[填空题]
1.A student investigates standing waves in strings. A string is connected to an oscillator where a function generator can adjust the frequency. The other end of the string passes through a pulley and supports a mass.
The student varied the mass $m$ and recorded the values for frequency $f$ for which the first harmonic wass visible on the string. The following graph shows the recorded data.
The uncertainty of the mass is negligible.
(1)Draw the line of best fit for the plotted data on the graph.
(2)By referring to the plotted data, explain why it cannot be stated that frequency is directly proportional to mass.
(3)Use the graph to determine the value for $f$ with its absolute uncertainty for for m=1.0 kg
2.The theory suggests that $f_2=km$
where $k$ is a constant.
The variation of $f^2$ with m is seen on the graph below.
(1)Show that the absolute uncertainty of $f^2$ is $±0.0\, kHz^2$ for m=$1.0\,kg$.
(2)The absolute uncertainty of $f^2$ is $0.03\,kHz^2$ for $m=0.25\,kg$. Construct error bars for $f^2$ when $m=0.25\,kg$ and $.m=1.00\,kg$.
(3)State and explain whether the theory is supported by data or not.
3.Determine the unit of $k$, in fundamental SI units. k=
