Question

The loudness level of a sound, D, in decibels, is given by the formula D =10 log(10"), where I is the intensity of the sound, in watts per square meter. Decibel levels range from 0, a barely audible sound, to 160, a sound that will rupture an eardrum. a. The sound of a blue whale can be heard 500 miles away, reaching an intensity of 6.3x10° watts per square meter. Determine the decibel level of this sound. At close range, can the sound of a blue whale rupture the human eardrum? Be sure to justify your conclusion. b. What is the decibel level of a normal conversation, 3.2x10 watts per square meter?

Answer 1

we have the equation

$D=10\log (10^{(12)}\cdot I)$

Part a) we have

I=6.3x10^6

substitute in the given formula and solve for D

$\begin{gathered} D=10\log (10^{(12)}\cdot6.3\cdot10^6) \\ D=10\log (6.3\cdot10^{(18)}) \\ D=188 \end{gathered}$

we have that

188 is greater than 160

therefore

the sound of blue whale can rupture the human eardrum

Part b

For I=3.2x10^-6

substitute in the given formula

$\begin{gathered} D=10\log (10^{(12)}\cdot3.2\cdot10^{(-6)}) \\ D=10\log (3.2\cdot10^{(6)}) \\ D=65.05 \end{gathered}$

answer part b is 65 decibels