Q.57PE - College Physics (Urone)

Question

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.

Step-by-Step Solution

Answer

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

Step 1: Given Data

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

Step 2: 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 \(501.5\,Hz\).