1. You use a sound intensity meter scaled in dB. You measure the sound level pro

Question

1. You use a sound intensity meter scaled in dB. You measure the sound level produced by a single trombone player, and your instrument shows 76 dB. Now, the single player is joined by 75 more players, so there are 76 trombones, all playing at the same power. What's the sound intensity your instrument shows now?

2. The problem is similar as the last question -- but now the player playing at the 76db level was joined by 80 other players, making the total number of them equal to 81. The increase of SIL is therefore 10*log(81)dB = 19.1dB, and the new SIL is 95.1dB. However, there is also a question by how much the pressure amplitude of the sound wave increases. Try to figure out.

Please provide your thoroughly calculation and the formula you used as well as the explanation.

Explanation / Answer

1) for a single player, the sound intensity level SIL =10*log(I/Io)dB = 76bB. When the single player is joined by 75 others, the sound's power I increases 76 times, right? So the new sound intensity level is now
SIL' = 10*log(76*I/Io)dB.
We take advantage of the log property: log(x*y) = log(x) + log(y) -- so that
SIL' = 10*[log(76)+log(I/Io)]dB = 10*log(76)dB + 10*log(I/Io).
The second term is "the initial SIL", equal to 76dB. Hence, SIL' is larger than "the initial SIL" by 10*log(76)dB = 18.8 dB, and the new sound intensity level is SIL' = 94.8dB.
I used the number of 76 for both the initial decibels and for the number of players -- just "to make the problem a bit funny". But the same solution scheme will work, of course, for any other number combination. For instance, for the initial SIL = 80db and for 99 new players, the increase in SIL will be 10*log(100)db = 20 dB, and the new sound intensity level is SIL' = 80dB + 20dB = 100db.

2)

SIL is therefore 10*log(81)dB = 19.1dB, and the new SIL is 95.1dB.

I =    intensity [W/m2]
Pmax = pressure amplitude [Pa]
=    density [kg/m3]
v =    wave speed [m/s]

I = P2max/2v

P2max= I*2v

Pmax=( I*2v)-2

we know I

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