During takeoff, the sound intensity level of a jet engine is 170db at a distance of 34 m. what's the sound intensity level at a distance of 1.0 km?

Explanation:

Sound intensity level is a logarithmic quantity and is defined as:

Where:

is the sound intensity

is the reference sound intensity

In this case we are given a sound intensity (during takeoff at a distance ):

(1)

Now, from (1) we have to find .

Dividing both sides of the equation by :

(2)

(3)

Applying logarithm properties on both sides:

(4)

Isolating :

(5)

(6)

(7) This is the sound intensity at a distance of 34 m

On the other hand, we know the sound intensity is inversely proportional to the square of the distance :

This means:

 (7)

Where

Finding from (7):

 (8)

 (9)

 (9) This is the sound intensity at a distance of 1km

Now, knowing the value of we will be able to find the sound intensity level at a distance of 1km:

(10)

(11)

Finally:

(12) This is the sound intensity level at a distance of 1 km.

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