MCQ
In a city sound intensity level increases uniformly by about $1\ dB$ annually. How many years will it take for intensity of sound to become double ..... $year$
- A$1$
- B$2$
- ✓$3$
- D$4$
✓
Answer
Correct option: C.
$3$
c
$\mathrm{L}=10 \log \frac{\mathrm{I}}{\mathrm{I}_{0}}$
$\mathrm{L}=10 \log \frac{\mathrm{I}}{\mathrm{I}_{0}}$
$I = {I_0}{(10)^{\frac{L}{{10}}}} = {I_0}{e^{\left( {\ln 10} \right)\frac{L}{{10}}}}$
$\frac{\mathrm{dI}}{\mathrm{dL}}=\frac{\ln 10}{10} \mathrm{I}$
${\frac{\mathrm{dI}}{\mathrm{I}}=\frac{\ln 10}{10} \mathrm{dL}} $
${\int_{\mathrm{I}}^{2 \mathrm{I}} \frac{\mathrm{d} \mathrm{I}}{\mathrm{I}}=\frac{\ln 10}{10} \int_{0}^{\mathrm{t}} \frac{\mathrm{dL}}{\mathrm{dt}} \mathrm{dt}} $
${\ln 2=\frac{\ln 10}{10} \int_{0}^{\mathrm{t}}(1) \mathrm{d} \mathrm{t}} $
${\rm{t}} \simeq 3\,{\rm{years}}$
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