The loudness, L. measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as

L - 10log , where lo - 10- and is the least intense sound a human ear can hear. Jessica is listening to soft music at a

sound intensity level of 109 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 on her headphones. How many times louder is Braylee's music

than Jessica's?

Option A is correct.

Braylee's music is 3 times louder than Jessica's.

Step-by-step explanation:

Full Complete Questions

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as

L = 10log (I/I₀), where lo = 10⁻¹² W/m²

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 W/m² 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 W/m² on her headphones. How many times louder is Braylee’s music than Jessica’s?

times louder

3 times louder

30 times louder

90 times louder

Solution

The loudness of a sound intensity is given as

L = 10 log (I/I₀)

For Jessica

I = 10⁻⁹ W/m²

I₀ = 10⁻¹² W/m²

L = 10 log (10⁻⁹/10⁻¹²)

L = 10 log (10³)

L = 10 × 3 = 30 dB

For Braylee

I = 10⁻³ W/m²

I₀ = 10⁻¹² W/m²

L = 10 log (10⁻³/10⁻¹²)

L = 10 log (10⁹)

L = 10 × 9 = 90 dB

How many times louder is Braylee's music than Jessica's?

The factor by which Braylee's music is louder than Jessica's = (90/30) = 3

Braylee's music is 3 times louder than Jessica's.

Hope this Helps!!!