensity lie on the contour sounds just as loud as any other sound on the contour, although the frequency and intensity of the two sounds will differ. So for example, a 60 Hz tone at a 65 dB intensity level and a 330 Hz tone at a 40 dB intensity level both sound as loud as a 1000 Hz tone at a 30 dB intensity level and all have a loudness level of 30 phons.

Figure 35
Figure 35 Equal loudness contours. The bottom curve, 0 phons, shows the absolute sensitivity of the ear as a function of frequency. All tones lying on the same loudness contour sound equally loud, although their intensities (and frequencies) may differ, and are assigned the same value of phons


What do you notice about the contours as loudness level increases from 0 to 120phons?


The contours change in shape and become much flatter.

What this indicates is that at high intensity levels, the frequency of a sound becomes less important in the perception of loudness. Look at the 120 phon contour. In order to sound equally loud, a 60 Hz tone, a 300 Hz tone and a 1000 Hz tone need to differ by a maximum of 5 dB in intensity (125 dB SPL, 123 dB SPL and 120 dB SPL respectively). This contrasts with the 30 phon contour where, in order to sound equally loud, the three tones differ by as much as 35 dB. This in effect means that we are relatively more sensitive to low-frequency tones than to high-frequency tones at high loudness levels. Below about 70 phons, low-frequency tones require a higher intensity to achieve comparable loudness with higher-frequency tones. This is especially true for sounds with frequencies below about 1000 Hz.

Because of the relationship between intensity and loudness, complex sounds that are identical in frequency may sound different because of variations in loudness. You may have experienced this if you listen to voices heard from a loudspeaker at full volume. Because we are more sensitive to low-frequency sounds at high loudness levels, they will seem to have much greater low-frequency components, giving them a ‘boomy’ sound. Similarly, musical recordings made at high volume and then played softly often seem to be lacking in the bass range. This is because at low intensity levels we are relatively less sensitive to low-frequency tones and so the music sounds ‘tinny’. Many stereos compensate for this effect by having a ‘loudness’ switch that adds extra bass at low volume levels.