Final answer:
The decibel level decreases by more than 10 dB when the power of a sound source is tripled but the distance from the source is also tripled; the decrease due to distance outweighs the increase from power.
Step-by-step explanation:
When considering the change in decibel level due to a source broadcasts sound's power increase and an observer moving away from the sound source, we must look at two factors: the increase in power and the increased distance. The power has increased by a factor of 3, which corresponds to a change in decibel level up by less than 10 dB, because doubling the intensity of sound typically results in an increase of about 3 dB. However, if the distance from the sound source is also tripled, the intensity of the sound will decrease as a function of the square of the distance due to the inverse-square law of sound propagation. This would mean the intensity is decreased by a factor of 3 squared (9), which corresponds to a decrease in decibel level by slightly more than 10 dB, as a factor of 10 decrease in intensity corresponds to a reduction of 10 dB in sound level.
The net effect on the decibel level is difficult to precisely quantify without actual intensity measurements, but the decibel level will decrease because the effect of distance on decreasing intensity (and hence decibels) outweighs the effect of the increased power. Thus, the resulting change in decibel level when both power is increased by a factor of 3 and the distance is tripled would be option 1) The decibel level goes down by more than 10 dB.