Final answer:
To find the final intensity after a +3 dB increase from the initial intensity of 3 mW/cm², we double the intensity, resulting in a final intensity of 6 mW/cm².
Step-by-step explanation:
The question given is related to the concept of decibel levels and intensity changes in waves, specifically sound in this context. An initial intensity of a wave is 3 mW/cm2 (which is equivalent to 0.03 W/m2 when converted to standard SI units), and we are looking to find the final intensity after a 3 dB increase.
To calculate this, we use the formula for decibel change: ∆L = 10 log(I2/I1), where ∆L is the change in sound level in dB, I1 is the initial intensity, and I2 is the final intensity. Rearranging this formula to solve for I2 gives us I2 = I1 * 10^(∆L/10). A decibel change of +3 dB is equivalent to a doubling of the intensity. Therefore, if we double the initial intensity of 3 mW/cm2, we get a final intensity of 6 mW/cm2, which corresponds to option b.