Respuesta :
The definition of decibels and the properties of logarithms allow us to find the intensity of the two speakers is 73 dβ
The sound is produced by the longitudinal vibrations of the air, it is medium in form of intensity that is defined by the relation between the power per unit area
I =[tex]\frac{P}{A}[/tex]
Where I is the sound intensity, P the power and A the area
The physical units of this magnitude are [watts/ m²]. The audible intensities by the human being range from 10⁻¹² to 10¹² w / m², this measurement range is very wide, it is practical to use a logarithmic scale for the measurement, defined by the relation
[tex]\beta = 10 \ log(\frac{I}{I_o} )[/tex]
Where β is the intensity, I and I₀ are the actual intensities and the reference intensity (minimum audible).
In this exercise indicate that the intensity of a speaker is 70 dβ, let's find the intensity that it emits
I = [tex]I_o \ 10^{\beta /10}[/tex]
Since the two speakers are the same intensity and are together, the total intensity is
[tex]I_{total} = 2 I[/tex]
Now let's find the intensity in decibels units is
[tex]\beta = 10 \ log ( \frac{2I}{Io} )[/tex]
Using the properties of logarithms
log (a + b) = log a + log b
β = 10 (log 2 + log[tex]\frac{I}{I_o}[/tex] )
β = 10 log 2 + 10 log [tex]\frac{I}{I_o}[/tex]
Let's calculate
β = 3.01 + 70
β = 73 dβ
In conclusion using the definition of decibels and the properties of logarithms we can encode the intensity of the two speakers is 73 dβ
Learn more about making sound intensity here:
https://brainly.com/question/3382513
