Final answer:
The difference in sound intensity levels between S1 and S2, with S1 being three times as intense as S2, is approximately 4.77 dB. Therefore, the answer closest to this value is 6 dB, although it is not one of the options provided exactly.
Step-by-step explanation:
Difference in Sound Intensity Levels
We are given that sound S1 is three times the intensity of sound S2. The sound intensity level in decibels (dB) is calculated using the logarithmic scale based on powers of 10. To find the difference in decibels between two sounds when their intensity levels are known, we use the formula:
L1 - L2 = 10 × log10(I1 / I2)
where L1 and L2 are the sound levels in decibels of sounds S1 and S2 respectively, and I1 and I2 are their respective intensities.
When the intensity of S1 is three times that of S2, the ratio (I1 / I2) is 3/1 or 3. Now we plug in this ratio to the formula:
L1 - L2 = 10 × log10(3)
This calculation will give the difference in decibels:
L1 - L2 ≈ 10 × 0.477 = 4.77 dB
So the correct difference in sound intensity levels between S1 and S2, measured in decibels, is approximately 4.77 dB. Thus, none of the options a), b), c), or d) are precisely correct; however, if rounding to the nearest whole number, the closest answer would be b) 6 dB.
Note that if one sound is twice as intense as another, the difference in sound intensity levels is 3 dB. This is a common reference used in acoustics and is useful for double or half intensity comparisons.