Decibel Level Calculation for Rocket Engines

What is the decibel level created by a cluster of 2 rocket engines at a distance of 48 meters?

Given data: a rocket engine creates a decibel level of 129 db at a distance of 10 m.

Answer:

The decibel level created by a cluster of 2 rocket engines at a distance of 48 m is approximately 120 db.

When calculating the decibel level created by a cluster of 2 rocket engines at a distance of 48 meters, we need to consider the initial decibel level of a single rocket engine at a distance of 10 meters. In this case, the single rocket engine creates a decibel level of 129 dB at 10 meters.

Adding another identical sound source increases the total decibel level by about 3 dB. So, for a cluster of 2 rocket engines, we add 3 dB to the initial decibel level of 129 dB, resulting in approximately 132 dB.

However, sound intensity diminishes with distance according to the inverse square law. To calculate the new intensity at 48 meters, we use the formula:

I₂ = I₁ - 20log(d₂/d₁)

Where:

- I₁ is the initial intensity (129 dB)

- d₁ is the initial distance (10 m)

- d₂ is the new distance (48 m)

Plugging the values into the formula, we get:

I₂ = 129 dB - 20log(48/10) ≈ 117.34 dB

Since we are dealing with a cluster of 2 rocket engines, we add 3 dB to the calculated intensity, making the total decibel level approximately 120 dB. Therefore, a cluster of rocket engines at a distance of 48 meters would produce around 120 dB.