What is the final intensity if a wave's initial intensity is 2 mW/cm² with an increase of 10 dB?

• A. 4 mW/cm²
• B. 8 mW/cm²
• C. 12 mW/cm²
• D. 20 mW/cm²

Answer: (D)

To determine the final intensity after an increase of 10 dB, it's important to understand how the decibel scale relates to intensity. The formula for the change in intensity in decibels is given by:

[

\text{dB} = 10 \log_{10} \left( \frac{I_f}{I_i} \right)

]

where (I_f) is the final intensity and (I_i) is the initial intensity.

Given that the initial intensity (I_i) is 2 mW/cm² and the increase is 10 dB, we can rearrange the formula to find the final intensity:

[

10 = 10 \log_{10} \left( \frac{I_f}{2} \right)

]

Dividing both sides by 10 yields:

[

1 = \log_{10} \left( \frac{I_f}{2} \right)

]

Since the logarithm base 10 of a number is equal to 1 when that number is 10, we have:

[

\frac{I_f}{2} = 10

]

Multiplying both sides by 2 gives:

[

I_f =