﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  131 
  

  

  is 
  well 
  pronounced 
  the 
  wire's 
  vibrations 
  will 
  be 
  felt 
  and 
  

   checked 
  at 
  each 
  touch, 
  and 
  even 
  though 
  the 
  touches 
  may 
  be 
  

   repeated 
  very 
  quickly, 
  a 
  marked 
  vibration 
  is 
  felt 
  each 
  time. 
  

   If, 
  however, 
  owing 
  to 
  the 
  considerable 
  mistiming, 
  the 
  

   response 
  is 
  very 
  feeble, 
  the 
  vibrations 
  are 
  scarcely 
  detectable 
  

   even 
  after 
  longer 
  intervals 
  are 
  allowed 
  for 
  their 
  elicitation. 
  

   And 
  when 
  the 
  mistiming 
  is 
  pushed 
  still 
  farther, 
  no 
  response 
  

   whatever 
  can 
  be 
  felt. 
  This 
  was 
  the 
  state 
  of 
  things 
  for 
  

   positions 
  of 
  the 
  bridge 
  just 
  a 
  few 
  millimetres 
  beyond 
  those 
  

   given 
  in 
  Table 
  IV., 
  which 
  record 
  the 
  last 
  perceptible 
  effects. 
  

  

  Table 
  IV. 
  

   Helmholtz's 
  Experiment. 
  

  

  Frequencies 
  of 
  Forks 
  

  

  128 
  

  

  256 
  

  

  384 
  

  

  512 
  

  

  Number 
  of 
  Segments 
  

  

  1 
  

  

  2 
  

  

  3 
  

  

  4 
  

  

  

  Extreme 
  Lengths 
  (in 
  cm.) 
  of 
  

   Steel 
  Wire 
  lor 
  responses 
  just 
  

   perceptible 
  

  

  72-3 
  

  

  680 
  

  

  720 
  

  

  68-5 
  

  

  717 
  

   69 
  5 
  

  

  715 
  

  

  R9-4- 
  

  

  

  

  Differences 
  of 
  Lengths 
  

  

  4-3 
  

  

  35 
  

  

  22 
  21 
  

  

  Intervals 
  (in 
  cents) 
  of 
  mis- 
  

   tunings 
  above 
  and 
  below 
  

  

  Is3 
  

  

  43 
  

  

  27 
  

  

  25 
  5 
  

  

  Mistunings 
  : 
  M= 
  ^ 
  

  

  p 
  n 
  " 
  

  

  0-0611 
  

  

  00496 
  

  

  00311 
  

  

  00294 
  

  

  This 
  experiment 
  was 
  one 
  of 
  the 
  early 
  ones 
  carried 
  out 
  

   before 
  the 
  theory 
  was 
  fully 
  developed, 
  and 
  is 
  only 
  roughly 
  

   quantitative. 
  It 
  indicates 
  that 
  the 
  range 
  of 
  resonance 
  de- 
  

   creases 
  with 
  increase 
  of 
  frequency, 
  and 
  that 
  all 
  the 
  ranges 
  

   are 
  less 
  than 
  the 
  corresponding 
  ones 
  in 
  the 
  case 
  of 
  Melde's 
  

   experiment. 
  And 
  these 
  results 
  are 
  in 
  accord 
  with 
  theory, 
  

   for 
  the 
  k 
  is 
  clearly 
  much 
  smaller 
  for 
  the 
  dense 
  smooth 
  steel 
  

   wire 
  than 
  for 
  the 
  light 
  fluffy 
  silk 
  line. 
  It 
  is 
  not, 
  however, 
  

   easy 
  to 
  determine 
  k 
  for 
  this 
  wire 
  ; 
  as 
  if 
  the 
  wire 
  is 
  plucked 
  

   and 
  let 
  go 
  and 
  the 
  amplitude 
  observed 
  by 
  a 
  reading 
  micro- 
  

   scope, 
  one 
  is 
  troubled 
  by 
  a 
  rotation 
  of 
  the 
  plane 
  of 
  transverse 
  

   vibration. 
  Thus, 
  at 
  first, 
  the 
  amplitude 
  appears 
  to 
  decrease 
  

  

  K 
  2 
  

  

  