Question

A community is concerned about a plan to bring train service to their downtown from the town’s outskirts. The current sound intensity level, even though the rail yard is blocks away, is 70 dB downtown. The mayor assures the public that there will be a difference of only 30 dB in sound in the downtown area. Should the townspeople be concerned? Why?

Short answer

Yes, People should be considered because sound intensity(loudness) will be very high in downtown.

Step-by-step solution

Relation between sound intensity and sound intensity level difference

The relation between sound intensity and sound intensity level difference is given by

${\beta }_2-{\beta }_1=10{\log }_{10}\left(\frac{l_2}{l_1}\right)$

Here ${\beta }_2-{\beta }_1$is the sound intensity level difference in dB and $l_2$is the intensity of sound when train is brought to downtown and $l_1$is the intensity when the train is at outskirts.

Real change in intensities

$$\begin{gathered} {\beta }_2-{\beta }_1=30dB \\ 30=10{\log }_{10}\left(\frac{l_2}{l_1}\right) \\ \frac{l_2}{l_1}={10}^3 \\ {l}_2={10}^3{l}_1 \end{gathered}$$

Conclusion

We can see that the intensity of sound in downtown will be a thousand times greater when train will reach downtown than that when it is on the outskirts of the city. That’s why People should be considered.