Sound attenuation is an important in fabricating walls betweenrooms in luxury hotels. Three wall cavity fillers have beenidentified for use. The desired reduction in sound is based on thedecibel level heard on the opposite side of a wall from the sidewhere the sound intensity is at 88 decibels using the A weightingmethod. The sound heard in an adjoining room should be no more than57 decibels. The science of sound is that sound is a wave with themagnitude of the sound measured as pressure (P). The formula forthe decibel scale is 20*log(P/P_ref) whereP_ref = 20 µPa. One µPa is equal to 10^-6Pa.

a. What is the P of 88 decibels inpascals?    

b. What is the P of 57 decibels inpascals?     

For this problem, sound attenuation rating of material ismeasured by the fraction of sound pressure that penetrates througha layer of material thickness. A material rated as 0.75 per inchmeans the sound intensity pressure after passing through an inch ofmaterial is 75 percent of the starting value. Sound attenuationbased on this measure is geometric so if there was 2 inches ofmaterial the resultant sound pressure intensity would be the ratingsquared or 0.75² of the starting pressure. When sizingthe thickness to meet a specified sound reduction the practice isto round up to the next quarter of inch (0.25 inch) unit. If thecalculated needed thickness was 1.64 inches the rounded updimension would be 1.75 inches and all calculations and designsizing would use that dimension. Use the data on the materialslocated below to answer the questions.

Material	Sound Rating	Cost per cubic foot
A	0.36	3.05
B	0.29	3.30
C	0.40	2.40

c. What is the design thickness ofMaterial A is required to meet thespecification?   

d. What is the design thickness ofMaterial B?

e. What is the design thickness ofMaterial C?   

f. What is the cost per square foot ofwall based on the thickness calculated above using the materialthat is the most expensive to install in a wall to meet thespecification?   

g. What is the cost per square foot ofwall based on the thickness calculated above using the materialthat is the least expensive to install in a wall to meet thespecification?