while we pretended that l ′ was the length of the entire string, in reality, you probably had some loose at both ends, some looped over the pendulum, some wrapped in knots, and so on. this can be quite an important systemic error, depending on your setup. – qualitative impact: discuss the direction of the impact of this on each part of the experiment (and state when it would have had no impact). – quantitative impact: estimate how much total length of string could have been "tied up" in this way (and remember that it’s the stretched length that matters for the gold string, so take that into account when you make that estimate). be sure to explain how you made your estimate. how much relative error could we have had in l ′ ? compare to your other relative (random) errors; how much would this impact our results? – conclusions for results: consider this systemic error and your size estimates as compared to your other errors. all things considered, which measurement do you think is better to determine mass density: the direct measurement, or the wavesbased measurement? consider the equivalent question for the wave velocity: do you trust part i or part ii more? – experimental design: try to come up with a good way to measure stretched mass density (directly) that avoids this problem. (it’s fine if it’s a little impractical, but it shouldn’t be too impractical.)