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Vibrations of Stretched Strings — Syllabus

ICSE · Class 11 · Physics

What Vibrations of Stretched Strings covers in ICSE Class 11 Physics: 4 topics, for the 2026-27 session. Part of the ICSE Class 11 Physics syllabus.

53 questions32 flashcards19 formulas & key relations5 concepts

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Diagram of a string fixed at both ends vibrating in its fundamental mode (first harmonic), showing one loop, two nodes at the fixed ends, and one antinode at the center. The wavelength is twice the st
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4 Topics · ICSE Class 11 Physics · 2026-27

Topics in Vibrations of Stretched Strings

1

1. Stretched String and Wave Speed

  • A string is a wire or fibre of uniform diameter and is perfectly flexible, with no rigidity.
  • A wire clamped at both ends and plucked in the middle produces transverse progressive waves that travel towards both ends.
  • The speed of transverse waves on a stretched wire depends on tension T and mass per unit length m.
2

2. Laws of Vibrations of Stretched Strings

  • Law of Length: for a given string under a given tension, frequency varies inversely as vibrating length.
  • Law of Tension: for a uniform string of given length and material, frequency varies directly as the square-root of tension.
  • Law of Mass: for a given tension and vibrating length, frequency varies inversely as the square-root of mass per unit length.
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3. Standing Waves and Modes of Vibration

  • A wave moving on the string reflects at the fixed end with a phase change of pi.
  • Superposition of incident and reflected waves produces a stationary wave.
  • The resultant equation is not a travelling wave because its argument is not of the form vt ± x.
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4. Positions of Nodes and Antinodes

  • In the pth mode, there are p + 1 nodes.
  • Nodes are at x = 0, l/p, 2l/p, 3l/p, ..., l.
  • Antinodes are at x = l/(2p), 3l/(2p), 5l/(2p), ..., (2p - 1)l/(2p).

Key Concepts

Central concept: Transverse stationary waves in a stretched string fixed at both ends, along with their frequency relations, harmonics, nodes, antinodes, sonometer use, and tuning fork vibration properties.

StringTransverse waves on a stringReflection at fixed endsStationary waveBoundary conditionsFundamental modeOvertones and harmonicsNodes and antinodes

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Frequently Asked Questions

What are the important topics in Vibrations of Stretched Strings for ICSE Class 11 Physics?
Key topics in Vibrations of Stretched Strings include Stretched String and Wave Speed, Laws of Vibrations of Stretched Strings, Standing Waves and Modes of Vibration, Positions of Nodes and Antinodes. Study these first, then practise questions on each for Class 11 exams.
How should I revise Vibrations of Stretched Strings for Class 11 exams?
Learn the core ideas first, then work through the 53 practice questions on Vibrations of Stretched Strings. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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