The intensity level from a loudspeaker is 100 dB at a distance of 10 m. What is its intensity level at a distance of 100 m?
1 Answer
Solution
Given,
β1 = 100 dB,
r1 = 10 m,
β2 = ?
r2 = 100 m
Now, we have, the intensity, \(I\propto\frac1{r^2}\)
Then, \(\frac{I_2}{I_1}=\frac{r_1^2}{r_2^2}=\left(\frac{10}{100}\right)^2\)
∴ \(\frac{I_2}{I_1}=0.01\)
Again, the difference of intensity level at these two points is;
\(\beta_2-\beta_1=10\cdot\log_{10}\left(\frac{I_2}{I_1}\right)=10\times\log_{10}\left(0.01\right)=-20\) dB
∴ β2 = β1 - 20 = (100 - 20) dB = 80 dB
Hence, the required intensity level is 80 dB.
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