Question

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

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

Answer 1

Answer: (A)

$1000$

Loudness of two sounds are given as $L_2=60dB$ and $L_1=30dB$

Loudness of sound $L=10{\log }_{10}\frac{I}{I_o}$

$⟹$ $L_2-L_1=10{\log }_{10}\frac{I_2}{I_1}$

Or $60-30=10{\log }_{10}\frac{I_2}{I_1}$

Or ${\log }_{10}\frac{I_2}{I_1}=3$

Or $\frac{I_2}{I_1}={10}^3=1000$

Thus $60dB$ sound is $1000$ times more intense than $30dB$ sound.