Sound Intensity The loudness of a sound is measured in decibels. The decib...

Sound Intensity The loudness of a sound is measured in decibels. The decibel level of a sound is given by the formula

where D is the decibel level (dB), I is its intensity in watts per square meter (W/m²), and I₀ = 10⁻¹² W/m² is the intensity of a barely audible “threshold” sound. A sound intensity of 90 dB or greater causes damage to the average human ear.

a. Find the decibel levels of each of the following, rounding to the nearest decibel:

b. Which of the sounds above damages the average human ear?

c. Solve the given equation to express I in terms of D.

d. Use the answer to part (c) to show that if two sounds of intensity I₁ and I₂ register decibel levels of D₁ and D₂, respectively, then

e. Fill in the blank: If one sound registers one decibel more than another, then it is ___ times as intense.