The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by Find the rate of change in the number of decibels when the intensity is watt per square centimeter.Round your answer to the nearest decibel.
A) 317 decibels per watt per square cm
B) 25,645 decibels per watt per square cm
C) 2,849 decibels per watt per square cm
D) 230,802 decibels per watt per square cm
E) 2,851 decibels per watt per square cm

Question

​The relationship between the number of decibels β and the intensity of a sound I in watts per square centimeter is given by  Find the rate of change in the number of decibels when the intensity is  watt per square centimeter.Round your answer to the nearest decibel.
A) ​317 decibels per watt per square cm 
B) ​25,645 decibels per watt per square cm 
C) ​2,849 decibels per watt per square cm 
D) ​230,802 decibels per watt per square cm 
E) ​2,851 decibels per watt per square cm

Quizplus · Accepted Answer

Taking the derivative of the given equation with respect to I, we get:

β' = (10/ln10) * (1/I)

Plugging in I = 0.0192, we get:

β' = (10/ln10) * (1/0.0192) ≈ 2,849 decibels per watt per square cm (rounded to the nearest decibel).

Therefore, the best choice is C.

​The Relationship Between the Number of Decibels β and the Intensity

The Relationship Between the Number of Decibels β and the Intensity