C.4
Standing Waves & Resonance
Formation of standing waves, nodes and antinodes, harmonics in strings and pipes, resonance, natural frequency and damping.
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C.4 Standing Waves & Resonance
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Key Concepts, Standing Waves & Resonance
Formation of Standing Waves
A standing wave forms when two identical waves travel in opposite directions through the same medium and superpose. This typically happens when a progressive wave reflects back from a boundary and interferes with the incoming wave. For a stable standing wave to form, the frequency must be just right so that the reflections reinforce rather than cancel. Unlike a progressive wave, a standing wave does not transfer energy along the medium: energy is stored in the oscillation of the medium itself.
Nodes, Antinodes and Phase
A node is a point of zero displacement at all times: the two waves always cancel here. Nodes are spaced half a wavelength apart. An antinode is a point of maximum displacement: the two waves always reinforce here, and particles here oscillate with maximum amplitude. Adjacent antinodes are also half a wavelength apart. All points between two adjacent nodes oscillate in phase with each other (they reach maximum displacement at the same time), but points on opposite sides of a node are in antiphase (180° out of phase).
Standing Waves in Strings and Pipes
For a string fixed at both ends, nodes must form at both boundaries. The fundamental (first harmonic) has one antinode in the middle and length L = λ/2, giving f₁ = v/2L. The nth harmonic has frequency f_n = nf₁. For a pipe closed at both ends, the same analysis applies. For a pipe open at both ends, antinodes form at both open ends. A pipe closed at one end has a node at the closed end and an antinode at the open end: only odd harmonics are present and the fundamental has f₁ = v/4L. Being able to draw correct standing wave diagrams with boundary conditions is a key exam skill.
Resonance and Natural Frequency
Every object has one or more natural frequencies at which it oscillates freely when disturbed. When a periodic driving force is applied, the amplitude of oscillation depends on how close the driving frequency is to the natural frequency. Resonance occurs when the driving frequency matches the natural frequency: amplitude becomes very large (and is limited only by damping). At frequencies well above or below the natural frequency, the amplitude is small. On an amplitude-frequency graph, the resonance peak is tall and narrow for lightly damped systems, and shorter and broader for heavily damped systems.
Damping
Damping is the process by which energy is removed from an oscillating system, reducing its amplitude over time. Light damping: the system continues to oscillate with amplitude that decreases exponentially; the oscillations persist for many cycles. Critical damping: the system returns to equilibrium as quickly as possible without oscillating; used in car suspension and galvanometer needles. Heavy (overdamping): the system returns to equilibrium slowly without oscillating. Resonance peaks are lower and broader for more heavily damped systems; in some applications (like car suspension), heavy damping is desirable to prevent dangerous resonance.
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Frequently Asked Questions, IB Physics Standing Waves & Resonance
What is Standing Waves & Resonance in IB Physics? ↓
Formation of standing waves, nodes and antinodes, harmonics in strings and pipes, resonance, natural frequency and damping. This topic is part of Theme C (Wave Behaviour) in the current IB Physics syllabus.
Is Standing Waves & Resonance SL or HL in IB Physics? ↓
Standing Waves & Resonance is covered by both SL and HL students in the current IB Physics syllabus. HL students study additional depth and extension content beyond the SL core.
What equations do I need for IB Physics Standing Waves & Resonance? ↓
The key equations for Standing Waves & Resonance are covered in the concept tutorial above. For a structured set of notes with all equations, conditions and worked examples, the GradePod Exam Pack includes a revision note template for every topic.
What are common exam mistakes in IB Physics Standing Waves & Resonance? ↓
Common mistakes are covered in detail in the exam technique video above. The GradePod Exam Pack also includes exam-style questions with mark schemes so you can see exactly how marks are awarded and where students typically drop them.
How do I revise Standing Waves & Resonance for the IB Physics exam? ↓
Follow the GradePod three-step method. First, watch the concept tutorial and tick off each learning objective on the checklist above as you go. Second, watch the exam technique video to see how IB-style questions are answered under exam conditions. Third, use the Exam Pack to practise independently with knowledge questions, exam questions and mark schemes. That's it. It works. I promise.