wave_mechanics critical_thinking Question 40
Question: A person speaking normally produces a sound intensity of 40 dB at a distance of 1 m. If the threshold intensity for reasonable audibility is 20 dB, the maximum distance at which he can be heard clearly is
Options:
A) 4 m
B) 5 m
C) 10 m
D) 20 m
Show Answer
Answer:
Correct Answer: C
Solution:
$ dB=10{\log _{10}}( \frac{I}{I _{0}} ) $ ; where $ I _{0}={{10}^{-12}}W{{m}^{-2}} $ Since $ 40=10{\log _{10}}( \frac{I _{1}}{I _{0}} ) $
Therefore $ \frac{I _{1}}{I _{0}}=10^{4} $ ….(i) Also $ 20=10{\log _{10}}( \frac{I _{2}}{I _{0}} ) $
Therefore $ \frac{I _{2}}{I _{0}}=10^{2} $ ….(ii)
Therefore $ \frac{I _{2}}{I _{1}}={{10}^{-2}}=\frac{r _{1}^{2}}{r _{2}^{2}} $
Therefore $ r _{2}^{2}=100r _{1}^{2} $
Therefore $ r _{2}=10m $
BETA
