The ear responds to intensities which can vary over a range of 10^12. (That is,

ID: 2120903 • Letter: T

Question

The ear responds to intensities which can vary over a range of 10^12. (That is, an

undamaged ear can detect sounds from the threshold of hearing, 10%u221212 W/m^2, to the

threshold of pain, 1 W/m^2.)

Suppose you built an instrument which could measure distances which change over this same range of magnitudes.

Suppose the smallest distance the instrument could measure is 0.1 mm (or 100 micrometers), the typical width of a

human hair.

What would be the largest distance it could measure? Give an example of

a physical situation involving this distance.

the largest distance is

S = 0.1 x 100 = 10 mm = 10 x 10^-3 m

the largest distance is 100 times the smallest distance as the threshold of hearing is 10^12

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