Question 23M.3.HL.TZ1.1
| Date | May 2023 | Marks available | [Maximum mark: 8] | Reference code | 23M.3.HL.TZ1.1 |
| Level | HL | Paper | 3 | Time zone | TZ1 |
| Command term | Calculate, Deduce, Draw, Estimate, Identify, Suggest | Question number | 1 | Adapted from | N/A |
A student attaches one end of a copper wire to an oscillator operating at a fixed frequency. The other end of the wire passes over a pulley to weights that hang vertically. The first harmonic standing wave is established by using the slider to change the length of the wire. The procedure is repeated for different weights.
The mass m of the weights and the wavelength of the wave are related by
where μ is a constant, is the frequency of the wave and g = 9.8 m s−2 .
Deduce the unit of μ in terms of fundamental SI units.
[1]
[μ] = «» kg × m−1
Accept kg/m.
Do not accept g m−1.
Standing wave. Quite straightforward question focused on various aspects of experiment.
The graph shows the data obtained by the student, plotted to show the variation of m with .
Draw the line of best fit for these data.
[1]
straight line through all error bars ✓
Most students were able to draw the line of best fit and realised that it does not go through the origin.
Identify the evidence for a systematic error in the data.
[1]
line does not go through the origin «and all error bars» ✓
Suggest a possible reason for the systematic error.
[1]
mass of tray of weights neglected/friction at pulley/friction at slider/thickness of slider/zero off-set error ✓
Do not allow vague answers like friction neglected / error in length measurement.
Better students identified possible reasons for systematic error (mass of tray, friction of pulley or friction between slider and wire omitted).
Calculate the gradient of the graph.
[2]
large enough triangle Δm ≥ 50 g✓
answer in range 0.210 − 0.240 «kg m−1» ✓
Accept answers in g m−2.
Do not allow ECF from MP1.
Most students calculated the gradient well, but some made mistakes in the gram/kilogram conversion.
The percentage uncertainty of the gradient is 6.0 %. The frequency of the wave is (60.0 ± 2.0 %) Hz.
Estimate, using the answer to (b)(iv), μ for the string. Include the percentage uncertainty of μ in your answer.
[2]
μ = «» = 6.229 × 10−4 «kg × m−1»
percentage uncertainty = 6.0 + 2 × 2.0 = 10 % ✓
Accept μ in the range 5.7 to 6.6.
Allow answer in g m−1 .
Allow ECF from (b).
Better students also found the constant and percentage error of the calculated constant. Weaker students used insufficiently large triangles to calculate gradients, made mistakes in units, and arithmetic errors in c).