Final answer:
A child with a hearing loss of 60 dB near 5000 Hz requires a 60 dB increase in intensity for the 5000-Hz tone to be audible. Since each 10 dB increase represents a 10-fold increase in intensity, the 5000-Hz tone needs to be 1,000,000 times more intense than the 400-Hz tone to be barely audible. Therefore, the correct answer is d.
Step-by-step explanation:
When a child has a hearing loss of 60 dB near 5000 Hz, it means that the child needs 60 dB more sound at 5000 Hz to hear it compared to a person with normal hearing. Since the child has normal hearing elsewhere, we can assume that the child can hear the 400-Hz tone at the same intensity as a person with normal hearing.
To determine how much more intense the 5000-Hz tone is compared to the 400-Hz tone, we need to calculate the difference in intensity between the two tones based on the decibel (dB) scale. The dB scale is logarithmic, meaning that each 10 dB increase represents a 10-fold increase in intensity.
In this case, the child needs 60 dB more sound at 5000 Hz to hear it compared to a person with normal hearing, while the 400-Hz tone is already audible to the child. Therefore, the 5000-Hz tone needs to be 60 dB more intense than the 400-Hz tone to be barely audible to the child.
Since each 10 dB increase represents a 10-fold increase in intensity, a 60 dB increase represents a 10^6 (1,000,000) times increase in intensity. Therefore, the correct answer is 1,000,000 times more intense.