9702 · 8.1
Stationary waves flashcards
Revision flashcards for Cambridge 9702 Stationary waves (syllabus 8.1). Flip, recall, then mark a real past-paper question.
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How are stationary waves typically formed?
By the superposition of two identical progressive waves travelling in opposite directions.
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What distinguishes the energy transfer in a stationary wave?
There is no net transfer of energy along the wave. Energy is stored within the segments.
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Define a 'node' in a stationary wave.
A node is a point where the particles consistently have minimum (often zero) displacement due to continuous destructive interference.
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Define an 'antinode' in a stationary wave.
An antinode is a point where the particles experience maximum displacement from their equilibrium position due to continuous constructive interference.
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What is the distance between two adjacent nodes in terms of wavelength (λ)?
λ/2.
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What is the distance between an adjacent node and an antinode?
λ/4.
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What is the phase relationship between particles located between two adjacent nodes?
They vibrate in phase with each other.
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What is the phase relationship between particles on opposite sides of a node?
They are in antiphase (180° out of phase).
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State the formula for the fundamental frequency of vibration of a stretched string.
$f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$ (L=length, T=tension, $\mu$=mass per unit length).
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What is the 'fundamental frequency' (first harmonic) of a vibrating string?
The lowest frequency at which a stationary wave can form, typically with one antinode between fixed ends.
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What is the boundary condition for displacement at a closed end of an air column?
A displacement node (zero displacement).
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What is the boundary condition for displacement at an open end of an air column?
A displacement antinode (maximum displacement).
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For a pipe of length L closed at one end, what is the wavelength of the fundamental frequency?
λ = 4L. This corresponds to the first harmonic.
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For a pipe of length L open at both ends, what is the wavelength of the fundamental frequency?
λ = 2L. This corresponds to the first harmonic.
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Compare the amplitude of particles in a stationary wave versus a progressive wave.
In a stationary wave, amplitude varies from zero (nodes) to maximum (antinodes). In a progressive wave, all particles oscillate with the same amplitude.