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!

 

[rwisz]

I would approach this problem by first understanding the concept of sound intensity level and how it is measured. The sound intensity level is a logarithmic measure of the sound intensity, which means that a small change in the intensity level corresponds to a large change in the actual sound intensity. In addition, the human ear perceives a doubling of the sound intensity as an increase in loudness by a factor of 2.

In this scenario, we have five trumpet players with a sound intensity level of 75dB. If we want to know the sound intensity level of 30 such trumpet players, we can use the equation Beta = (10dB)log10(I/I0) to calculate the intensity level.

First, we need to find the ratio of the sound intensity of 30 trumpet players to that of 5 trumpet players. Since we know that an increase in sound intensity by a factor of 10 results in an increase in perceived loudness by a factor of 2, we can say that the ratio of 30 players to 5 players is 6:1. This means that the sound intensity of 30 players is 6 times greater than that of 5 players.

Next, we can plug this ratio into the equation to find the sound intensity level of 30 players:

Beta = (10dB)log10(6/1) = (10dB)log10(6) = 10(0.778) = 7.78dB

Therefore, the sound intensity level of 30 trumpet players would be 7.78dB higher than the sound intensity level of 5 players. Adding this to the initial intensity level of 75dB, we get a final intensity level of 82.78dB.

In conclusion, the sound intensity level of 30 trumpet players would be 82.78dB. It is important to note that this calculation assumes that the trumpet players are all playing at the same intensity level. If some players are playing louder or softer than others, the result may differ.