When sound passes through a building wall, a certain proportion is transmitted into the interior while the rest is reflected or absorbed. The ratio of sound transmitted into the interior is called the transmission rate. When the acoustic output of a speaker is $W$ (watts), the intensity $P$ (decibels) of sound transmitted into the interior at a distance of $r$ (m) from the speaker in a building with transmission rate $\alpha$ is as follows. $$\begin{aligned} & P = 10 \log \frac { \alpha W } { I _ { 0 } } - 20 \log r - 11 \\ & \text{(where } I _ { 0 } = 10 ^ { - 12 } \text{ (watts/m}^2\text{) and } r > 1 \text{.)} \end{aligned}$$ A speaker is emitting sound with an acoustic output of 100 (watts). When the intensity of sound transmitted into the interior of a building with transmission rate $\frac { 1 } { 100 }$ is 59 (decibels) or less, what is the minimum distance between the speaker and the building? (Assume that sound spreads uniformly in space and that factors other than transmission rate are not considered.) [4 points]
(1) $10 ^ { 2 } \mathrm{~m}$
(2) $10 ^ { \frac { 17 } { 8 } } \mathrm{~m}$
(3) $10 ^ { \frac { 13 } { 6 } } \mathrm{~m}$
(4) $10 ^ { \frac { 9 } { 4 } } \mathrm{~m}$
(5) $10 ^ { \frac { 5 } { 2 } } \mathrm{~m}$