Stationary Waves & Resonance — A/L Physics

What must I remember about Stationary Waves & Resonance?

• Stationary (Standing) Wave Formation: Formed by the continuous superposition of two identical progressive waves travelling in opposite directions with the same frequency, wavelength, and amplitude.
• Nodes and Antinodes: Nodes (N) are points of permanently zero displacement and maximum pressure variation; Antinodes (A) are points of maximum displacement and minimum pressure variation; Separation between two successive nodes (or antinodes) is λ/2; Separation between a node and adjacent antinode is λ/4.
• Transverse Stationary Waves on Stretched Strings: Fixed at both ends: Fundamental (1st harmonic) f1 = v / (2L) = (1 / 2L) √(T / μ); nth harmonic fn = n * f1 = (n / 2L) √(T / μ); all integer harmonics (1, 2, 3, ...) are present.
• Longitudinal Stationary Waves in Air Columns: Open organ pipe (both ends open): fn = n (v / 2L), all harmonics present; Closed organ pipe (one end closed): fn = (2n - 1)(v / 4L), ONLY ODD harmonics (1, 3, 5, ...) present.

Test yourself (1 minute)

1. End Correction (c) in Resonance Tubes

   The displacement antinode forms slightly outside the open end of a tube of internal diameter D: End correction c ≈ 0.3 * D; for open pipe effective length L_eff = L + 2c; for closed pipe L_eff = L + c.

2. Sonometer Laws

   1) Law of Length: f ∝ 1/L (constant T, μ); 2) Law of Tension: f ∝ √T (constant L, μ); 3) Law of Mass: f ∝ 1/√μ (constant L, T).

3. Acoustic Resonance Condition

   Occurs when the frequency of an external periodic driving force matches a natural resonant frequency of the oscillating system, causing maximum transfer of energy and maximum amplitude.

Practise Stationary Waves & Resonance questions today

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 3: Waves & Sound

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Where does Stationary Waves & Resonance fit in the syllabus?

Unit 3.4 · Year 1 · Term 2