So as a part of a laboratory assignment, I am trying to determine the relative error of the speed of wave propagation a string. The string is in tension using a weight.
What variables I have thus far:
String length $l = 2.56m$ with an $l$ error of $0.002m$
String mass $m_s = 0.0009kg$ with an $m_s$ error of $0.0001kg$
Mass of the weight $m_w = 0.1kg$ with an $m_w$ error of $0.0001kg$
Acceleration g is $9.82m/s^2$.
The force exterted on the string:
$F=0.1kg*9.82m/s^2=0.982N$
Linear density of the string:
$m_l=0.0009kg/2.56m=0.000352$
I've determined the speed of the wave thusly:
$$ V = \sqrt{\frac Fm_l} = 52.82m/s $$
And here is the relative error calculation:
$$ \frac {v_s}{\lvert v\rvert} = \sqrt{(\frac{l}{l})^2+(\frac{m_s}{m_s})^2+(\frac{m_w}{m_w})^2} = 0.11112 $$
But this $0.11112$ value is incorrect when i have it checked. Any tips?