Waves questions

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• AQA 7408 · June 2025 · Paper 3A · Q1 · 8 marks

  8 marks

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  This question was about an investigation of how the frequency of a stationary wave on a string varied with tension. The main ideas tested were • identification of the control variables in required practical activity 1 (specification reference 3.7.5.5 and 8.3.2 PS2.4) • use of an oscilloscope as a voltmeter and as a clock (3.7.5.5) In part 01.1 what should have been a straightforward opening question proved tricky and only 17% obtained both marks. No credit was given for a careless annotation to Figure 1 to identify the length of string that should be controlled. In part 01.2 just under 50% correctly identified that m has a maximum range of 170 g. Part 01.3 was a bit mixed, although many could determine the peak voltage and divide by root 2. For the second mark we wanted a voltage between 13.0 and 13.2, so a 2-sf answer was not accepted. © 2025 AQA For part 01.4 nearly 70% correctly determined the period although a few thought that the time- base setting of 20 ms div−1 referred to minor divisions, thus getting about 530 ms. Here as elsewhere, some lost a mark, thinking they should round their 106 to 110 (mistakenly claiming this was 2 sf). A majority saw the intention of part 01.5 and made the expected quantitative comparison between the waveforms in Figure 2. The students who misinterpreted the time-base in the same way as above got about 375 ms and were not penalised. A few students took the novel approach of comparing the number of horizontal divisions for one cycle of each waveform. This was a valid idea and was not penalised.

  Text version

  This question is based on an investigation into how the frequency f of the first-harmonic stationary wave on a string varies with tension (required practical activity 1). A horizontal string runs from a vibration generator to a pulley, then vertically to a hanger carrying slotted masses of total mass m, so the tension is mg. A variable-frequency ac supply drives the vibration generator and an oscilloscope is connected across the supply. The frequency is varied until the first harmonic appears and the process is repeated for different m.

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• AQA 7408 · June 2024 · Paper 1 · Q3 · 10 marks

  10 marks

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  This question on refraction and diffraction grating was set in the context of the analysis of light from stars. The complex prism in Figure 1 is designed to separate out light into its different wavelengths whilst keeping the rays horizontal. The ray diagram in question 03.1 was drawn correctly by almost 50% of students. These spotted that the exit ray leaving normally means that the ray in B must be horizontal. Completing the diagram then simply requires joining the ray entering A to the one in B. Many untidy diagrams were seen, and students should be encouraged to use a ruler when drawing ray diagrams of this kind. Question 03.2 was marked according to the student’s answer to 03.1. This meant that both marks for this question could be given even if 03.1 was incorrect. Students who referred to angles, without stating the boundary they were referring to, were not awarded the mark for their reasoning. Question 03.3 is another question that is on the specification that most students could not answer. There is a list of acceptable answers in the mark scheme that schools could refer to when teaching this. Answers that referred to the use of diffraction gratings in teaching were not rewarded. The calculation in 03.4 was completed successfully by most students. The structure of the mark scheme allowed the award of intermediate marks provided it was clear what the student was doing. Students should be encouraged to set out their work carefully so that examiners can identify the steps and award marks appropriately. A common error was to provide the slit separation, rather than the number of lines per metre, and therefore not get the last mark. Question 03.5 was one of the hardest on the paper. Many students made no attempt at analysis and made assumptions that led to zero marks. The best answers identified that the angles in the two situations would be the same. Students who did not do this often discussed percentage error in the angle being measured as the difference between them. It was also clear that many students did not understand the difference between accuracy and precision.

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  Two triangular prisms A and B are joined along a diagonal face. A horizontal ray enters A through its sloping left face and later emerges horizontally through the vertical right face of B. Inside the joined block, the ray meets the diagonal A-B boundary. A spectrum contains peaks X at about 380 nm and Y at about 390 nm. Peak X is observed at a first-order diffraction angle of 28.2 degrees.

