Final answer:
To determine the sound intensity level at Hensville Park (570 m away), we use the inverse square relationship of sound intensity with distance. By knowing the intensity at the Maritime Academy (669 m away) is 0.2 W/m², we can calculate that the intensity at Hensville Park is approximately 0.2755 W/m². Then, we can calculate the sound intensity level in decibels using the standard formula.
Step-by-step explanation:
The question asks to determine the sound intensity level at a location that is 570 meters away from the source of the fireworks, given that the sound intensity is 0.2 W/m² at another location that is 669 meters away. The sound intensity I is related to the distance r from the source in an inverse square relationship, given by the formula I = P / (4πr²), where P is the power of the sound source.
For two different distances, r1 and r2, from the same sound source, this relationship implies that I1 / I2 = (r2²) / (r1²). Using the distance r1 = 669 m and r2 = 570 m and the intensity I2 = 0.2 W/m² at r1, we can calculate the intensity I1 at r2.
Since I1 / 0.2 W/m² = (669 m / 570 m)²,
then I1 = 0.2 W/m² × (669 m / 570 m)².
I1 = 0.2 W/m² × (1.1737)²
I1 = 0.2 W/m² × 1.3776
I1 ≈ 0.2755 W/m²
The sound intensity level L in decibels (dB) can be found using the formula L = 10 × log10(I / I0), where I0 = 1× 10⁻¹² W/m² is the reference intensity level. Substituting the calculated intensity gives the intensity level at the 570 m location.