Question

You live on a busy street, but as a music lover, you want to reduce the traffic noise. If you install special sound-reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity $\left(in\frac{w}{m^2}\right)$?

• A. ${10}^{-3}$
• B. ${10}^{-1}$
• C. $\frac{1}{2}$
• D. ${10}^{-4}$

Answer 1

The correct option is A

${10}^{-3}$

Let the initial intensity be $I_1$

Corresponding initial intensity level will be

${\beta }_1=10log\left(\frac{I_2}{I_0}\right)$

Now you have to reduce intensity level by 30 dB

${\beta }_2=10log\frac{I_2}{I_0}$

we know ${\beta }_1-{\beta }_2=30=10log\frac{I_1}{I_0}-10log\frac{I_2}{I_0}$

$\Rightarrow 30=10log\left(\frac{I_1}{I_0}\right)$

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

$\frac{I_2}{I_1}={10}^{-3}$