Final answer:
A 5000-Hz tone must be 1,000,000 times more intense than a 400-Hz tone if both are barely audible to a child with a 60 dB hearing loss at 5000 Hz due to noise exposure.
Step-by-step explanation:
In addressing the question of hearing loss at different frequencies, we need to understand the concept of decibels (dB) and the intensity of sound. The decibel scale is logarithmic, which means that for each 10 dB increase in sound level, the intensity of sound is multiplied by a factor of 10. So, if a child has a hearing loss of 60 dB near 5000 Hz and normal hearing at other frequencies, then a 5000-Hz tone would need to be 1,000,000 (106) times more intense than a tone at the threshold of hearing for it to be barely audible to them. This is because 60 dB represents a factor of 10 multiplied by itself 6 times (106).
A 400-Hz tone at the threshold of normal hearing will be at 0 dB of loss. If both the 5000-Hz tone with 60 dB of loss and the 400-Hz tone are barely audible to the child, then the 5000-Hz tone must be 1,000,000 times more intense than the 400-Hz tone. This demonstrates the significant impact that hearing loss at a certain frequency can have on the required intensity of sound for it to be perceived.