IB DP Physics: SL复习笔记4.5.3 Boundary Conditions for Standing Waves

Boundary Conditions

  • Stationary waves can form on strings or in pipes
  • In both cases, progressive waves travel in a medium (i.e. the string or air) and superimpose with their reflections
  • The number of nodes and antinodes that fit within the available length of medium depends on:
    • The frequency of the progressive waves
    • The boundary conditions (i.e. whether the progressive waves travel between two fixed ends, two free ends or a fixed and a free end)

Standing Waves on Stretched Strings

  • When guitar strings are plucked, they can vibrate with different frequencies
  • The frequency with which a string vibrates depends on:
    • The tension, which is adjusted using rotating 'tuning pegs'
    • The mass per unit length, which is the reason why a guitar has strings of different thicknesses

4-5-3-standing-waves-on-stretched-strings_sl-physics-rn

Standing wave on a guitar string

  • For a string, the boundary condition can be
    • Fixed at both ends
    • Free at both ends
    • One end fixed, the other free
  • At specific frequencies, known as natural frequencies, an integer number of half wavelengths will fit on the length of the string
    • As progressive waves of different natural frequencies are sent along the string, standing waves with different numbers of nodes and antinodes form

Standing Waves in Pipes

  • When the air within a pipe vibrates, longitudinal waves travel along the pipe
  • Simply blowing across the open end of a pipe can produce a standing wave in the pipe
  • For a pipe, there is more than one possible boundary condition, theses are pipes that are:
    • Closed at both ends
    • Open at both ends
    • Closed at one end and open on the other

Nodes & Antinodes

  • When a progressive wave travels towards a free end for a string, or open end for a pipe:
    • The reflected wave is in phase with the incident wave
    • The amplitudes of the incident and reflected waves add up
    • A free end is a location of maximum displacement - i.e. an antinode

4-5-3-pipe-open-at-both-ends_sl-physics-rn

Standing wave inside a pipe open at both ends

  • When a progressive wave travels towards a fixed end for a string, or closed end for a pipe:
    • The reflected wave is in anti-phase with the incident wave
    • The two waves cancel out
    • A fixed end is a location of zero displacement - i.e. a node
    • The open end is therefore a location of maximum displacement - i.e. an antinode

4-5-3-pipe-open-at-one-end_sl-physics-rn

Standing wave inside a pipe open at both ends

 

 

 

 

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