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Q.55PE

Expert-verifiedFound in: Page 630

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**The factor of \({\rm{1}}{{\rm{0}}^{{\rm{ - 12}}}}\)in the range of intensities to which the ear can respond, from threshold to that causing damage after brief exposure, is truly remarkable. If you could measure distances over the same range with a single instrument and the smallest distance you could measure was\(1\;{\rm{mm}}\), what would the largest be?**

The largest distance is \(1{0^9}\;m\).

The factor is\(1{0^{ - 12}}\).

The smallest distance is\(d = 1\;mm = 1{0^{ - 3}}\;m\).

**The expression for the factor of intensity is given by,**

**\(f = \frac{d}{D}\) **

**Here \(f\) is the factor of intensity, \(d\) is the smallest distance that can be measured, \(D\) is the possible largest distance.**

The factor of intensity for the smallest distance \({\rm{d}}\) and the largest distance \({\rm{D}}\) is,

\(\frac{d}{D}\)

Plugging the values,

\(\begin{aligned}{}1{0^{ - 12}} &= \frac{{1{0^{ - 3}}}}{D}\\D &= \frac{{1{0^{ - 3}}}}{{1{0^{ - 12}}}}\\D &= 1{0^9}\;m\end{aligned}\)

Therefore the largest distance is \({10^9}\,{\rm{m}}\).

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