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• AQA 7408 · June 2024 · Paper 1 · Q7 · 7 marks

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  This question tested the knowledge and understanding of stationary waves based on a displacement– time graph. Most students who did not get the mark for question 07.1 assumed that the amplitude of the stationary wave and progressive waves were the same. The calculation in question 07.2 was answered correctly by over 75% of students. Answers using a distance divided by time approach, rather than the wave equation, were not credited. Students were split almost 50:50 between those who thought the phase difference in question 07.3 was zero and those who thought it was π rad. Many students found question 07.4 quite difficult. There were three clear marking points which meant the question produced a spread of marks and discriminated quite well. A major issue for many students was the poor quality of the sine wave. Most students understood that the period was 1.6 ms but far fewer recognised that the amplitude was 4 mm. Section B The multiple-choice questions tested many of the topics not covered in Section A. There were five very accessible questions that were correctly answered by more than 70% of students. These were B12, B18, B14, B27 and B29. There were two very demanding questions answered correctly by fewer than 12% of students. These were B10 and B25. In B10 most students chose option B. This suggests that they did not realise that, when the energy transfer rate stays the same, using light of higher frequency means fewer photons per second and therefore a lower current. In B25 most students chose option B. In fact, the correct answer was the least popular option. Careful analysis, using a sketch graph for example, would show that the answer is C. There were several other questions where the most popular answer was incorrect. In B15 most students chose C, which is the distance between two nodes, or half the wavelength. In B20 most students chose B, presumably because they did not take into account the increased time of flight. In B22 most students chose D, despite a terminal speed being mentioned in the stem of the question.

  Text version

  A 1.05 m string supports a stationary wave at 625 Hz. At t=0 the displacement-distance graph is sinusoidal with nodes at 0, 0.35, 0.70 and 1.05 m, and alternating antinodes of about +7 mm, -7 mm and +7 mm. Point S is near x=0.05 m and has displacement +4 mm at t=0.

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• AQA 7408 · June 2023 · Paper 1 · Q4 · 14 marks

  14 marks

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  Questions about refraction and total internal reflection have been asked several times in the past and usually prove to be relatively challenging to many students.

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  Porro prisms are used in binoculars to reverse the path of the light. The prism is in the shape of a right-angled isosceles triangle. Figure 7 shows a ray of light, at normal incidence on the longest side, passing through a glass Porro prism. Figure 7 The critical angle for light in the prism is 41.5 degrees.

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• AQA 7408 · June 2023 · Paper 1 · Q6 · 9 marks

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  [06.1] It was clear that many students had little idea about how the equation for SHM can be obtained. Having the force equation on page 20 of the question paper gave some students a starting point, but relating it to the acceleration with a negative sign, or stating which factors were constant, was rarely seen. Commonly students simply stated the conditions for SHM without relating it to the context.

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  A weighted pencil floats vertically in water with submerged length l. If pushed down by displacement y and released, the additional buoyancy provides restoring force F = -A rho g y, where A is pencil cross-sectional area and rho is water density. The pencil oscillates about equilibrium.

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• AQA 7408 · June 2022 · Paper 1 · Q6 · 6 marks

  6 marks

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  This question on refraction proved to be reasonably discriminating and produced a good spread of marks. In order to earn the mark in 06.1 students had to make it clear why a ray bending away from the normal indicates an increase in refractive index. The best answers were supported either by a discussion of Snell’s Law or by a consideration of the change in speed. The calculation in 06.2 was more straightforward but many students struggled to identify the angle of incidence. Rounding errors were also relatively common. It is clear from the rubric to the examination paper that students are expected to have a protractor. It is expected, therefore, that students should be able to draw reflected rays accurately. Many students realised that total internal reflection was taking place in 06.3, but drew rays that were obviously incorrect. This question discriminated very well, with only the most able students likely to get all three marks. SECTION B The easiest questions were 13, 16, 8, 17, 10, 31, 15 and 11. The hardest questions were 21, 25, 27 and 26. All these had distractors that were more popular than the correct answer. In question 21 the most popular answer by far was A, the maximum order visible. B was the next most popular, presumably because these students realised that there was also a central maximum. Responses to question 25 indicated how poorly Newton’s third law of motion is understood. The correct answer was the least popular option. Clearly many students do not realise that the pair of forces act on different objects and are the same type of force. In question 27 all four options were similarly popular. It was clear that many students did not spot the word ‘extra’ in the question, for example. Question 26 was a difficult multi-step calculation. Most students chose B, and the next most popular was D, the correct answer.

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  Two prisms form a rectangular block. Prism A has refractive index 1.62 and prism B has refractive index 1.35. A horizontal ray enters A normally. The A-B boundary slopes at 43 degrees to the horizontal, and the refracted ray in B then reaches the horizontal B-air boundary at P.

