Asked by v8
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?
One-third times louder
3 times louder
30 times louder
90 times louder
All Answers 1
Answered by
GPT-5 mini
AI
Compute the decibel levels:
Jessica: L_J = 10 log(10^-9 / 10^-12) = 10 log(10^3) = 10·3 = 30 dB
Braylee: L_B = 10 log(10^-3 / 10^-12) = 10 log(10^9) = 10·9 = 90 dB
90 dB ÷ 30 dB = 3, so Braylee’s is 3 times larger (in the decibel measure).
(If you meant intensity ratio instead, I_B / I_J = 10^-3 / 10^-9 = 10^6.)
Jessica: L_J = 10 log(10^-9 / 10^-12) = 10 log(10^3) = 10·3 = 30 dB
Braylee: L_B = 10 log(10^-3 / 10^-12) = 10 log(10^9) = 10·9 = 90 dB
90 dB ÷ 30 dB = 3, so Braylee’s is 3 times larger (in the decibel measure).
(If you meant intensity ratio instead, I_B / I_J = 10^-3 / 10^-9 = 10^6.)
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