<p>Loudness is a subjective measure of how strong a sound feels, as it can vary between individuals. A more objective way to measure sound strength is the sound intensity level, $L$, given by the formula $L=10\lg \frac{I}{{{I}_{0}}}$,</p>
<p>where&nbsp;$I$ represents the sound intensity in W/m$^{2}$, and ${{I}_{0}}$ is the minimum sound intensity detectable by the human ear (also measured in W/m$^{2}$). The unit of $L$ is decibels (dB).</p>
<ol class="i-list"><li><div class="list-item-paragraph">What is the lowest value of $L$ (in dB) that the human ear can detect?</div></li><li><div class="list-item-paragraph">If&nbsp;$L=90$ dB when&nbsp;$I={{10}^{-3}}$ W/m$^{2}$, find the minimum sound intensity detectable by the human ear.</div></li><li><div class="list-item-paragraph">Find the sound intensity level for a refrigerator with a sound intensity of $4\times {{10}^{-8}}$ W/m$^{2}$.</div></li><li><div class="list-item-paragraph">Given that the sound intensity level of a machine is $120$ dB, find the corresponding sound intensity $I$.</div></li></ol>

Loudness is a subjective measure of how strong a sound feels, as it can vary between individuals. A more objective way to measure sound strength is the sound intensity level, $L$, given by the formula $L=10\lg \frac{I}{{{I}_{0}}}$,

where $I$ represents the sound intensity in W/m$^{2}$, and ${{I}_{0}}$ is the minimum sound intensity detectable by the human ear (also measured in W/m$^{2}$). The unit of $L$ is decibels (dB).

What is the lowest value of $L$ (in dB) that the human ear can detect?

If $L=90$ dB when $I={{10}^{-3}}$ W/m$^{2}$, find the minimum sound intensity detectable by the human ear.

Find the sound intensity level for a refrigerator with a sound intensity of $4\times {{10}^{-8}}$ W/m$^{2}$.

Given that the sound intensity level of a machine is $120$ dB, find the corresponding sound intensity $I$.

Exponential and Logarithmic Functions - Applications of Exponential and Logarithmic Functions

Question 3f456120

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