Question

How many times more intense is a $60\, dB$ sound than a $30\, dB$ sound ?

• A. $1000$
• B. $2$
• C. $100$
• D. $4$

Answer 1

Answer: (A)

$ L =10 \log _{10} \frac{I}{I_{0}} $
$60 =10 \log _{10} \frac{I_{1}}{I_{0}} $
$\Rightarrow \,\,\,\, \frac{I_{1}}{I_{0}}=10^{6}\,\,\,\,\,\,\,\,...(i)$
Similarly,
$30=10 \log _{10} \frac{I_{2}}{I_{0}}$
$\frac{I_{2}}{I_{0}}=10^{3}$
Dividing Eq. (i) by Eq. (ii), we get
$\frac{I_{1}}{I_{2}}=1000$