Question

A person has a hearing threshold 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz. How much more intense must a 100-Hz tone be than a 4000-Hz tone if they are both barely audible to this person?

a) 40 times more intense
b) 100 times more intense
c) 1000 times more intense
d) 10,000 times more intense

Answer 1

A 100-Hz tone must be 10,000 times more intense than a 4000-Hz tone to be barely audible to a person with a hearing threshold of 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz.

The correct otion is; Intensity = 100,000 dB

Step-by-step explanation:

To determine how much more intense a 100-Hz tone must be than a 4000-Hz tone to be barely audible to a person with a hearing threshold of 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz, we need to compare the intensity levels in dB for both frequencies.

Using the formula:

Intensity in dB = 10 * log10(Intensity / Reference Intensity)

Where the Reference Intensity is the threshold intensity for normal hearing at each frequency, which is 0 dB.

For the 100-Hz tone:

10 dB = 10 * log10(Intensity / 0 dB)

log10(Intensity / 0 dB) = 1

Intensity = 10 dB

For the 4000-Hz tone:

50 dB = 10 * log10(Intensity / 0 dB)

log10(Intensity / 0 dB) = 5

Intensity = 100,000 dB

Therefore, the 100-Hz tone must be 10,000 times more intense than the 4000-Hz tone to be barely audible to this person.