Question

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as where and is the least intense sound a human ear can hear. Jessica is listening to soft music at a sound intensity level of 10-9 on her computer while she does her homework. Braylee is completing her homework while listening to very loud music at a sound intensity level of 10-3 on her headphones. How many times louder is Braylee's music than Jessica's?

Answer 1

the answer is B. or 3 times louder

Explanation:

Answer 2

The music that Braylee is listening is 3 times louder than the music Jessica is listening.

Explanation:

Given:

Sound Intensity level of Jessica music = {tex]10^{-9}[/tex]

Sound Intensity level of Braylee music = {tex]10^{-3}[/tex]

Now we convert intensity level to loudness of music.

we know that loudness is measured as,
`L=10*\,log\;(I)/(I_o)`

The loudness of music that Jessica is listening given by,

`L_j=10*\,log\;(10^(-9))/(10^(-12))=10*\,log\,10^3=10*3log\,10=30Db`

The loudness of music that Braylee is listening given by,

`L_j=10*\,log\;(10^(-3))/(10^(-12))=10*\,log\,10^9=10*9log\,10=90Db`

So, Number of time Braylee's music louder than Jessica's =
`(90)/(30)=3`

Therefore, The music that Braylee is listening is 3 times louder than the music Jessica is listening.