The loudness of a diesel truck in decibels when the diesel truck is travelling at 40 miles per hour, 50 feet away, intensity 10 times that of a passenger car travelling 50 miles per hour, 50 feet away, whose loudness is 70 decibel and loudness L ( x ) is given by L ( x ) = 10 log x I 0 , where x is the intensity of sound measured in watts per square meter and I 0 = 10 − 12 watt per square meter is the least intense sound that human ear can detect.
The loudness of a diesel truck in decibels when the diesel truck is travelling at 40 miles per hour, 50 feet away, intensity 10 times that of a passenger car travelling 50 miles per hour, 50 feet away, whose loudness is 70 decibel and loudness L ( x ) is given by L ( x ) = 10 log x I 0 , where x is the intensity of sound measured in watts per square meter and I 0 = 10 − 12 watt per square meter is the least intense sound that human ear can detect.
Solution Summary: The author determines the loudness of a diesel truck in decibels when the truck is travelling at 40 miles per hour, 50 feet away.
The loudness of a diesel truck in decibels when the diesel truck is travelling at 40 miles per hour, 50 feet away, intensity 10 times that of a passenger car travelling 50 miles per hour, 50 feet away, whose loudness is 70 decibel and loudness L(x) is given by L(x)=10logxI0, where x is the intensity of sound measured in watts per square meter and I0=10−12 watt per square meter is the least intense sound that human ear can detect.
Expert Solution & Answer
Answer to Problem 130AYU
Solution:
The loudness of the truck is 80 decibels
Explanation of Solution
Given information:
The diesel truck is travelling 40 miles per hour, 50 feet away, intensity 10 times of a passenger car travelling 50 miles per hour, 50 feet away, whose loudness is 70 decibel loudness L(x)=10logxI0 and I0=10−12 watt per square meter.
Explanation:
Loudness is defined as L(x)=10logxI0
Loudness of the passenger car 70=10logx10−12
Divide both sides by 10,
⇒7=logx10−12
As y=logax and x=ay, where a>0 and a≠1, are equivalent
Change 7=logx10−12 to the exponential form,
⇒107=x10−12
⇒x=10−5
So, the intensity of the car is x=10−5
The intensity of the truck is 10 times the intensity of the passenger car
Intensity of the truck 10⋅10−5=10−4
Loudness of the diesel truck L(10−4)=10log10−410−12
=10log(108)
=10⋅8
=80
Therefore, the loudness of the truck is 80 decibels
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