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A hearing test is conducted on an aged person. It is found that her threshold of hearing is 20 decibels at $1 \mathrm{kHz}$ and it rises linearly with frequency to 60 decibels at $9 \mathrm{kHz}$. The minimum intensity of sound that the person can hear at $5 \mathrm{kHz}$ is-
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The correct answer is:
100 times than that at $1 \mathrm{kHz}$
at $5 \mathrm{KHz}$ Hearing capacity $=40 \mathrm{~dB}$ Intensity at $1 \mathrm{KHz}$
$$
\begin{array}{l}
\beta=10 \log \left(\frac{\mathrm{I}}{\mathrm{I}_{0}}\right) \\
\mathrm{I}=\mathrm{I}_{0} 10^{\left(\frac{\beta}{10}\right)} \\
(\mathrm{I})_{1 \mathrm{KHz}}=\mathrm{I}_{0} 10^{(20 / 10)}=\mathrm{I}_{0}(10)^{2} \\
(\mathrm{I})_{5 \mathrm{KHz}}=\mathrm{I}_{0} 10^{(40 / 10)}=\mathrm{I}_{0}(10)^{4} \\
\frac{(\mathrm{I})_{1 \mathrm{KHz}}}{\mathrm{I}_{5 \mathrm{KHz}}}=\frac{1}{100}
\end{array}
$$
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