Final answer:
To reach the pain threshold level of 120 dB from an initial sound intensity of 90 dB, 1000 pig-callers would be required because a 30 dB increase corresponds to a thousandfold increase in sound intensity.
Step-by-step explanation:
The question asks how many pig-callers producing a sound with an intensity level of 90 dB would be needed to reach a pain threshold level of 120 dB, which typically represents a sound intensity that is painful to the human ear. The decibel scale is logarithmic, meaning each increase of 10 dB represents a tenfold increase in sound intensity. Therefore, an increase from 90 dB to 120 dB is a 30 dB increase, which corresponds to a 10³ (or 1000) times increase in sound intensity. If one pig-caller generates 90 dB, reaching 120 dB would require 1000 pig-callers, assuming no interference and that the sound intensities simply add together. This is because 1000 sources of the same intensity would result in a tenfold increase in intensity three times (10 x 10 x 10), just as going from 90 dB to 120 dB is three tenfold increases in the intensity level (30 dB).