5 Sound is measured in a logarithmic scale using a unit call

5. Sound is measured in a logarithmic scale using a unit called a decibel. The formula looks similar to the Richter scale for earthquakes:

d = 10 log(P/Po) where P is the power or intensity of the sound and Po is the weakest sound that the human ear can hear. One hot water pump has a noise rating of 50 decibels. One dishwasher, however, has a noise rating of 62 decibels. The dishwasher noise is how many time more intense than the hot water pump noise?

Solution

given d = 10 log(P/Po)

hot water pump has a noise rating of 50 decibel

50 = 10 log(P_waterpump/Po)

log(P_waterpump/Po)=5

(P_waterpump/Po)=10⁵

P_waterpump=10⁵Po

dishwasher has a noise rating of 62 decibels

62 = 10 log(P_dishwasher/Po)

log(P_dishwasher/Po) =6.2

(P_dishwasher/Po) =10^6.2

P_dishwasher=Po 10^6.2

P_dishwasher/P_waterpump=(Po 10^6.2)/(Po 10⁵)

P_dishwasher/P_waterpump=10^6.2-5

P_dishwasher/P_waterpump=10^1.2

P_dishwasher=10^1.2P_waterpump

P_dishwasher=15.85*P_waterpump

dishwasher noise is 15.85 times more intense than the hot water pump noise