Trumpet players, sound intensity level

AI Thread Summary
The sound intensity level of five trumpet players is 75 dB, and the discussion revolves around calculating the intensity level for 30 trumpet players. It is noted that increasing sound intensity by a factor of 10 results in a perceived loudness increase of about 2. The attempt at a solution indicates that 30 trumpet players produce an intensity that is six times greater than that of five players. The calculation leads to an estimated sound intensity level of approximately 96 dB for 30 trumpet players, confirming that the increase is less than double the original level. The logic checks out, as the increase in decibels aligns with the expected intensity ratio.
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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!
 
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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?
 
0.75?
3/4?
 
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!
 

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