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Chapter 1: Q.57PE (page 11)

What are the closest frequencies to \[500\;{\rm{Hz}}\]that an average person can clearly distinguish as being different in frequency from \[500\;{\rm{Hz}}\]? The sounds are not present simultaneously.

Short Answer

Expert verified

The frequency more than given frequency that could be distinguished by average person is \(501.5\,Hz\).

Step by step solution

01

Given Data

The frequency is \[f = 500\;Hz\].

02

Calculation of the closest frequencies  

The distinguishable frequency range is,

\[{f^{'}} = f\left( {1 \pm 0.003} \right)\]

Plugging the values,

\[\begin{array}{c}{f^{'}} = 500\left( {1 \pm 0.003} \right)\\ = 500 \pm 1.5\\ = 498.5\;Hz,\,or\;501.5\;Hz\end{array}\]

Therefore the frequency more than given frequency that could be distinguished by average person is \(501.5\,Hz\).

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