The velocity V of sound in air at temperature T is given by where T is measured in kelvins (K) and V is in m/s. Assume that T = 300 ± 0.4 K. Estimate V, and find the uncertainty in the estimate.

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.