Curves of Equal Loudness

Physics Department, Yarmouk University, Irbid Jordan

Phys. 645 Environmental Physics Dr. Nidal M. Ershaidat Doc. 4

CURVES OF EQUAL LOUDNESS

A) Definition

Human perception of sound is represented by the so-called “curves of equal loudness”. These are based on the work of Fletcher and Munson at Bell labs in the 30s, or perhaps refinements made more recently by Robinson and Dadson. The values of the curves are averages over a large number of humans. Reactions of the subjects to different sounds are registered and averages are made. Actually these curves are contours. The horizontal axis represents the frequency. On the vertical axis are represented the sound pressure level (SpL) in dB. Sometimes the sound intensity level is used instead of the SpL. (We know that Lp = LI + 0.14).

Figure 1: Curves of Equal Loudness.

B) Loudness scale: Phons

Two different 60 decibel sounds will not in general have the same loudness. Saying that two sounds have equal intensity is not the same thing as saying that they have equal loudness. Since the human hearing sensitivity varies with frequency, it is useful to plot equal loudness curves which show that variation for the average human ear. If 1000 Hz is chosen as a standard frequency, then each equal loudness curve can be referenced to the decibel level at 1000 Hz. This is the basis for the measurement of loudness in phons. 0 phons at 1,000 Hz is set at 0 decibels, the threshold of hearing. The hearing threshold of 0 phons then lies along the lowest equal loudness contour. If the intensity level at 1,000 Hz is raised to 20 dB, the second curve is followed. It is important to realize that the phon is used only to describe sounds that are equally loud. It cannot be used to measure relationships between sounds of differing loudness. For instance, 40 phons is not twice as loud as 20 phons. The loudness of complex sounds can be measured by comparison to 1000Hz test tones, and this type of measurement is useful for research, but for practical sound level measurement, the use of filter contours has been commonly adopted to approximate the variations of the human ear.

C) Reading curves of equal loudness

Figure 2: Information from the curves of Equal Loudness.

To find the phon value of an intensity measurement, find the db reading and frequency on the graph, then see which curve it lands on. Mainly, these curves show that it is difficult to hear low frequency of soft sounds, and that the ear is extra sensitive between 1 and 6 kilohertz.

Figure 3: Three example curves from the equal loudness curves are shown below, corresponding to very soft, midrange and very loud sounds. Examination of these three curves makes it evident that there is considerable difference between the ear's response at different sound levels. The response to very loud sounds is much "flatter" or more uniform than the response to very soft sounds, although it still shows the prominent enhancement of sensitivity between about 2000-5000Hz associated with the ear canal resonance. Where the curve dips between 2000-5000Hz, this implies that less sound intensity is necessary for the ear to perceive the same loudness as a 120dB, 1000Hz tone. In contrast, the strong rise in the curve for 0 phons at low frequencies shows that the ear has a notable discrimination against low frequencies for very soft sounds. Since the vertical axis is in decibels, the flat horizontal line at 65dB represents an equal intensity at all frequencies. The example sounds A, B, C and D all have the same sound

intensity of 65dB. However, this does not imply that they have the same loudness to the human ear. We can say that sounds A and D have the same loudness since both are on the same equal loudness curve. This curve passes through 60dB at 1000Hz, so we characterize all sounds on that equal loudness curve, including sounds A and D, as having a loudness of 60 phons. Sound B is above the 60 phon curve, so that implies that it would be perceived as louder than A or D. In fact, since sound B is at 1000Hz and has an intensity of 65 dB, we can say that its loudness is 65 phons. The perceived loudness at 1000 Hz is the reference point for defining the equal loudness curve through that point, so the numerical value of phons and dB is always the same at 1000 Hz. Finally, we could say that sound C at 65dB is the loudest of the four sounds since it shows the greatest displacement above the 60 phon curve. From this graph, we cannot determine what that phon level is; that would require experimental comparison with 1000 Hz tones. D) Sones The use of the phon as a unit of loudness is an improvement over just quoting the level in decibels, but it is still not a measurement which is directly proportional to loudness. Using the rule of thumb for loudness, the sone scale was created to provide such a linear scale of loudness. It is usually presumed that the standard range for orchestral music is about 40 to 100 phons. If the lower end of that range is arbitrarily assigned a loudness of one sone, then 50 phons would have a loudness of 2 sones, 60 phons would be 4 sones, 70 phons would be 8 sones, etc. For the purpose of measuring sounds of different loudness, the SONE scale of subjective Loudness was invented. One sone is arbitrarily taken to be 40 phons at any frequency, i.e. at any point along the 40 phon curve on the graph. Two sones are twice as loud, e.g. 40 + 10 phons = 50 phons. Four sones are twice as loud again, e.g. 50 + 10 phons = 60 phons. The relationship between phons and sones is shown in the chart, and is expressed by the equation: Phon = 40 + 10 log2 (Sone)

References: 1. http://hyperphysics.phy-astr.gsu.edu/hbase/sound/eqloud.html

2. http://www.sfu.ca/sonic-studio/handbook/Phon.html