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raketka [301]
3 years ago
10

What is the decibel level of the sound of a monster truck with intensity 10−2 watts per square inch? Use a logarithmic model to

solve.
Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0

Answer:

BdB = 68.10 decibels

Step-by-step explanation:

BdB = 10 log10 I / Io

where BdB is the sound intensity level in decibels, I is the sound intensity on the linear scale (W / m²) and I0 is the hearing threshold (10^-12 W / m²).

Converting Io de 10^-12 W/m² to W/in², tenemos

10^-12 W/m² = 1.5500031000062x10^-9 W/in²

So, applying the equation or formula,

BdB = 10 log10 (10 ^ -2 W/in² / 1.5500031000062x10^-9 W/in² )

BdB = 10 log10 (0.64516x10^6)

BdB = 10 log10 (6,451,600)

Being log10 (6,451,600) = 6.8096674332398761189214526331036, then

BdB = 10 x 6.8096674332398761189214526331036

BdB = 68.096674332398761189214526331036

BdB = 68.10 decibels

Pie3 years ago
3 0

The decibel level of the sound of a monster truck is \fbox{\begin\\\ \beta(db)=68.1\\\end{minispace}}

Further explanation:

Decibel is defined as a unit which is used to measure the relative loudness or intensity of the sound.  

In the question it is given that the intensity of the sound of a monster truck is 10^{-2} watts per square inch.  

The formula which is used to calculate the decibel level of a sound is as follows:  

\fbox{\begin\\\ \beta(db)=10\text{log}\left(\dfrac{I}{I_{0}}\right)\\\end{minispace}}  

Here, I represents the intensity of the sound of a monster truck and I_{0} represents the threshold intensity of hearing at 1000\text{hz}.  

The value of the threshold intensity of hearing at 1000\text{hz} is 10^{-12} watts per square meter.  

This implies that the valiue of I_{0} is 10^{-12} watts per square meter.  

The intensity of the sound of a monster is given in unit of per square inch.  

The relation between per square inch and per square meter is as follows:    

\fbox{\begin\\\ 1\text{square inch}=\dfrac{1}{1550}\text{square meter}\\\end{minispace}}

So, the intensity of a monster truck is converted into per square meter as follows:  

10^{-12}\text{watts per square inch}=(\frac{10^{-2}}{1550}\text{watts per square meter})  

\fbox{\begin\\\ 10^{-12}\text{watts per square inch}=6.4516\times10^{-6}\text{watts per square meter}\\\end{minispace}}  

This implies that the value of I is 6.4516\times10^{-6} watts per square meter.

Now, substitute the value of I and I_{0} in the equation \fbox{\begin\\\ \beta(db)=10\text{log}(\frac{I}{I_{0}})\\\end{minispace}}.

\beta(db)=10\text{log}\left(\frac{6.4516\times10^_{-6}}{10^_{-12}}\right)

\beta(db)=10\text{log}(6451600)

\beta(db)=10\times6.809667

\fbox{\begin\\\ \beta(db)=68.09667433\\\end{minispace}}

The approximated value of the above equation is as follows:

\fbox{\begin\\\ \beta(db)=68.1\\\end{minispace}}

From the above calculation it is concluded that the decibel level of the sound of a monster truck is \fbox{\begin\\\ \beta(db)=68.1\\\end{minispace}}.

Learn more:

  1. A problem to complete the square of quadratic function brainly.com/question/12992613
  2. A problem to determine the slope intercept form of a line brainly.com/question/1473992
  3. Inverse function brainly.com/question/1632445  

Answer details

Grade: Middle school

Subject: Mathematics  

Chapter: Logarithms

Keywords:  Logarithms, sound, intensity, power of sound, watts, decibel, decibel level, monster truck, logarithm function, unit, conversion of unit, square inch, square meter.

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