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

Answer:

72.04 dB.

Explanation:

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

$60dB = 10log(\dfrac{I}{I_0} )$

where $I_0 = 1*10^{-12}W/m^2$

solving for $I$ we get:

$6 = log(\dfrac{I}{I_0} )$

$10^6 =\dfrac{I}{1*10^{-12}}$

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

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

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

which on the decibel scale gives

$dB = 10log(\dfrac{16*10^{-6}}{1*10^{-12}} )$

$dB = 72.04\: dB$.

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