Auditory Research

How would you answer someone who had asked you the question “How loud was that sound?” Probably, you would reply by comparing the sound in question to some other sound that was familiar to the questioner. For example, you might reply, “It was as loud as a balloon bursting”, or “It was not louder than a whistling kettle.” If you wanted to be numerical, you might even venture, “It was about twice as loud as a thunderclap.” These answers to the question of “How loud…” all have an element in common: They represent a subjective estimate of the quality of loudness. In fact, that is what loudness is generally believed to be all about. The objective measure of sound is the power of the sound source, which can be measured in watts or in decibels, using a sound level meter. And the subjective measure of sound is believed to be loudness, which is measured by ?? (your ear and brain?) Or at least, that’s what the teacher would have given you good marks / grades for.

It may come as some measure of surprise that we are advocating an objective measure of loudness. That is, we have determined a quantity that can be measured with a physical instrument that tells us exactly how loud a particular sound appears to you. It should not be too surprising, because after all, your brain operates on electrical and chemical principles, and the brain is the source of the subjective impression of loudness. So what we have found may be one of the physical cues by which the brain permits you to make your judgment of loudness.

The objective measure of loudness that we have discovered is the error made by a person in identifying the physical or objective intensity of a certain sound. For example, suppose that you were required, after some training, to identify a set of unknown tones (sounds) as having the objective intensity of 30 decibels or 42 decibels … or 89 decibels. This task is not all that easy, and you would make errors, sometimes identifying a tone of 50 decibels incorrectly as 41 or 55 decibels etc. Suppose we identify the range in decibels that encompassed two-thirds of your identifications as the home range. For example, your home range might have extended from 45 to 55 decibels. Then, it transpires that the louder the tone you are given to identify, the wider will be your home range. For example, for tones of 5 decibels, your home range might be 4 – 6 decibels (range = 6 – 4 = 2 decibels), while for tones of 45 decibels, your home range might be 41 to 49 decibels (range = 49 – 41 = 8 decibels).

Then we can show … and this is the kicker … that your impression of loudness will be quantified approximately by the square of the range of error. So for the 5 decibel tone, your subjectively experienced loudness will be 2 x 2 = 4, and for the 45 decibel tone, your impression of loudness would be 8 x 8 = 64. That is, the 45 decibel tone is about 16 times louder than the 5 decibel tone (64 ÷ 4 = 16) The square of the range is an objectively measured quantity. So loudness can be estimated objectively. If you glance back now at the “Overview” section of our website, you will appreciate that loudness is measured by the uncertainty in our apprehension of objective sound intensity. That is, the louder the sound, the more uncertain we are about its exact decibel value. In a sense, “Loudness = Uncertainty”.