| Date | May 2015 | Marks available | 4 | Reference code | 15M.2.SL.TZ1.5 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 1 |
| Command term | Calculate and Determine | Question number | 5 | Adapted from | N/A |
Question
This question is in two parts. Part 1 is about a thermistor circuit. Part 2 is about vibrations and waves.
Part 1 Thermistor circuit
The circuit shows a negative temperature coefficient (NTC) thermistor X and a 100 kΩ fixed resistor R connected across a battery.
The battery has an electromotive force (emf) of 12.0 V and negligible internal resistance.
Part 2 Vibrations and waves
The cone and dust cap D of a loudspeaker L vibrates with a frequency of 1.25 kHz with simple harmonic motion (SHM).
(i) Define electromotive force (emf).
(ii) State how the emf of the battery can be measured.
The graph below shows the variation with temperature T of the resistance RX of the thermistor.
(i) Determine the temperature of X when the potential difference across R is 4.5V.
(ii) State the range of temperatures for which the change in the resistance of the thermistor is most sensitive to changes in temperature.
(iii) State and explain the effect of a decrease in temperature on the ratio
\[\frac{{{\rm{voltage across X}}}}{{{\rm{voltage across R}}}}\].
Define simple harmonic motion (SHM).
D has mass 6.5 \( \times \) 10−3 kg and vibrates with amplitude 0.85 mm.
(i) Calculate the maximum acceleration of D.
(ii) Determine the total energy of D.
The sound waves from the loudspeaker travel in air with speed 330 ms−1.
(i) Calculate the wavelength of the sound waves.
(ii) Describe the characteristics of sound waves in air.
A second loudspeaker S emits the same frequency as L but vibrates out of phase with L. The graph below shows the variation with time t of the displacement x of the waves emitted by S and L.
(i) Deduce the relationship between the phase of L and the phase of S.
(ii) On the graph, sketch the variation with t of x for the wave formed by the superposition of the two waves.
Markscheme
(i) the work done per unit charge in moving a quantity of charge completely around a circuit / the power delivered per unit current / work done per unit charge made available by a source;
(ii) place voltmeter across battery;
(i) VX = 7.5 V;
\(I\left( { = \frac{{4.5}}{{100 \times {{10}^3}}}} \right) = 4.5 \times {10^{ - 5}}{\rm{A}}\) or \(\frac{{{V_X}}}{{{V_R}}} = \frac{{{R_x}}}{{{R_R}}}\);
\({R_x}\left( { = \frac{{7.5}}{{4.5 \times {{10}^{ - 5}}}}} \right) = 1.67 \times {10^5}\Omega \) or \({R_x}\left( { = \frac{{7.5}}{{4.5}} \times 100 \times {{10}^3}} \right) = 1.67 \times {10^5}\Omega \);
T= −37 or −38ºC
(ii) −50 to (up to) −30 °C / at low temperatures;
(iii) as the temperature decreases Rx increases;
same current through R and X so the ratio increases or VX increases and VR decreases so the ratio increases;
(periodic) motion in which acceleration/restoring force is proportional to the displacement from a fixed point;
directed towards the fixed point / in the opposite direction to the displacement;
(i) ω=(2πf = 2π×1250)7854 rad s–1;
a0 =(−ω2x0 = −78542 ×0.85×10–3 =) (−)5.2×104 ms−2 ;
(ii) correct substitution into \({E_T} = \frac{1}{2}m{\omega ^2}{x_0}^2\) irrespective of powers of 10;
0.14 to 0.15 J;
(i) 0.264 m;
(ii) longitudinal;
progressive / propagate (through the air) / travels with constant speed (through the air);
series of compressions and rarefactions / high and low (air) pressure;
(i) S leads L / idea that the phase of L is the phase of S minus an angle;
\(\frac{1}{8}\) period / 1×10–4 s / 0.1 ms;
\(\frac{{\rm{\pi }}}{4}\) / 0.79 rad / 45 degrees;
(ii) agreement at all zero displacements;
maxima and minimum at correct times;
constant amplitude of 1.60 mm;
