Question

The difference of sound levels between two points is $40dB$. What is the ratio of pressure amplitudes between the two points?

• A. $10$
• B. $200$
• C. $100$
• D. $400$

Answer 1

The correct option is C $100$

Difference between of loudness of sound $\Delta L=10{\log }_{10}\frac{I_2}{I_1}$
Given : $\Delta L=40dB$
$\therefore$ $40=10{\log }_{10}\frac{I_2}{I_1}$
Or ${\log }_{10}\frac{I_2}{I_1}=4$
$⟹\frac{I_2}{I_1}={10}^4$
We know that, intensity of sound $I\propto P^2$
where $P$ is the pressure amplitude.
$\therefore$ $\frac{P_2}{P_1}=\sqrt{\frac{I_2}{I_1}}=\sqrt{{10}^4}=100$