Perception. The Weber–Fechner law concerns a person’s sensed perception of various strengths of stimulation involving weights, sound, light, shock, taste, and so on. One form of the law states that the rate of change of sensed sensation S with respect to stimulus R is inversely proportional to the strength of the stimulus R . So d s d R = k R where k is a constant. If we let R 0 be the threshold level at which the stimulus R can be detected (the least amount of sound, light, weight, and so on, that can be detected), then S ( R 0 ) = 0 Find a function S in terms of R that satisfies these conditions.
Perception. The Weber–Fechner law concerns a person’s sensed perception of various strengths of stimulation involving weights, sound, light, shock, taste, and so on. One form of the law states that the rate of change of sensed sensation S with respect to stimulus R is inversely proportional to the strength of the stimulus R . So d s d R = k R where k is a constant. If we let R 0 be the threshold level at which the stimulus R can be detected (the least amount of sound, light, weight, and so on, that can be detected), then S ( R 0 ) = 0 Find a function S in terms of R that satisfies these conditions.
Solution Summary: The author calculates the rate of change of S with respect to stimulus is inversely proportional to the strength of the stimulus.
Perception. The Weber–Fechner law concerns a person’s sensed perception of various strengths of stimulation involving weights, sound, light, shock, taste, and so on. One form of the law states that the rate of change of sensed sensation S with respect to stimulus R is inversely proportional to the strength of the stimulus R. So
d
s
d
R
=
k
R
where k is a constant. If we let R0 be the threshold level at which the stimulus R can be detected (the least amount of sound, light, weight, and so on, that can be detected), then
S
(
R
0
)
=
0
Find a function S in terms of R that satisfies these conditions.
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