AQA A-Level Physics Paper 3 (3A), June 2025: Question 1

8 marks · Medium difficulty · Practical Techniques & Data Analysis

Analyse an investigation into the relationship between first-harmonic stationary wave frequency and tension, determining control variables, Vrms, period from an oscilloscope display, and evaluating the effect of doubling mass.

Practise this question

Question

The question presents an experimental setup for investigating stationary waves on a string. Figure 1 shows a string stretched over a bench from a clamped vibration generator connected to a variable-frequency AC supply and an oscilloscope, passing over a pulley to a hanger and slotted masses. Subquestions 01.1 and 01.2 ask for two control variables and to identify a correct statement about the mass values. Figure 2 displays an oscilloscope screen with two sinusoidal waveforms: one solid line for m = 100 g and one dashed line for m = 200 g, with y-gain 5 V/div and time-base 20 ms/div. Subquestions 01.3 to 01.5 ask to determine the root mean square voltage, the period of the 100 g waveform, and deduce whether the waveforms match the expected relationship when mass is doubled.
Question text

01 This question is based on an investigation into how the frequency of the first-harmonic

stationary wave on a string varies with tension (required practical activity 1).

Figure 1 shows the arrangement for this investigation.

Figure 1

The tension in the string is equal to the weight mg of the total mass m tied to

the string.

The frequency is changed until the first-harmonic stationary wave appears on the

string. This frequency f is determined using the oscilloscope.

3 m

The process is repeated for different values of .

01.1 Identify two control variables for the arrangement shown in Figure 1.

You may annotate Figure 1 as part of your answer.

[2 marks]

01.2 The total mass m is made from a mass hanger and up to three slotted masses.

One 20 g, one 50 g and one 100 g slotted mass are provided.

The hanger has a mass of 100 g.

The hanger must not be removed from the string.

Which statement is correct?

Tick ( ) one box.

[1 mark]

m has a maximum range of 170 g.

m has a maximum of 7 different values.

m values are evenly distributed across the range.4

The frequency f is calculated using the waveform displayed on the oscilloscope.

Figure 2 shows the waveforms displayed on the oscilloscope when m = 100 g and

when m = 200 g.

Figure 2

m = 100 g

m = 200 g

The y-voltage gain setting is 5 V div−1.

20 ms div−51

The time-base setting is .

01.3 Determine Vrms, the root mean square voltage of the ac supply.

[2 marks]

Vrms = V

01.4 Determine the period of the waveform on Figure 2 when m = 100 g.

[1 mark]

period = ms

01.5 Deduce whether Figure 2 shows the expected result of doubling m from

100 g to 200 g.

[2 marks]

Mark scheme

Show the mark scheme The mark scheme outlines: 01.1 awards 2 marks for mass per unit length of string and length of string between vibration generator and pulley. 01.2 awards 1 mark for selecting 'm has a maximum range of 170 g'. 01.3 awards 2 marks for peak voltage between 18.0 and 19.0 V, calculating Vrms = Vpeak / sqrt(2), giving Vrms between 13.0 and 13.2 V. 01.4 awards 1 mark for period between 104 and 107 ms. 01.5 awards 2 marks for determining T200 (73.5 to 75.6 ms) or f200 (13.2 to 13.6 Hz), comparing the ratio T100/T200 or f200/f100 to sqrt(2) ≈ 1.41, and reaching a reasoned conclusion.

Question Answers Additional comments/Guidance Mark AO

01.1 mass per unit length of string OWTTE 1 quantitative properties only 2 AO1

answers may be in either order

for 1 condone minor slip ‘wire’;

condone ‘μ ’ of string;

‘type of string’ / ‘same string’ are neutral

length (of string) between vibration generator and pulley 2 for 2 accept ‘distance between vibration

generator and pulley’ / ‘length of horizontal

acceptable limits for defining L in Figure 1: (part of) string;

allow clear annotation to Figure 1 to

limits for correctly identify dimension (correct by eye):

maximum L allow use of a symbol, eg L

limits for condone ‘amplitude of supply output voltage’ /

minimum L ‘output voltage’ or WTTE

‘ac frequency’ (or WTTE) / ‘total (suspended)

mass’ / ‘length of vibrating section (of string)’ /

‘diameter of string’ (or WTTE) / ‘amount of

string between generator and pulley’/

‘temperature of string’ / ‘positions of

generator etc’ are neutral

01.2 m has a maximum range of 170 g. CAO 1 AO3

6Question Answers Additional comments/Guidance Mark AO

01.3 Vpeak in range 18(.0) to 19(.0) (V) for 1 allow Vrms = 0.71 × their Vpeak etc; 2 AO2

allow Vpeak to peak in range 36(.0) to

OR 38(.0) (V)

theirVpeak OR

calculates Vrms using 1 theirV

2 peak to peak

Vrms =

3.7 ± 0.1

allow Vrms correct in cm, ie OR

7.4 ± 0.2

Vrms in range 13.0 to 13.2 (V) 2 for 2 max 4 sf;

condone 4 sf rounding to 3 sf in range

do not accept 2 sf 13 (V)

