Stationary Waves & Resonance — A/L Physics

How do I practise Stationary Waves & Resonance?

1 question with a worked solution

1. A sonometer wire of length 0.50 m and mass per unit length 2.0 × 10⁻³ kg m⁻¹ vibrates in its fundamental mode under a tension of 80 N. What is the fundamental frequency of vibration?
   1. A) 100 Hz
   2. B) 200 Hz
   3. C) 400 Hz
   4. D) 50 Hz
   Check my answer

   Correct answer: B) 200 Hz

   The wave speed on a stretched string is v = √(T / m) = √(80 / (2.0 × 10⁻³)) = √40000 = 200 m s⁻¹. For the fundamental mode of a wire fixed at both ends, length L = λ / 2 => λ = 2L = 2 × 0.50 m = 1.0 m. Fundamental frequency f = v / λ = 200 m s⁻¹ / 1.0 m = 200 Hz.

   Show worked solution

   Step 1: Calculate wave speed v = √(T / m) = √(80 / 2.0 × 10⁻³) = 200 m s⁻¹. Step 2: Fundamental wavelength λ = 2L = 2 × 0.50 = 1.0 m. Step 3: Frequency f = v / λ = 200 / 1.0 = 200 Hz. Answer: 200 Hz.
   Modelled on: the A/L Physics examination pattern

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Where does Stationary Waves & Resonance fit in the syllabus?

Unit 3.4 · Year 1 · Term 2