Final answer:
The sound intensity level in decibels (dB) of a sound with an intensity of 2.51 x 10^4 W/m^2 is approximately 164 dB, which does not match any of the given options.
Step-by-step explanation:
The intensity level in decibels (dB) of a sound is calculated using the formula:
L = 10 log10(I / I0)
where:
- L is the sound intensity level in dB
- I is the sound intensity in watts per meter squared (W/m²)
- I0 is the reference sound intensity, which is 10-12 W/m² (threshold of hearing)
Given an intensity (I) of 2.51 x 104 W/m², the calculation is as follows:
L = 10 log10(2.51 x 104 / 10-12)
L = 10 log10(2.51 x 1016)
L = 10(16 + log10(2.51))
L ≈ 10(16 + 0.4)
L ≈ 10 x 16.4
L ≈ 164 dB
Therefore, none of the given options are correct.