01.4 T100 in range 104 to 107 (ms) period must be expressed in units of time; 1 AO3

allow 0.104 to 0.107 s if answer line amended

01.5 determines T200 OR f200 for 1 their T200 in range 73.5 to 75.6 ms OR 2 AO3

AND f200 in range 13.2 to 13.6 Hz;

attempts to compare T200 with T100 (their 01.4) OR condone use of T100 and T200 in cm OR in div;

f f ignore POT but must be consistent between

attempts to compare 200 with 100 (based on their 01.4) 1

values for T100/200 or f100/200 ;

allow any quantitative comparison;

expected pairs of values:

condone a qualitative comparison

T100 = 105.4 ms T200 = 74.5 ms

f100 = 9.49 Hz f200 = 13.4 Hz award 2 as follows:

states Figure 2 is the expected result with

T100 = 5.30 cm T200 = 3.73 cm their T

100 ≥1.34 AND ≤1.48 (OR 1.4) etc

their T200

OR

states Figure 2 is not the expected result

their T100 their f200 with

compares OR to 2 OWTTE

their T200 their f100

their T100

<1.13 OR >1.69 ;

AND their T

makes a reasoned judgement (to show if their evidence is

otherwise accept either conclusion

consistent with doubling m) 2

OR ‘cannot tell’

Total 8

How to answer it

Investigation of First-Harmonic Stationary Waves on a String

Required Practical 1 • Waves & Oscilloscope Skills

What this question tests

This practical exam question evaluates experimental design, reading and interpreting oscilloscope traces, and applying standing wave physics:

  • Control variables in the Melde's string experiment (Required Practical 1).
  • Combinatorial reasoning with slotted masses and physical constraints.
  • Oscilloscope calculations: Finding peak voltage, root mean square voltage ( Vrms ), and period ( T ) from grid divisions and scale settings.
  • Deductive reasoning: Relating string tension to frequency and wave period using f = (1 / 2L) × √(T / μ) .

Part 01.1: Identifying Control Variables

String stationary waves setup • [2 Marks]

✅ Correct Answers (Choose Any Two)

  1. Mass per unit length of the string ( μ ).
  2. Vibrating length of string between the vibration generator and the pulley ( L ).
Mark allocation: 1 mark per correct quantitative variable identified (AO1).

💡 Key Knowledge

The frequency of the first harmonic is governed by:

f = (1 / 2L) × √(T / μ)

Since the independent variable is tension ( T = mg ) and the dependent variable is frequency ( f ), both length ( L ) and linear mass density ( μ ) must remain constant.

🧠 Exam Technique: Be Quantitative

Always state measurable, quantitative properties rather than vague descriptions:

  • Write "mass per unit length of string" rather than just "same string" or "type of string" (the mark scheme treats "type of string" as neutral).
  • Define the length precisely as the "length of string between vibration generator and pulley". You can also clearly annotate this span on Figure 1.

❌ Common Errors

  • Stating "frequency" or "tension/mass" as control variables — these are the independent and dependent variables!
  • Saying "total length of string" instead of the vibrating length between the nodes (generator and pulley).

Part 01.2: Mass Combinations & Range

Data evaluation & constraints • [1 Mark]

✅ Correct Answer

☑ m has a maximum range of 170 g.

Mark allocation: 1 mark (AO3, Correct Answer Only).

📐 Step-by-Step Breakdown

  1. Minimum mass: Hanger cannot be removed, so minimum suspended mass is with zero slotted masses: mmin = 100 g .
  2. Maximum mass: Hanger plus all three slotted masses (20 g + 50 g + 100 g): mmax = 100 + 20 + 50 + 100 = 270 g .
  3. Range: Range = mmax − mmin = 270 g − 100 g = 170 g .

