Question

If a sound absorber attenuates the sound level by $20dB$. The factor by which the intensity decreases is

• A. $1000$
• B. $10000$
• C. $10$
• D. $100$

Answer 1

The correct option is D

$100$

Solution :

Step 1: Given data:

The sound absorber attenuates the sound level by${\beta }_1-{\beta }_2=20dB$

Step 2: Formula used:

Suppose that the intensity of the sound will be $I$ and $I\text{'}$.

Therefore the loudness of sound initially,

Know that,

$$\begin{gathered} {\beta }_1=10\log \left(\frac{I}{I_0}\right) \\ {\beta }_2=10\log \left(\frac{I\text{'}}{I_0}\right) \end{gathered}$$

Therefore substitute the values of ${\beta }_1,{\beta }_2$.

$$\begin{gathered} {\beta }_1-{\beta }_2=20dB \\ 10\log \left(\frac{I}{I_0}\right)-10\log \left(\frac{I\text{'}}{I_0}\right)=20 \\ \log \left(\frac{I}{I_0}\right)-\log \left(\frac{I\text{'}}{I_0}\right)=2 \\ \log \left(\frac{I}{I\text{'}}\right)=2 \end{gathered}$$

Simplify further,

$$\begin{gathered} I={10}^{2}I\text{'} \\ I\text{'}=\frac{I}{100} \end{gathered}$$

Therefore the intensity decreases is$100$.

Hence, the correct option is (D).