Final answer:
The combined intensity of two sound sources with levels of 45.8 dB and 86.2 dB is approximately the sum of their individual intensities converted from decibel levels, which results in answer (b) 4.26 × 10-3 W/m².
Step-by-step explanation:
To calculate the combined intensity of two sources with sound levels of 45.8 dB and 86.2 dB, we must first convert each decibel level into intensity (W/m²) using the formula:
I = I0 × 10(level/10),
where I0 is the reference intensity, typically 10-12 W/m². Let's start by converting the 45.8 dB sound level to intensity:
I1 = 10-12 W/m² × 10(45.8/10),
which yields an intensity of 7.41 × 10-8 W/m². For the 86.2 dB sound level:
I2 = 10-12 W/m² × 10(86.2/10),
resulting in an intensity of 4.17 × 10-3 W/m². The combined intensity is the sum of these two intensities:
Itotal = I1 + I2,
thus Itotal = 7.41 × 10-8 W/m² + 4.17 × 10-3 W/m² which is approximately equal to 4.17 × 10-3 W/m², since the first intensity is much smaller, we can say the combined intensity is option (b) 4.26 × 10-3 W/m².