The Weber–Fechner law says that the relationship between stimulus and perception is logarithmic. Thus, if p denotes perInterestingly, this law seems to apply to all our senses, including taste, touch, sight, sound and smell. ception and S denotes the stimulus, then p(S) = k ln 

S S0



,

for some constants k and S0. The units of p and S are unspecified for this question. The units depend on whether you’re measuring vision or hearing or some other sense, so they vary a lot from experiment to experiment.

a. What is p(S0)?

b. The Weber–Fechner law is often written in the form p(S) = k ln(S) +C. Work out an equation for C in terms of S0 and k.

c. Write S as a function of p.

d. Set k = S0 = 1. Plot the graphs of p(S) and S(p).