Question

The sound intensity level at a seat that is a distance of 2.00 meters from a rock concert stage is 120 dB. (a) Calculate the Intensity, I1 , of the sound in W/m2 at that position. (b) Calculate the sound level in dB at a seat that is 32 meters from the stage, given that the intensity decreases with the square of the distance from the source.

Answer 1

`1\ \text{W/m}^2`

`0.0039\ \text{W/m}^2`

Step-by-step explanation:

`I_1` = Intensity of sound at 2 m away

Sound level = 120 dB

`r_1` = 2 m

`r_2` = 32 m

`I_0` = Threshold of sound =
`10^(-12)\ \text{W/m}^2`

Sound level is given by

`dB=10\log ((I_1)/(I_0))\\\Rightarrow I_1=10^{(dB)/(10)}I_0\\\Rightarrow I_1=10^{(120)/(10)}* 10^(-12)\\\Rightarrow I_1=1\ \text{W/m}^2`

The intensity of sound at 2 m away is
`1\ \text{W/m}^2`

`I_1=(P)/(4\pi r^2)`

`I\propto (1)/(r^2)`

`(I_1)/(I_2)=(r_2^2)/(r_1^2)\\\Rightarrow I_2=(I_1r_1^2)/(r_2^2)\\\Rightarrow I_2=(1* 2^2)/(32^2)\\\Rightarrow I_2=0.0039\ \text{W/m}^2`

The intensity of the sound 32 m away is
`0.0039\ \text{W/m}^2`