Final answer:
Doubling the intensity of a sound results in an increase of approximately 3 dB in its loudness level. This occurs because decibels are measured on a logarithmic scale. Thus, the correct option for how much the perceived loudness changes when sound intensity doubles is 3 dB.
Step-by-step explanation:
When the intensity of a sound is doubled, the perceived loudness in decibels (dB) does not double. Instead, sound levels in decibels are measured on a logarithmic scale, which is a representation of a ratio rather than direct proportionality to intensity.
To find the change in dB for a doubling of sound intensity, we can use properties of logarithms. Given that a tenfold increase in intensity corresponds to a 10 dB increase, we can solve for a twofold increase in intensity by calculating the ratio of the two intensities in decibels. Using the formula for sound intensity levels:
L = 10 × log(I2 / I1) dB
Where L is the sound level difference, I2 is the intensity of the second sound and I1 is the intensity of the first sound. For a double intensity ratio (I2 / I1) = 2, we have:
L = 10 × log(2) = 10 × 0.301 = 3.01 dB
Thus, a sound that is twice as intense as another will have a sound level approximately 3 dB higher.
The provide correct option in final answer to your question is c. 3 dB.