The same student also wants to measure the wind speed. The owner\'s manual for h

Question

The same student also wants to measure the wind speed. The owner's manual for his anemometer states it can measure wind speeds to a precision of plusminus 03 km/hr. However during a five-minute period of time, the digital readout shows a fluctuating number that ranges from 8.7 to 112 km/hr. The fluctuations seem to be evenly distributed throughout this range. So the student decides to use the middle value in this range for the wind speed. What should he record as an error/uncertainty in this value? What category does the plusminus 03 km/hr error fall into? If the fluctuations do not appear to be evenly distributed throughout this range, what procedure should the student use to obtain an approximate idea of how the wind speed is distributed? If the fluctuations do not appear to be evenly distributed throughout this range, what procedure should the student use to determine one best value for the wind speed and an error in this value?

Explanation / Answer

5. as the readings are evenly spread out from 8.7 to 11.2 km/hr

average reading = (11.2 + 8.7)/2 = 9.95 km/hr

error in reading = +-(11.2 - 8.7)/2 = +-1.25 km/hr

6. This error is not because of instrument error but because of fluctuating intrinsic property of the fluiud ( air in this case)

so this error falls into intrinsic random error of the air category

7. the +-0.3 km/hr is nothing but the least count of the instrument, and falls into systematic instrument error

8. if the wind speed is not evenly distributed, the student should plot the windspeed with time and try to see where does the windspeed lie in most of the time to gbet an approximate idea of the windspeed

9. if the fluctuations are not evenly distributed, then weighted average has to be taken

divide the readinngs into smaller classes of gaps of lets say 0.1 km/hr, and find out how many readings fall into that category

then, multiply the number of readings falling into that category( weight) by the actual reading , take the sum of all such weighed readings and divide b y total number of readings

this weighed average gives a good approximation to the value of the windspeed outisde

the error in this reading can be found by this formula

error = sqroot(sum of(xi - x)^2)/N

where xi is ith reading

x is the value of speed as stated

N is total number of readings

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