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

40 dB

100 dB

Step-by-step 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* log(I)/(I_0)\\\Rightarrow I(dB)=10* log(10^(-8))/(10^(-12))\\\Rightarrow I=40\ dB`

The intensity of "pianississimo" is 40 dB

`I(dB)=10* log(I)/(I_0)\\\Rightarrow I(dB)=10* log(10^(-2))/(10^(-12))\\\Rightarrow I=100\ dB`

The intensity of "fortississimo" is 100 dB