Question

How do I measure the uncertainty (accuracy) on the frequency of an alternating current source during an experiment from measurements of frequencies like 800.35 Hz, 799.35, 798.78 and 797.09 Hz?

Answer 1

To measure the uncertainty (accuracy) on the frequency of an alternating current source using the provided measurements, you can calculate the standard deviation, which provides an estimate of the spread or variability in the data set. The standard deviation reflects the uncertainty in the measured frequencies.

Here's a step-by-step process to calculate the standard deviation:

1. Calculate the mean (average) of the measured frequencies by summing up all the values and dividing by the total number of measurements. In this case: Mean = (800.35 Hz + 799.35 Hz + 798.78 Hz + 797.09 Hz) / 4

2. Calculate the deviation for each measurement by subtracting the mean from each individual frequency. The deviation represents the difference between each measurement and the average.

3. Square each deviation to eliminate negative signs and emphasize the magnitude of differences.

4. Calculate the mean of the squared deviations by summing up all the squared deviations and dividing by the total number of measurements.

5. Take the square root of the mean of the squared deviations to obtain the standard deviation. This value represents the uncertainty (accuracy) associated with the measured frequencies.

The standard deviation provides a measure of the spread or uncertainty in the data set. A larger standard deviation indicates greater variability and hence higher uncertainty.

Note that this calculation assumes that the measured frequencies follow a normal distribution. If there are specific systematic errors or other factors that might affect the accuracy differently, additional considerations may be necessary.