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Q.55PE

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Found in: Page 630

### College Physics (Urone)

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 $$1{0^9}\;m$$.

See the step by step solution

## Step 1: Given Data

The factor is$$1{0^{ - 12}}$$.

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

## Step 2: Concept

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.

## Step 3: Calculation of the 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 $${10^9}\,{\rm{m}}$$.