Question

L = loudness, in decibels (dB); I = sound intensity, in watts/m2; I0 = 10−12 watts/m2

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.

Answer 1

The sound intensity of the Pile Driver is 39.5
 or nearly 40 times the sound intensity of the jackhammer.


Given with Loudness in dB for pile driver = 112 dB
We have to convert it in terms of sound intensity.
First,
112dB/10 = 11.2 

Then we'll use this as exponent of 10
(10)^(11.2) = 1.5849 * 10 ^ 11

Then use the equation of Watts per square meter to find the intensity:
I / (10^-12 W/m^2) =1.5849 * 10 ^ 11
I = sound intensity = 0.158

Then compare:

Sound intensity of Pile Driver/ Sound intensity of Jackhammer
(0.158) / (0.004)
= 39.5
or nearly 40 times the jackhammer.

Answer 2

The sound intensity of the Pile Driver is 39.6  times the sound intensity of the jackhammer.

The given parameters are:

$L_p = 112dB$ --- the loudness of the pile driver

Start by converting the loudness as follows:

$L_p = \frac{112dB}{10}$

$L_p = 11.2dB$

Next, calculate the sound intensity (I) using:

$\frac{I}{10^{-12}}=10^{L_p}$

Substitute 11.2dB for Lp

$\frac{I}{10^{-12}}=10^{11.2}$

Make I the subject of formula

$I=10^{11.2} \times 10^{-12}$

$I=0.1585$

Lastly, we compare the sound intensities of the pile driver, and the jack hammer.

$I = \frac{I_p}{I_j}$

This gives

$I = \frac{0.1585}{0.004}$

Divide

$I = 39.6$

Hence, the sound intensity of the Pile Driver is 39.6  times the sound intensity of the jackhammer.

Read more about sound intensities at:

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