Airplane sound level with one jet engine shut down

[smith22]

A person standing a certain distance from an airplane with three equally noisy jet engines is feeling a sound level intensity bordering on pain, 120dB. What sound level would this person experience if the captain shut down one engine?

this is what I did:
B-120=10log.33
and ended up with 125 dB as the intensity

What am I doing wrong since I am reducing the factor by 3 and its still not working?

 

[Doc Al]

I see two problems:

(1) The sound level should be lower with only two engines running: log.33 is negative.

(2) You have the wrong ratio of intensities: What's the ratio of intensities for 3 engines versus 2 engines?

 

[geosonel]

A person standing a certain distance from an airplane with three equally noisy jet engines is feeling a sound level intensity bordering on pain, 120dB. What sound level would this person experience if the captain shut down one engine?

this is what I did:
B-120=10log.33
and ended up with 125 dB as the intensity

What am I doing wrong since I am reducing the factor by 3 and its still not working?

let I₀ be ref sound intensity level
sound level (db) w/3 engines = 120 db = 10 log₁₀( 3(I/I₀) )
= 10 log₁₀(3) + 10 log₁₀( I/I₀ )
= 10 log₁₀(2*(3/2)) + 10 log₁₀( I/I₀ )
= 10 log₁₀(3/2) + 10 log₁₀(2) + 10 log₁₀( I/I₀ )
= 10 log₁₀(3/2) + 10 log₁₀( 2(I/I₀) )
= 10 log₁₀(3/2) + (sound level (db) w/2 engines)