Trumpet players, sound intensity level

[LBRRIT2390]

Homework Statement

Five trumpet players have a sound intensity level of 75dB. What would be the sound intensity level of 30 such trumpet players? _______dB

Homework Equations

Increasing the sound intensity by a factor of 10 results in an increase in perceived loudness by approx. a factor of 2.

Beta = (10dB)log₁₀(I/I₀)
Where I₀ = 1.0x10^-12 W/m²

The Attempt at a Solution

I tried finding a ratio and applying that to the 2nd situation but my answers were wrong. Can someone please help me ASAP!

Thank you!

 

[ideasrule]

10 dB=1 bel, and that's 10^1. 100 dB=10 bel, and that's 10^10. 75=7.5 bel, which is equal to what power of ten?

 

[LBRRIT2390]

0.75?
3/4?

 

[TeacherRay]

The 30 trumpeters will be 6 times greater intensity than the 5 trumpeters. The ratio in decibels all "drop out" leaving log(6) = 0.78 (about).
30 trumpeters are louder than 6, so to get the new decibels it is 75 / 0.78 = 96 decibels.

Logic check - 6 x intensity is < 10 x, so we expect the difference in decibels to be < 2x.

cheers!