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The velocity V of sound in air at temperature T is given

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 3.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

The velocity  of sound in air at temperature  is given by , where  is measured in kelvins  and  is in . Assume that . Estimate , and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 4E

Step1 of 2:

We have velocity of sound in air = V

                               Temperature = T.

Also we have V =  and T = 3000.4K that is

Where V is measured in m/s. And T is measured in Kelvin.

We need to find the uncertainty in the estimate.


Step2 of 2:

Consider

V =  

       = 20.04

 = 347.1029

Hence, V = 347.1029.

Again consider the function V =  

Differentiate above equation with respect to T we get

  = 20.04

    = 20.04

       = 20.040.0577

                                                 = 1.1570

Hence, = 1.1570.

Now,

The estimate of uncertainty is given by

 

                  =

     = 0.4627

                                                      = 0.4627

Hence, = 0.4627.

Therefore, The estimate of uncertainty is V = 347.10290.4627.


Conclusion:

The estimate of uncertainty is V = 347.10290.4627.

 

 

Step 2 of 3

Chapter 3.3, Problem 4E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

This full solution covers the following key subjects: estimate, measured, air, Find, given. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 4E from 3.3 chapter was answered, more than 518 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 4E from chapter: 3.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “?The velocity of sound in air at temperature is given by , where is measured in kelvins and is in . Assume that . Estimate , and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 33 words.

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The velocity V of sound in air at temperature T is given