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 approximately 40 times that of the jackhammer when calculated using the decibel difference and rounded to the nearest ten.

Step-by-step explanation:

To find out how many times the sound intensity of the pile driver is the sound intensity of the jackhammer, we use the following formula to relate decibel levels and intensities:

L = 10 × log10(I / I0) (1).

Where L is the loudness in decibels, I is the sound intensity in watts per square meter, and I0 = 10⁻¹² W/m² is the reference intensity. The intensity level of a sound that is ten times more intense than another is 10 dB greater. Consequently, every 10 dB increase represents a tenfold increase in sound intensity.

Given that the loudness of the jackhammer is 96 dB and the loudness of the pile driver is 112 dB, we can calculate the difference in decibels:

ΔL = 112 dB - 96 dB = 16 dB.

Since we know that a 10 dB increase corresponds to a tenfold increase in intensity, a 16 dB increase would correspond to 1.6 tenfold increases. In other words, the pile driver's intensity is 10¹.6 times that of the jackhammer. Expressing it as 10¹.6:

10¹.6 = 10 x 10⁰.6 ≈ 10 x 4 = 40.

Therefore, the sound intensity of the pile driver is approximately 40 times that of the jackhammer when rounded to the nearest ten.

Answer 2

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.