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jordan is a big fan of space, space travel, and rockets, so he's super excited to be attending the launch of spacex's new startship rocket. jordan's friend malik is also attending the launch, but they're at different locations. if jordan is 40% closer to the launch site than malik, how much louder (in decibels) will the rocket launch sound be than for malik? you may assume that the sound produced by the rocket as it launches is emitted uniformly in all directions.

User Sgnsajgon
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Answer:4.43 decibels louder for Jordan compared to Malik

Step-by-step explanation:

To determine how much louder the rocket launch sound will be for Jordan compared to Malik, we need to use the inverse square law. This law states that as you move away from a sound source, the intensity of the sound decreases by the square of the distance. In other words, if you double the distance from a sound source, the intensity decreases to one-fourth of its original level.

Let's assume that the sound produced by SpaceX's new Starship rocket is at a constant intensity and emitted uniformly in all directions. If Jordan is 40% closer to the launch site than Malik, then we can assume that Jordan is at a distance of 0.6x from the launch site, where x is the distance from Malik to the launch site.

Using the inverse square law, we can calculate how much louder the rocket launch sound will be for Jordan compared to Malik:

(intensity at Jordan's location) / (intensity at Malik's location) = (distance from Malik's location)^2 / (distance from Jordan's location)^2

(intensity at Jordan's location) / (intensity at Malik's location) = (x)^2 / (0.6x)^2

(intensity at Jordan's location) / (intensity at Malik's location) = 1 / 0.36

(intensity at Jordan's location) = 2.78 x (intensity at Malik's location)

To convert this ratio of intensities into decibels, we can use the formula:

L = 10 log10 (I/I0)

where L is the sound level in decibels, I is the intensity of the sound, and I0 is a reference intensity of 10^-12 W/m^2.

Assuming that the reference intensity I0 is constant for both locations, we can simplify this formula to:

L = 10 log10 (intensity)

Therefore, the sound level for Jordan compared to Malik can be calculated as:

L = 10 log10 (2.78 x intensity) - 10 log10 (intensity)

L = 10 log10 (2.78)

L = 4.43 dB

Therefore, the rocket launch sound will be approximately 4.43 decibels louder for Jordan compared to Malik.

User Joshua Ulrich
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