Complete parts (a) through (c) below. a. For a house located about 1 meter from a street, the decibel level for busy street traffic is about 80 dB . If the house was located 130 meters from the street, how loud will the street noise be, in decibels? The street noise will be about \( \square \mathrm{dB} \). (Round to the nearest hundredth as needed.)

We start by recalling that if the sound source is modeled as a point source in free space, the sound intensity follows an inverse-square law. This means that when the distance increases from \( r_1 \) to \( r_2 \), the intensity decreases by a factor of \[ \left(\frac{r_1}{r_2}\right)^2. \] Because decibel level is defined in terms of a logarithmic measure of intensity, the change in decibel level when moving from \( r_1 \) to \( r_2 \) is given by \[ \Delta L = 10 \log \left(\frac{I_2}{I_1}\right) = 10 \log \left(\frac{r_1^2}{r_2^2}\right) = 20 \log \left(\frac{r_1}{r_2}\right). \] Given: - Initial level at \( r_1 = 1 \) meter is \( 80 \) dB. - New distance \( r_2 = 130 \) meters. Thus, the new decibel level \( L_2 \) is \[ L_2 = 80 + 20 \log\left(\frac{1}{130}\right). \] Since \[ 20 \log\left(\frac{1}{130}\right) = -20 \log(130), \] we need to compute \( \log(130) \). Using a calculator, we find \[ \log(130) \approx 2.113. \] Then, \[ -20 \log(130) \approx -20 \times 2.113 = -42.26. \] Thus, the new decibel level is \[ L_2 = 80 - 42.26 \approx 37.74 \text{ dB}. \] The street noise will be about \( 37.74 \) dB at a distance of 130 meters.