❌ Why the Other Options are Incorrect

  • "m has a maximum of 7 different values": The available added masses give 2³ = 8 combinations (0, 20, 50, 70, 100, 120, 150, 170 g added to 100 g), yielding 8 distinct values: 100 g, 120 g, 150 g, 170 g, 200 g, 220 g, 250 g, and 270 g.
  • "m values are evenly distributed": The increments alternate irregularly (e.g., +20 g, +30 g, +20 g, +30 g), so they are not evenly spaced.

Part 01.3: Calculating RMS Voltage

Oscilloscope y-gain & AC theory • [2 Marks]

📐 Step-by-Step Calculation

  1. Read peak displacement from trace:
    From the central horizontal axis to the maximum crest is 3.7 ± 0.1 div .
    (Alternatively, peak-to-peak = 7.4 divisions)
  2. Calculate peak voltage (Vpeak):
    Vpeak = 3.7 div × 5 V div⁻¹ = 18.5 V (acceptable range: 18.0 V to 19.0 V).
  3. Calculate Vrms:
    Vrms = Vpeak / √2 = 18.5 / 1.4142 = 13.08 V
  4. Final Answer: 13.1 V (accept 13.0 V to 13.2 V).
Marks: 1 mark for calculating peak voltage (18.0–19.0 V) or method Vpeak/√2 ; 1 mark for correct Vrms value (AO2).

💡 Essential Formulas

Vpeak = (vertical divisions from centre) × (y-voltage gain)

Vrms = Vpeak / √2 = 0.707 × Vpeak

Or directly from peak-to-peak: Vrms = Vpeak-to-peak / (2√2)

❌ Examiner Pitfalls to Avoid

  • Rounding to 2 s.f.: Writing 13 V is explicitly rejected by the mark scheme! Provide 3 significant figures ( 13.1 V ).
  • Using peak-to-peak instead of peak: Forgetting to divide total height by 2 before applying Vpeak / √2 gives a value twice as large (~26.2 V).

Part 01.4: Period of Waveform (m = 100 g)

Oscilloscope time-base analysis • [1 Mark]

📐 Measurement & Calculation

  1. Identify the solid trace ( m = 100 g ).
  2. Measure horizontal distance for one full wavelength / cycle:
    From 1st crest to 2nd crest: occupies approximately 5.25 to 5.35 divisions (centre value ≈ 5.27 div ).
  3. Multiply by the time-base setting ( 20 ms div⁻¹ ):
    Period T = 5.27 div × 20 ms div⁻¹ = 105.4 ms
  4. Allowed Range: 104 ms to 107 ms (or 0.104 s to 0.107 s ).
Mark allocation: 1 mark for period in the specified range with correct units (AO3).

🧠 Exam Technique: Waveform Tracking

Always measure between identical points on consecutive cycles:

  • Peak to peak: easy to locate the sharp turns at crests.
  • Zero crossings: measure across two consecutive zero-crossings in the same direction (not opposite directions, which is only half a period).
  • Watch the given unit: The answer line specifies ms. Do not write 0.105 without crossing out and replacing the unit with seconds!

Part 01.5: Evaluating the Effect of Doubling Mass

Standing wave physics & deduction • [2 Marks]

💡 The Theoretical Expectation

For a stationary wave on a fixed string:

f ∝ √T ∝ √m

Since period is the reciprocal of frequency ( Tperiod = 1 / f ):

Tperiod ∝ 1 / √m

When the mass doubles from 100 g to 200 g , the expected ratio of periods is:

T100 / T200 = √(200 / 100) = √2 ≈ 1.414

📐 Deductive Comparison

  1. Determine T200 (dashed line):
    One cycle occupies ≈ 3.73 div .
    T200 = 3.73 div × 20 ms div⁻¹ = 74.5 ms (allowed: 73.5 to 75.6 ms).
  2. Calculate experimental ratio:
    T100 / T200 = 105.4 ms / 74.5 ms = 1.415
  3. Compare with theory:
    1.415 ≈ √2 ≈ 1.414 (well within 1.34 to 1.48).
  4. Conclusion:
    Yes, Figure 2 shows the expected result because the period decreases by a factor of √2 .

✅ How Full Marks are Awarded

  • Mark 1: Determines T200 in range 73.5 to 75.6 ms (or f200 = 13.2 to 13.6 Hz ) AND attempts comparison between the two states.
  • Mark 2: Compares ratio to √2 (or 1.41 ) and makes a reasoned final judgement concluding that Figure 2 is consistent with theory.

Topics

Physics · Practical skills · Required Practicals · 3.3 Waves · 3.7 Fields and their consequences (A-level only) · Experimental design · Data analysis · AS practicals (1–6)

Question and mark scheme from the AQA A-Level Physics examination, Paper 3 (3A), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.