Question

In music a very soft sound called "pianississimo" (ppp) might have an intensity of about 10^−8W/m^2. A very loud sound called "fortississimo" (fff) might have an intensity of about 10^−2W/m^2. /0 is 10−12 W/m^2 for sound.a. Convert the intensity of "pianississimo" to intensity level (units of dB).b. Convert the intensity of "fortississimo" to intensity level (units of dB).

Answer 1

Answer:

40 dB

100 dB

Explanation:

$I_0$ = Threshold frequency = $10^{-12}\ W/m^2$

I = Intensity = $10^{-8}\ W/m^2$

I = Intensity = $10^{-2}\ W/m^2$

The intensity level is given by

$I(dB)=10\times log\frac{I}{I_0}\\\Rightarrow I(dB)=10\times log\frac{10^{-8}}{10^{-12}}\\\Rightarrow I=40\ dB$

The intensity of "pianississimo" is 40 dB

$I(dB)=10\times log\frac{I}{I_0}\\\Rightarrow I(dB)=10\times log\frac{10^{-2}}{10^{-12}}\\\Rightarrow I=100\ dB$

The intensity of "fortississimo" is 100 dB