Question

What intensity level does the sound in the preceding problem correspond to?

a) 110 dB
b) 115 dB
c) 120 dB
d) 125 dB

Answer 1

120 dB level is preceding.

The correct option is c) 120 dB.

Step-by-step explanation:

The sound intensity level (SIL) is given by the formula SIL = 10 * log10(I/I₀), where I is the sound intensity and I₀ is the reference intensity (usually taken as
`1.0 x 10^-^1^2 W/m²).`

In the context of the question, the sound intensity level is given as 120 dB. To find the corresponding sound intensity, we can rearrange the formula to solve for I:

`\[ 120 \, \text{dB} = 10 * \log_(10)(I/I₀) \]`

Dividing both sides by 10:

`\[ 12 = \log_(10)(I/I₀) \]`

Now, raising both sides as powers of 10:

`\[ 10^(12) = I/I₀ \]`

Multiplying both sides by I₀:

`\[ I = I₀ * 10^(12) \]`

So, the sound intensity is
`\(10^(12)\)` times the reference intensity. This corresponds to a sound intensity level of 120 dB.

Therefore, the correct answer is option c) 120 dB.