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Understanding Longitudinal Standing Waves

May 21, 2025

BTEC Applied Science Unit 1: Physics - Longitudinal Standing Waves

Overview

  • Longitudinal standing waves are different from transverse stationary waves (e.g., guitar strings).
  • These occur in pipes and tubes, unlike the progressive longitudinal waves, which are typical sound waves.

Progressive vs. Stationary Waves

  • Progressive Wave:
    • Particles oscillate parallel to wave direction.
    • Compressions travel (e.g., sound from a speaker).
    • Particles don't actually move but oscillate.
  • Stationary (Standing) Wave:
    • Occurs in musical instruments.
    • Created by a vibration that causes waves to travel, interfere, and result in constructive interference forming a stationary wave.

Types of Tubes

Closed at One End

  • Closed end must be a node, open end an antinode.
  • Node: Minimal particle vibration.
  • Antinode: Maximum particle vibration.
  • Fundamental Frequency: Length of tube = 1/4 wavelength (λ).
  • Harmonics:
    • Can't have second harmonic (node at open end not allowed).
    • Get odd harmonics: 1st, 3rd, 5th, etc.

Open at Both Ends

  • Both ends are antinodes, with a node in the middle.
  • Fundamental Frequency: Length of air column = 1/2 wavelength (λ).
  • Harmonics:
    • All harmonics possible: 1st, 2nd, 3rd, etc.

Example: Organ Pipe

  • 50 cm Pipe Open at Both Ends:
    • Length = 0.5 m, fundamental wavelength = 1 m.
    • Fundamental frequency: 300 Hz.
    • All harmonics present: multiples of 300 Hz.
  • Closed at One End:
    • Wavelength = 2 m (4× tube length).
    • Fundamental frequency: 150 Hz.
    • Only odd harmonics: 1st, 3rd, 5th, etc.

Factors Affecting Sound in Instruments

  • Length of Air Column:
    • Longer column = larger wavelength, lower frequency (e.g., trombone).
  • Valves and Holes:
    • Changes effective length and harmonics.
    • Open holes act as nodes.
  • Mouthpiece Type:
    • Affects fundamental frequency and harmonics.
    • Flute/Oboe: Behave like open end.
    • Clarinet/Trumpet: Behave like closed end (odd harmonics).

Example Questions

  1. Wooden Pipe 30 cm Open at Both Ends:
    • Consider length and harmonics possible.
  2. Six Mark Question: Factors affecting frequency and tone in musical instruments, based on air column vibration.

Study Tips

  • Understand the differences between progressive and stationary waves.
  • Be familiar with the characteristics of nodes and antinodes in closed and open tubes.
  • Practice calculating fundamental frequencies and harmonics in different tube conditions.
  • Learn to identify factors affecting sound production in wind instruments.

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