Final answer:
The two measurements of the speed of sound are consistent in both cases. The best estimate for the speed of sound is 335 m/s with a combined uncertainty of ±2 m/s for the first pair and ±5 m/s for the second pair. The second measurement in part (b), despite its large uncertainty, is consistent and therefore worth including.
Step-by-step explanation:
To determine whether two measurements of the speed of sound are consistent, we can compare their ranges. If their ranges overlap, the measurements are considered consistent.
(a) First Pair of Measurements
For the measurements 334±1 m/s and 336±2 m/s, the range for the first measurement is 333 to 335 m/s, and for the second measurement, it is 334 to 338 m/s. Since these ranges overlap, the two measurements are consistent. To find the best estimate of the speed of sound and its uncertainty, we average the means and combine the uncertainties in quadrature:
Best estimate of speed: (334 + 336) / 2 = 335 m/s
Combined uncertainty: √(1^2 + 2^2) = √5 ≈ 2.24 m/s, rounded to one significant figure gives ±2 m/s
(b) Second Pair of Measurements
For the measurements 334±1 m/s and 336±5 m/s, the range for the second measurement is 331 to 341 m/s. These ranges also overlap, making the measurements consistent. However, the second measurement has a much larger uncertainty.
Best estimate of speed remains 335 m/s because the means didn't change.
Combined uncertainty: √(1^2 + 5^2) = √26 ≈ 5.1 m/s, rounded to one significant figure gives ±5 m/s. The larger uncertainty means this measurement is less precise and could influence the final estimate's precision negatively, but since it is consistent with the first measurement, it is still worth including.