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• AQA 7408 · June 2022 · Paper 3A · Q1 · 8 marks

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  This question tested students’ understanding of the use of a CRO as a clock. In 01.1, nearly two-thirds correctly identified Y-shift. For full credit in 01.2, examiners wanted to see use of time contact rod of length 2 speed × = . Some students missed the factor of 2 or assumed that the time-base setting referred to minor divisions. It was disappointing that more than half of the students could not score. In 01.3 there was strong representation at each mark. Better students took note that they should add quantitative detail. Once it was clear that the new waveform would have twice the number of cycles and would therefore no longer be fully visible, most could correctly identify that the time- base should be adjusted. ‘X-gain’ was accepted for time-base and many correctly suggested changing the setting to 0.1 ms div−1. Some wrote that, when a rod of twice the length was used, the period / wavelength / frequency / speed of the waves would change.

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  Figure 1 shows apparatus used to measure the speed of sound in a steel rod. Figure 1 The steel rod is suspended from a beam using rubber bands. When the hammer is in contact with the end L of the steel rod, a circuit is completed and the signal generator is connected to the oscilloscope. Figure 2 shows the waveform then displayed on the oscilloscope. Figure 2

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• AQA 7408 · November 2021 · Paper 1 · Q2 · 11 marks

  11 marks

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  Answers to questions 02.1 and 02.2 were often vague and incomplete, lacking the detail necessary at A-level. This meant that very few students scored full marks on either question. Question 02.3 proved to be one of the least accessible on the paper. Only the occasional student demonstrated any awareness of the assumptions associated with Young’s slits. There are several situations involving two-source interference where the Young double-slit equation is invalid and students should be able to identify them. Despite being told that the equation could not be used, most students ignored this when attempting to answer question 02.4. This meant they could only obtain a maximum of 2 marks for this question.

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  A microwave transmitter and vertical rod receiver are about 2 m apart. Wavelength is about 3 cm. A movable vertical metal plate supplies a reflected path. A later double-slit has separation 0.12 m, receiver distance 0.45 m and transverse travel +/-0.25 m.

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• AQA 7408 · November 2021 · Paper 1 · Q3 · 7 marks

  7 marks

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  The speed calculation in question 03.1 was completed correctly by the majority of students. It was evident from the answers to question 03.2 that many students failed to grasp the geometry of the situation, or the significance of angle A. Although many students were able to use Snell’s Law to determine the critical angle, the mark was withheld when they indicated that they believed that the angle being calculated was A. Similar issues with the behaviour of light in an optical fibre were seen in question 03.4. Even those students who realised that light escaped the core at the boundary failed to get credit by omitting the partially reflected ray or drawing the transmitted ray closer to the normal.

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  A straight optical fibre has core refractive index 1.47 and cladding 1.41. A limiting incident ray enters from air and just undergoes total internal reflection at the straight core-cladding boundary.

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• AQA 7408 · November 2021 · Paper 3A · Q2 · 10 marks

  10 marks

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  This question was about the light emitted from different LEDs but included general ideas about the use of diffraction gratings, as used in Required Practical Activity 2. In question 02.1 students had to make an easy read-off from Figure 3 and then apply an equation available in the Formulae and Data booklet. Despite the low demand of the question, fewer than a third of the students were able to obtain full credit. Question 02.2 is one of several in the paper where those suggesting simple practically-based explanations were most likely to score. About 40% of students mentioned some relevant characteristic of the 5th maximum to score the available mark. It was clear that some did not understand what we wanted them to do in question 02.3 and many showed no evidence of working on Figure 4. In question 02.4 only 3% of the students successfully used data about both LEDs; some engineered an answer that duplicated the value in the Formulae and Data booklet. All students realised that c is the speed of light but not all recognised that e is the electronic charge and used 2.718 in their calculation. Question 02.5 was the least accessible part and only 10% of students used Figure 4 to determine the voltage drop across the LED before going on to deduce the minimum value of R.

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  Green LED LG and red LED LR have equal peak intensity. Their spectral peaks are about 565 nm and 635 nm. Extrapolated activation voltage for LG is 2.00 V; the LR current-voltage graph has a linear high-current section and at 21.0 mA its forward voltage is 2.01 V.

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• AQA 7408 · November 2020 · Paper 1 · Q3 · 12 marks

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  This question dealt with the ideas behind double-slit interference using the context of sound waves. It was pleasing to note that many students understood what was meant by coherence, but some failed to gain the mark for stating that the phase rather than the frequency was the same. In part 03.2, many students demonstrated an awareness of constructive and destructive interference without explaining how they come about. There was also a lot of confusion between phase difference and path difference. In 03.3, the best answers were by students who realised that the Young slit equation should not be used, and who worked out the path difference from first principles. In 03.4, a surprisingly large number of students failed to identify their answer to 03.3 as the wavelength of the sound. In 03.5, although the question specifically asked for a discussion of the amplitude, many students simply referred to a change in pitch. A large number of students also incorrectly suggested that the speed of the sound waves would change.

