Solve the solution.

Question

Solve the solution.

 

Sound levels in decibels (db) can be computed by f(x) = 160 + 10 log x, where x is the intensity of the sound in watts per square centimeter. The intensity of sound is 10^-5 watts per square centimeter. how many decibles does this quantity represent. What is the sound level?

 

decibles = ?

Answer 1

Hi Keith;

Sound levels in decibels (db) can be computed by f(x) = 160 + 10 log x, where x is the intensity of the sound in watts per square centimeter. The intensity of sound is 10^-5 watts per square centimeter. how many decibles does this quantity represent. What is the sound level?

f(x)=160+10 log x

f(x)=160+10 log 10^-5

10 log 10^-5=[(-5)(10)] log 10=-50 log 10

f(x)=160-(50 log 10)

log₁₀10=1

f(x)=160-50

f(x)=110

Answer 2

f(10^-5) = 160 + 10 log(10^-5)

 

= 160 + 10(-5)(log(10)) by Power Rule of Logarithms

 

= 160 - 50 = 110 dB sound level