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# Sensory adaptation and Weber's Law

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## Problem

Why is it that in a quiet room, a person simply has to whisper in order to communicate with someone, while at a rock concert, they need to yell as loudly as possible to convey a message? Auditory receptors are able to change sensitivity to a stimulus, which is called sensory adaptation. With regard to hearing, continuous loud sound cause a small muscle attached to one of the bones of the inner ear to contract, reducing the transmission of sound vibrations to the inner ear, where the vibrations are detected. This protective mechanism does not work well for sudden very loud noises such as rifle shots, as the muscle does not have time to contract before the intense vibrations pass through. In a quiet room, the muscle attached to the inner ear is relaxed, producing the ability to hear very low intensity sounds. The ratio of how loud a stimulus must be in order to hear it corresponds linearly with the background intensity, which is known as Weber’s Law. Weber’s Law can be expressed as the following:
$\frac{\Delta I}{I}$ = K
Weber’s Law is named after E.H. Weber, who in 1834 realized that the ratio of the increment threshold to the background intensity is constant. This works with sound as well$—$in a noisy room, you need to yell in order to be heard, while in a quiet room, you can whisper to be heard.
An experiment conducted to test whether or not Weber’s Law held true for tactile stimuli revealed a relationship between the background intensity and the difference threshold; this relationship is depicted in Figure $1$. Background intensity corresponded to the weight, in ounces, of a small marble placed on the palm of an individual, and the difference threshold corresponded to the amount of extra weight (in ounces) needed in order for the individual to recognize that any weight was added.
Figure $1$
If half a pound had to be added to a 20-pound weight in order for someone lifting the weight to recognize that extra weight has been added, what is the just noticeable difference?