The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 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?
Answers
Given : The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter,
L = 10 log (I / I₀) I₀ = 10⁻¹²
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.
To Find : How many times louder is Braylee’s music than Jessica’s?
Solution:
L = 10 log (I / I₀) I₀ = 10⁻¹²
Jessica is listening to soft music at a sound intensity level of 10⁻⁹
=> L = 10 log ( 10⁻⁹ / 0⁻¹² )
=> L = 10 log (10³ )
=> L = 10 * 3
=> L = 30 Db
Braylee is listening to very loud music at a sound intensity level of 10⁻³
=> L = 10 log ( 10⁻³ / 0⁻¹² )
=> L = 10 log (10⁹ )
=> L = 10 * 9
=> L = 90 Db
90 = 3 * 30
Braylee’s music is 3 times louder than jessica
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Answer:
B. 3 times louder
Step-by-step explanation: