AQA A-Level Physics Paper 1, June 2022: Question 19

✅ Correct Answer

A (first)

When the tension is increased to 4T , the new frequency of the first harmonic becomes 2f . Therefore, to achieve a frequency of 2f while keeping the string in its new state, the wave is simply playing the first harmonic at its new baseline frequency.

💡 Key Knowledge

• The speed of a transverse wave on a string is given by v = √(T / μ) , where T is tension and μ is mass per unit length.
• The frequency of the n -th harmonic is given by f_n = (n / 2L) √(T / μ) .
• Because L and μ remain constant, frequency is directly proportional to the square root of the tension ( f ∝ √T ).

📐 Step-by-Step Derivation

1. Initial state: First harmonic frequency is f₁ = f .
2. Apply change: Tension increases from T to 4T .
3. Calculate new fundamental frequency: Since f ∝ √T , scaling tension by a factor of 4 scales the frequency by √4 = 2 .
4. New first harmonic frequency: The new fundamental frequency is 2f .
5. Conclusion: A frequency of 2f corresponds directly to the first harmonic of the string under the new tension 4T .

❌ Common Errors

Many students incorrectly select B (second) because they see the multiplier 2 in 2f and assume it links directly to the second harmonic ( 2f₁ ). Always check how the physical parameters ( T , L , μ ) alter the fundamental frequency first before looking at harmonic numbers!