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  Two point-source loudspeakers P and Q are connected to one signal generator. O is their midpoint. A lies on the perpendicular bisector; B is 0.95 m sideways from A. The speaker separation is 0.30 m and OA=2.25 m.

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• AQA 7408 · June 2019 · Paper 1 · Q2 · 11 marks

  11 marks

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  [2.1] Here the students were expected to refer to the normal, or to explain what the normal is. Answers that referred to the prism rather than the surface of the prism did not gain the mark.

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  A rain sensor sends a 45 degree ray through index-1.52 windscreen glass, reflecting at inner/outer surfaces A,B,C before detector. Water index is 1.33.

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• AQA 7408 · June 2019 · Paper 1 · Q3 · 8 marks

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  [3.3] This calculation was clearly familiar to many students and most students received both marks. For the remainder, there was confusion between the number of lines per millimetre and the slit separation. This route leads to an answer of about 10-10 °. Students should be encouraged to check answers that appear unreasonable; this one clearly is.

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  White light diffracts through a single slit, then green filter to screen.

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• AQA 7408 · June 2019 · Paper 1 · Q6 · 5 marks

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  [6.1] This question caused no problems for the majority of students. Common errors were confusing the negative and positive velocities (giving an answer of 0.5 ms), or treating Figure 8 as a v-t graph (giving an answer of 2.0 ms).

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  Loudspeaker cone point executes SHM with amplitude4.2 mm and period2.0 ms. Its displacement-time graph starts at +4.2 mm at t=0, crosses zero while falling at0.50 ms, reaches -4.2 mm at1.0 ms, crosses zero while rising at1.5 ms, and returns to +4.2 mm at2.0 ms.

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• AQA 7408 · June 2018 · Paper 1 · Q2 · 10 marks

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  [02.4] Most answers missed the point of the question. There were many responses that explained the excitation and de-excitation process, some in much detail, but did not explain clearly that the energy transfer to excite the electron in the atom has to occur with an exact amount of energy being supplied to the electron instantaneously. Many students quoted a ‘one to one interaction’, but this seemed to be a learned response and provided insufficient evidence of them understanding what this means.

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  Electron data (v/10^7 m s^-1,lambda/10^-11 m) are(1.5,4.9),(2.5,2.9),(3.5,2.1). A diffraction tube sends electrons through thin graphite to a fluorescent screen showing rings.

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• AQA 7408 · June 2018 · Paper 1 · Q3 · 10 marks

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  [03.2] This was answered very well by a great majority (81.1%) of the students.

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  A violin string fixed at both ends has vibrating length0.33 m. At tension25 N its fundamental is370 Hz. A circular tuning peg diameter7.02 mm is rotated75 degrees; tension-extension graph shows initial extension about11 mm and new tension about35-36 N.

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• AQA 7408 · June 2017 · Paper 1 · Q2 · 7 marks

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  Question 02.1 required students to analyse the data given and demonstrate that it was consistent with the given relationship. Just over half of students were able to do this. Common errors were confusion between linear and proportional relationships, and attempts to derive the expression algebraically without using the data. The calculation in question 02.2 proved to be one of the more challenging in the paper. The main reason for this was a lack of appreciation of how to find the mass per unit length of the nylon string; this did limit them although they were able to pick up a mark for a correct substitution of tension and frequency in the appropriate formula. The explanation, required in 02.3, of why the result might be different if much larger masses were used, was not well answered. The majority did not appreciate that the nylon would get thinner and this would reduce the mass per unit length. Common responses tried to invoke Hooke’s law notwithstanding the fact that nylon does not obey this law.

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  A nylon string of fixed length vibrates in its first harmonic. Suspended mass m/kg and frequency f/Hz data are (0.50, 110), (0.80, 140), (1.20, 170). The string density is 1150 kg m^-3 and diameter 5.0 x 10^-4 m.

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• AQA 7408 · June 2017 · Paper 1 · Q3 · 6 marks

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  The first two parts of this question on refraction proved to be straightforward, with three-quarters of students scoring full marks. The third part, which involved a certain amount of judgement, was less well done. Many students mixed up the blue and red light, stating that the red light would undergo total internal reflection. Some did pick up on the fact that if the refractive indices of both media increased by the same proportion then there would be no change and all three rays would follow the same path. This approach received full credit.

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  A monochromatic ray is incident normally on the curved face of a semicircular glass block, then reaches the plane face. The glass refractive index is 1.6. A liquid film can be placed on the plane face.

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