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What is the intensity level in decibels of a sound that has an intensity level of 2.51 x 10^4 W/m^2?

a) 96 dB
b) 102 dB
c) 108 dB
d) 110 dB

1 Answer

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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.

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