The sound of a band is rated as 50 dB at a distance of 30.0 m. What is the sound intensity level of the band when one is 10.0 m from the band?
A) 59.5 dB
B) 57.3 dB
C) 55.2 dB
D) 52.9 dB
E) 50.1 dB

Question

Quizplus · Accepted Answer

The sound intensity level increases by 6 dB each time the distance is halved (or decreases by 6 dB each time the distance is doubled) due to the inverse square law of sound intensity. Moving from 30.0 m to 10.0 m is effectively halving the distance twice (30 to 15 to 7.5, but since 10 is closer than 7.5, it's slightly less than two full halvings). However, for simplicity and direct calculation, we consider moving from 30 m to 15 m (one halving) and then from 15 m to 7.5 m (another halving), which would increase the sound level by 6 dB for each halving. Since the original sound level is 50 dB, adding 6 dB twice gives us an increase of 12 dB, resulting in a sound level of 62 dB. However, since 10 m is a bit further than 7.5 m, the actual increase would be slightly less than 12 dB, making 59.5 dB the closest and most reasonable choice given the options.

The Sound of a Band Is Rated as 50 DB