Final answer:
The sound intensity level of a rocket engine with an intensity of 2.67 × 10⁻µ watts/cm² is approximately 34 decibels when converted and calculated using the standard formula for sound decibel levels.
Step-by-step explanation:
To find the number of decibels for the power of sound given, we can use the formula for sound intensity level in decibels, which is ß(dB) = 10 log10(I / Io). The reference intensity (Io) is 10⁻¹² W/m², which corresponds to the threshold of hearing, or 0 decibels. The intensity given is 2.67 × 10⁻µ W/cm², which we need to convert to watts per meter squared (W/m²) before plugging into the formula.
To convert to W/m², we multiply the intensity by 10´ because 1 m² = 10´ cm². Therefore, the intensity is 2.67 × 10⁻¹ W/m². Now, we use the formula:
ß(dB) = 10 log10(2.67× 10⁻¹/10⁻¹²) = 10 log10(2.67 × 10³) = 10(3.43) ≈ 34.3 dB.
After rounding to the nearest decibel, the sound intensity level of the rocket engine is approximately 34 dB.