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The volume of air in a bottle affects its resonant frequency.
It is suggested that the resonant frequency $f$ is related to the volume $V$ by the equation $$ f^2 = \frac{k}{V} $$ where $k$ is a constant.
Design a laboratory experiment to determine whether this equation is correct. You should draw a diagram showing the arrangement of your equipment. In your account you should pay particular attention to
(a) the procedure to be followed,
(b) the measurements to be taken,
(c) the control of variables,
(d) how to analyse the data,
(e) the safety precautions to be taken.
558
533
508
An experiment is carried out to investigate how the resistance $R$ of a thermistor varies with temperature $T$.
An ohmmeter is used to measure $R$. The equipment is set up as shown in Fig. 2.1.
It is suggested that $R$ and $T$ are related by the equation $$R = \frac{T^h}{g}$$ where $g$ and $h$ are constants.
(a) A graph is plotted with $\lg R$ on the y-axis and $\lg T$ on the x-axis. Express the gradient and y-intercept in terms of $g$ and $h$. [1]
(b) Values of $T$ and $R$ are given in Fig. 2.2.
Calculate and record values of $\lg \left(\frac{T}{K}\right)$ and $\lg \left(\frac{R}{\Omega}\right)$ in Fig. 2.2. Include the absolute errors in $\lg \left(\frac{R}{\Omega}\right)$. [3]
(c) (i) Plot a graph of $\lg \left(\frac{R}{\Omega}\right)$ against $\lg \left(\frac{T}{K}\right)$. Include error bars for $\lg \left(\frac{R}{\Omega}\right)$. [2]
(ii) Draw the line of best fit and a worst acceptable straight line on your graph. Both lines should be clearly labelled. [2]
(iii) Determine the gradient of the line of best fit. Include the error in your answer. [2]
(iv) Determine the y-intercept of the line of best fit. Include the error in your answer. [2]
(d) Using your answers to (c)(iii) and (c)(iv), determine the values of $g$ and $h$. Include the error in your values. You need not be concerned with the units of $g$ and $h$. [3]
531
577
592
