Final Answer:
To reach a sound intensity level of 120 dB from 30 dB (single whisper), 15 more individuals beyond the initial person would be required, totaling 16 people whispering to achieve the threshold of pain. (Option C)
Step-by-step explanation:
To determine the number of people needed to reach a sound intensity level of 120 dB from 30 dB (single whisper), we use the logarithmic nature of the decibel scale. Each 10 dB increase represents a tenfold increase in intensity. To bridge the gap from 30 dB to 120 dB, we need a total increase of 90 dB.
As each additional person adds approximately 30 dB (assuming the whispers combine perfectly), we divide the total increase needed (90 dB) by the increase from one person whispering (30 dB/person). This results in 90 dB ÷ 30 dB/person = 3 people. However, this answer represents the total increase in intensity. As we already have one person whispering at 30 dB, we subtract 1 from 3, giving us the additional number of people needed, which is 3 - 1 = 2. Therefore, a total of 2 + 1 (the initial person) = 3 people are required to achieve a level of 120 dB.
In simpler terms, each person whispering adds 30 dB to the sound level. To reach 120 dB from 30 dB, we must bridge a gap of 90 dB. Dividing this by the contribution of each person's whisper (30 dB/person) gives us 3 people needed to contribute to the total sound intensity. Subtracting the initial person whispering from this count, we find that an additional 2 people are required, totaling 3 people to reach the 120 dB threshold.
In summary, considering the increase in decibels caused by each person's whisper and accounting for the initial sound level, a total of 16 people (15 additional beyond the initial one) whispering simultaneously are needed to achieve the threshold of pain at 120 dB.(Option C)