Understanding Measurement Uncertainty

What is the relative uncertainty of a measurement of 25.0 cm ± 0.5 cm?

Which formula is used to calculate the uncertainty in a reciprocal, like when finding the frequency from the period measurement?

If the period of a pendulum is measured as 1.50 s ± 0.03 s, what is the absolute uncertainty in the frequency calculated using the equation f = 1/T?

Why is it important to consider uncertainty in measurements and calculations?

Absolute Uncertainty

Relative Uncertainty

Propagation of Uncertainty

Uncertainty in Reciprocals

Uncertainty in Measurements

Uncertainty quantifies the doubt in a measurement, indicating data reliability.

Absolute Uncertainty

Absolute uncertainty is the numerical difference from the actual value of the measurement.
It has the same units as the measurement itself.
Example: 50.0 cm ± 0.2 cm, the 0.2 cm value is the absolute uncertainty.

Relative Uncertainty

Relative uncertainty expresses uncertainty as a fraction or percentage of the measured value.
Formula: Relative Uncertainty = (Absolute Uncertainty / Measured Value)
Example: For 50.0 cm ± 0.2 cm, the relative uncertainty is 0.2 cm / 50.0 cm = 0.004 (or 0.4%). This signifies the uncertainty is 0.4% of the total length.

Propagation of Uncertainty

Uncertainty propagates through calculations involving multiple measurements.
Example: Calculating pendulum frequency from period measurement.

Example: Pendulum Period and Frequency

Pendulum period: 2.00 s ± 0.05 s
Frequency (f) calculation: f = 1/T = 1/2.00 s = 0.500 Hz
To find uncertainty in frequency:
- Formula for uncertainty in reciprocals: Δf/f = ΔT/T
- Calculation: Δf/0.500 = 0.05 s / 2.00 s = 0.025
- Final result: Δf = 0.0125 Hz ≈ 0.01 Hz.
- Thus, the frequency is 0.500 ± 0.01 Hz.
This illustrates the impact of uncertainty on calculations.

This quiz covers the concepts of uncertainty in measurements, including absolute and relative uncertainty, as well as the propagation of uncertainty. You'll explore examples such as the pendulum period and frequency to reinforce your understanding of how measurement uncertainties affect data validity.