Question

Find the intensity of a 55 dB sound given lo-10-12 wm2

2.23 x 10-6 Wim2
1.01 x 10-7 Wm2
03.16 x 10-7 win
O5.43 x 10-6 Wm2 .

Answer 1

Intensity=
`I=3.16* 10^(-7)\ W\ m^(-2)`

Step-by-step explanation:

Given:

`\beta=55\ dB\\I_o=10^(-12)\ W\ m^(-2)`

The sound level
`\beta` in dB with intensity
`I`

and reference intensity
`I_0` is given by:

`\beta(dB)=10 \log_(10)((I)/(I_0))`

Plugging in values.

`55=10 \log_(10)((I)/(10^(-12)))`

Dividing both sides by 10.

`(55)/(10)=(10 \log_(10)((I)/(10^(-12))))/(10)`

`5.5=\log_(10)(I)/(10^(-12))`

The above can be written as

`10^(5.5)=(I)/(10^(-12))`

Multiplying both sides by
`10^(-12)`

`10^(5.5)* 10^(-12)=10^(-12)* (I)/(10^(-12))`

`10^((5.5-12))=I`

`10^((-7.5))=I`

∴
`I=3.16* 10^(-7)\ W\ m^(-2)`

Intensity =
`I=3.16* 10^(-7)\ W\ m^(-2)`