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College Physics (Urone)
Found in: Page 630

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Short Answer

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 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 \[90 \times 1{0^{ - 3}}\;mi/h\].

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