INVERSE SQUARE LAW: How many decibels does the intensity of a sound increase if the distance to the source is decreased by a factor of 10?
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PROVE: Inverse Square Law for Sound A law of physics states that the intensity of sound is inversely proportional to the square of the distance $d$ from the source: $I=k / d^{2}$. (a) Use this model and the equation $$ B=10 \log \frac{I}{I_{0}} $$ (described in this section) to show that the decibel levels $B_{1}$ and $B_{2}$ at distances $d_{1}$ and $d_{2}$ from a sound source are related by the equation $$ B_{2}=B_{1}+20 \log \frac{d_{1}}{d_{2}} $$ (b) The intensity level at a rock concert is $120 \mathrm{dB}$ at a distance $2 \mathrm{m}$ from the speakers. Find the intensity level at a distance of $10 \mathrm{m}$.
Exponential and Logarithmic Functions
Logarithmic Scales
Decibels (Refer to Example 4.) If the intensity $x$ of a sound increases by a factor of $10,$ by how much does the decibel level increase?
Properties of logarithms
if the intensity of a horn increase by 10, then what is the increase in decibels?
Adi S.
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