Refer to this example for a review of the concepts that play roles in this probl

Question

Refer to this example for a review of the concepts that play roles in this problem. Civil engineers use a transit theodolite when surveying. One version of this device determines distance by measuring the time required for an ultrasonic pulse to reach a target, reflect from it, and return. When calibrated properly, the device uses the speed of sound appropriate for the ambient air temperature to determine the distance between the theodolite and the target. Suppose a theodolite is calibrated so that it gives the correct value for a distance when used at a temperature of 290 K. When used at a temperature of 299 K, however, the device gives an incorrect value for the same distance. What percentage error would there be in the incorrect value measured by the theodolite? Is the incorrect value smaller than or greater than the correct value? Assume that air behaves as an ideal gas, so that v = sqrt kT m applies.

I understand part b. I just don't understand how to calculate the percent error. I already tried 299-290/299 x 100% and 299-290/290x 100%. I'm at a loss.

Explanation / Answer

As distance =Velocity *time

And velocity increases as the temperature rises thus the distance measured will be smaller as time measured will be smaller in case of higher temperature

Thus percentage error will be = [Sqrt(290)-sqrt(299)]*100/sqrt(290)

=-1.54%

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