Question

One violin creates a sound whose intensity level is 60dB. Find the intensity level of 16 violins, each playing at this intensity.

Answer 1

72.04 dB.

Step-by-step explanation:

The intensity level of 60dB corresponds to the sound intensity
`I` given by the equation

`60dB = 10log((I)/(I_0) )`

where
`I_0 = 1*10^(-12)W/m^2`

solving for
`I` we get:

`6 = log((I)/(I_0) )`

`10^6 =(I)/(1*10^(-12))`

`\boxed{I = 1*10^(-6) W/m^2}`

Now, when 16 violins are playing the intensity
`I` becomes

`{I = 16(1*10^(-6) W/m^2)`

which on the decibel scale gives

`dB = 10log((16*10^(-6))/(1*10^(-12)) )`

`dB = 72.04\: dB`.

Thus, playing 16 violins together gives the intensity level of 72 dB.