Question

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

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

Answer 1

The correct option is A

$1000$

Step 1: Given Information

Intensity of sound$\left(I\right)$= $60dB$

Step 2: Calculate How many times more intense a $60dB$ sound than a $dB$ sound

$L=10{\log }_{10}\left(\frac{I}{I_0}\right)$

Where $I$= Intensity of sound and $I_o$= Max intensity of sound

$60=10{\log }_{10}\left(\frac{I_1}{I_0}\right)$

$\left(\frac{I_1}{I_0}\right)={10}^6$----------(1)

Similarly,

$30=10{\log }_{10}\left(\frac{I_2}{I_0}\right)$

$\left(\frac{I_1}{I_0}\right)={10}^3$-------------(2)

Divide equation (1) by equation (2) we get

$\left(\frac{I_1}{I_2}\right)=1000$.

Hence, the correct option is (A).