Question

The loudness of s pile driver is 112dB . About how many times the sound intensity of a pile driver? round to the nearest ten

Answer 1

Answer: 40 ( to the nearest ten)

Explanation:

Complete question :

The loudness of a jack hammer is 96 dB . Its sound intensity is about 0.004.

The loudness of a compactor is 94 dB . Its sound intensity is about 0.0025.

The sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor.

The loudness of a pile driver is 112 dB . About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.

Given that:

Sound intensity of jackhammer = 0.004

Sound intensity of compactor = 0.0025

Sound intensity of jackhammer is about 1.6 times the sound intensity of a compactor

Each factor of 10 in intensity corresponds to 10dB

Pile driver with loudness of 112dB ⇒
`(112)/(10)=11.2`

Hence, 10^11.2 = 1.58489 × 10^11

Hence, sound intensity (I) in watts per m²

I = 1.58489 × 10^11 × 10^-12

I = 1.58489 × 10-1

I = 0.158489

Comparing the intensity of pile driver and jackhammer :

Intensity of piledriver / Intensity of jackhammer

`(0.158489)/(0.004)`

= 39.622 ≅ 40 ( to the nearest ten )

Answer 2

`db = 10 log_(10) ((I)/(I_o))`

With db =112 db,
`I_o =10^(-12) W/m^2` and solving for I the intensity we have:

`(db)/(10)= log_(10) ((I)/(I_o))`

`(112)/(10)= log_(10) ((I)/(10^(-12)))`

Now we can exponentiate with base 10 and we got:

`10^(11.2) = (I)/(10^(-12))`

And solving we got:

`I= 10^(-12) * 10^(11.2) = 0.158 (W)/(m^2) = 0.16 (W)/(m^2)`

Explanation:

We knwo that the loudnes os 112 db and we want to find the intensity. So then we can use the following formula:

`db = 10 log_(10) ((I)/(I_o))`

With db =112 db,
`I_o =10^(-12) W/m^2` and solving for I the intensity we have:

`(db)/(10)= log_(10) ((I)/(I_o))`

`(112)/(10)= log_(10) ((I)/(10^(-12)))`

Now we can exponentiate with base 10 and we got:

`10^(11.2) = (I)/(10^(-12))`

And solving we got:

`I= 10^(-12) * 10^(11.2) = 0.158 (W)/(m^2) = 0.16 (W)/(m^2)`