How many times is $90\text{ dB}$ sound more intense than $40\text{ dB}$ sound?

How many times is $90\text{ dB}$ sound more intense than $40\text{ dB}$ sound?
  1. 5
  2. 50
  3. 500
  4. $10^5$

Solution

Here, $90 - 40 = 10 \log \frac{I_1}{I_0} - 10 \log \frac{I_2}{I_0}$ or $50 = 10 \log \left(\frac{I_1}{I_2}\right)$ $\therefore \frac{I_1}{I_2} = 10^5$

Practice more Waves and Sound questions on Aicharya