EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.3, Problem 80E

To determine

Tofind:the difference in loudness between an average office with an intensity of 1.26×10−7 watt per square meter and a broadcast studio with an intensity of 3.16×10−10 watt per square meter.

Expert Solution & Answer

Answer to Problem 80E

26 dB

Explanation of Solution

Given:

The relationship between the number of decibels β and the intensity of a sound I (in watts per square meter) is:

β=10logI10−12=10(logI+12)

Concept Used:

Product property of logarithm states that for a positive real numbers a such that a≠1 :

loga(uv)=logau+logav

Power property of logarithm states that for a positive real numbers a such that a≠1 :

logaun=nlogau

Quotient property of logarithm states that for a positive real numbers a such that a≠1 :

loga(uv)=logau−logav

First find the number of decibels in average office with an intensity of 1.26×10−7 watt per square meter

Substitute I=1.26×10−7 in β=10(logI+12) ,

βoffice=10(log(1.26×10−7)+12)

Using product property,

βoffice=10(log(1.26)+log(10−7)+12)

Using the power property,

βoffice=10(log(1.26)−7log(10)+12)

Using logbb=1 ,

βoffice=10(log(1.26)−7log10(10)+12)=10(log(1.26)−7+12)=10(log(1.26)+5)=10log(1.26)+50

Now, find the number of decibels in broadcast studio with an intensity of 3.16×10−10 watt per square meter

Substitute I=3.16×10−10 in β=10(logI+12) ,

βstudio=10(log(3.16×10−10)+12)

Using product property,

βstudio=10(log(3.16)+log(10−10)+12)

Using the power property,

βstudio=10(log(3.16)−10log(10)+12)

Using logbb=1 ,

βstudio=10(log(3.16)−10log10(10)+12)=10(log(3.16)−10+12)=10(log(3.16)+2)=10log(3.16)+20

Now find the difference,

βoffice−βstudio=10log(1.26)+50−(10log(3.16)+20)=10log(1.26)+50−10log(3.16)−20=10[log(1.26)−log(3.16)]+30

Using quotient property,

βoffice−βstudio=10[log(1.263.16)]+30≈26

Hence, the difference in loudness is approximately 26 dB.

Chapter 3.3, Problem 79E

Chapter 3.3, Problem 81E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 51E Ch. 3.5 - Prob. 52E Ch. 3.5 - Prob. 53E Ch. 3.5 - Prob. 54E Ch. 3.5 - Prob. 55E Ch. 3.5 - Prob. 56E Ch. 3.5 - Prob. 57E Ch. 3.5 - Prob. 58E Ch. 3.5 - Prob. 59E Ch. 3.5 - Prob. 60E Ch. 3.5 - Prob. 61E Ch. 3.5 - Prob. 62E Ch. 3.5 - Prob. 63E Ch. 3.5 - Prob. 64E Ch. 3.5 - Prob. 65E Ch. 3.5 - Prob. 66E Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - 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Tofind: the difference in loudness between an average office with an intensity of 1.26 × 10 − 7 watt per square meter and a broadcast studio with an intensity of 3.16 × 10 − 10 watt per square meter.

Concept explainers

Videos

Tofind:the difference in loudness between an average office with an intensity of 1.26×10−7 watt per square meter and a broadcast studio with an intensity of 3.16×10−10 watt per square meter.

Answer to Problem 80E

Explanation of Solution

Chapter 3 Solutions