Final answer:
The sound intensity level of a jet engine at 1.0 km from the source will be approximately 109.6 dB, calculated using the inverse square law formula for sound propagation.
Step-by-step explanation:
To determine the new sound intensity level at a distance of 1.0 km from a jet engine that has a sound intensity level of 140 dB at 30 m, we will use the inverse square law for sound intensity. The inverse square law states that the sound intensity level decreases by 6 dB each time the distance from the source is doubled. However, for a large change in distance, it is more accurate to use the formula:
L2 = L1 - 20 log10(d2/d1)
Where L2 is the new sound intensity level, L1 is the original sound intensity level (140 dB), d2 is the new distance (1.0 km or 1000 m), and d1 is the original distance (30 m). Plugging in the values we get:
L2 = 140 dB - 20 log10(1000 m / 30 m)
L2 = 140 dB - 20 log10(33.33)
L2 = 140 dB - 30.4 dB
L2 = 109.6 dB
Therefore, the sound intensity level at a distance of 1.0 km from the jet engine is approximately 109.6 dB, which is still quite loud but significantly lower than the 140 dB experienced at 30 m.