Question

Sound attenuation is an important in fabricating walls between rooms in luxury hotels. Three wall cavity fillers have been identified for use. The desired reduction in sound is based on the decibel level heard on the opposite side of a wall from the side where the sound intensity is at 88 decibels using the A weighting method. The sound heard in an adjoining room should be no more than 57 decibels. The science of sound is that sound is a wave with the magnitude of the sound measured as pressure (P). The formula for the decibel scale is 20*log(P/P_ref) where P_ref = 20 µPa. One µPa is equal to 10^-6 Pa.

a. What is the P of 88 decibels in pascals?    

b. What is the P of 57 decibels in pascals?     

For this problem, sound attenuation rating of material is measured by the fraction of sound pressure that penetrates through a layer of material thickness. A material rated as 0.75 per inch means the sound intensity pressure after passing through an inch of material is 75 percent of the starting value. Sound attenuation based on this measure is geometric so if there was 2 inches of material the resultant sound pressure intensity would be the rating squared or 0.75² of the starting pressure. When sizing the thickness to meet a specified sound reduction the practice is to round up to the next quarter of inch (0.25 inch) unit. If the calculated needed thickness was 1.64 inches the rounded up dimension would be 1.75 inches and all calculations and design sizing would use that dimension. Use the data on the materials located 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 of Material A is required to meet the specification?   

d. What is the design thickness of Material B?

e. What is the design thickness of Material C?   

f. What is the cost per square foot of wall based on the thickness calculated above using the material that is the most expensive to install in a wall to meet the specification?   

g. What is the cost per square foot of wall based on the thickness calculated above using the material that is the least expensive to install in a wall to meet the specification?

Answer 1