Final answer:
The decibel level for a sound with an intensity of about 3.0 x 10⁻⁶ Wm⁻² is approximately 70 dB, which is option B. The intensity of a 100 dB sound is about 1.0 x 10⁻⁴ W/m².
Step-by-step explanation:
The student is asking about the decibel level for a sound with an intensity of about 3.0 x 10⁻⁶ Wm⁻² and the intensity for a sound that corresponds to 100 dB. To find the decibel level from intensity, we can use the formula:
ß = 10 × log10(I/I0),
where ß is the decibel level, I is the intensity of the sound in watts per meter squared, and I0 is the reference intensity, typically set at the threshold of human hearing (1.0 x 10⁻¹² W/m²). Plugging the given intensity into the formula, we have:
ß = 10 × log10(3.0 x 10⁻⁶ / 1.0 x 10⁻¹²)
This calculation yields a decibel level of approximately 70 dB, which corresponds to option B. For the second part, the intensity I for a 100 dB sound can also be calculated by rearranging the formula:
I = I0 × 10⁽ß/10)
Substituting ß with 100 and I0 with 1.0 x 10⁻¹² gives us an intensity of about 1.0 x 10⁻⁴ W/m² for a sound level of 100 dB.