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Q.56PE

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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 frequencies to which the ear responds vary by a factor of ${\rm{1}}{{\rm{0}}^{\rm{3}}}$. Suppose the speedometer on your car measured speeds differing by the same factor of ${\rm{1}}{{\rm{0}}^{\rm{3}}}$, and the greatest speed it reads is ${\rm{90}}{\rm{.0}}\;{\rm{mi/h}}$. What would be the slowest nonzero speed it could read?

The smallest speed is $90 \times 1{0^{ - 3}}\;mi/h$.

See the step by step solution

## Step 1: Given Data

The factor is $1{0^3}$.

The greatest speed is $V = 90.0\;mi/h$.

## Step 2: Concept

The expression for the factor of intensity is given by,

$$f = \frac{d}{D}$$

Here $$f$$ is the factor of intensity, $$v$$ is the smallest speed that can be measured, $$V$$ is the possible largest distance.

## Step 3: Calculation of the largest distance

The factor of intensity for the smallest speed ${\rm{v}}$ and the greatest speed ${\rm{V}}$ is,

$f = \frac{v}{V}$

Plugging the values,

\begin{aligned}{c}1{0^3} &= \frac{{90}}{V}\\V &= \frac{{90}}{{1{0^3}}}\\V &= 90 \times 1{0^{ - 3}}\;mi/h\end{aligned}

Therefore the smallest speed is $90 \times 1{0^{ - 3}}\;mi/h$.