Question
Decibels (Refer to Example 2.) Use the formula $D(x)=10 \log \left(10^{16} x\right)$ to determine the decibels when the intensity of a sound is $x=10^{-1 / 2}$ watt per square centimeter.
Step 1
Step 1: We are given the formula $D(x)=10 \log \left(10^{16} x\right)$ and we are asked to find the decibels when the intensity of the sound is $x=10^{-1 / 2}$ watt per square centimeter. Show more…
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Refer to the following: $$\text { Decibel: } D=10 \log \left(\frac{I}{I_{T}}\right) \quad I_{T}=1 \times 10^{-12} \mathrm{W} / \mathrm{m}^{2}$$ Calculate the decibels associated with attending $a$ football game in a loud college stadium if the intensity is $I=1 \times 10^{-0.3} \mathrm{W} / \mathrm{m}^{2}$
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The loudness level of a sound, $D,$ in decibels, is given by the formula $$ D=10 \log \left(10^{12} I\right) $$ where $I$ is the intensity of the sound, in watts per meter.$^{2} .$ Decibel levels range from $0,$ a barely audible sound, to $160,$ a sound resulting in a ruptured eardrum. (Any exposure to sounds of I30 decibels or higher puts a person at immediate risk for hearing damage.) Use the formula to solve What is the decibel level of a normal conversation, $3.2 \times 10^{-6}$ watt per meter $^{2} ?$
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The formula for measuring sound intensity in decibels $D$ is defined by the equation $D=10 \log \left(\frac{1}{I_{0}}\right),$ where $I$ is the intensity of the sound in watts per square meter and $I_{0}=10^{-12}$ is the lowest level of sound that the average person can hear. How many decibels are emitted from a large orchestra with a sound intensity of 6.3$\cdot 10^{-3}$ watts per square meter?
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