Q18E - University Physics with Modern Physics

Question

You live on a busy street, but as a music lover, you want to reduce the traffic noise. (a) 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 $\mathbf{(}\mathbf{W}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}\mathbf{)}\mathbf{?}$ (b) If, instead, you reduce the intensity by half, what change (in dB) do you make in the sound intensity level?

Step-by-Step Solution

Answer

Therefore, the reduction in sound level is 0.01

STEP 1 Concept of the Reduction in loudness of the sound

Reduction in loudness of the sound is given by the following equation: $\mathbf{L}\mathbf{=}\mathbf{10}\mathbf{log}\left(\frac{l}{l_0}\right)$ were, where ${\mathbf{l}}_{\mathbf{0}}$  is the original sound intensity.

STEP 2 Calculate the factor of reduction

Substitute given value for L in dB into equation (1), we obtain the needed factor of reduction as follows:

$$\begin{gathered} -20=10\log \left(\frac{\mathrm{l}}{{\mathrm{l}}_0}\right)/10 \\ \log \left(\frac{\mathrm{l}}{{\mathrm{l}}_0}\right)=-2 \\ \frac{\mathrm{l}}{{\mathrm{l}}_0}={10}^{-2} \\ \frac{\mathrm{l}}{{\mathrm{l}}_0}=0.01 \end{gathered}$$

Therefore, the reduction in sound level is 0.01