﻿494 
  Prof. 
  C. 
  V. 
  Raman 
  on 
  the 
  Wolf-note 
  in 
  

  

  latter 
  case, 
  the 
  vibration 
  is 
  increased 
  by 
  the 
  addition 
  of 
  load 
  

   till 
  the 
  stage 
  is 
  reached 
  at 
  which 
  p 
  = 
  aq, 
  the 
  amplitude 
  then 
  

   becoming 
  very 
  large. 
  Subsequent 
  additions 
  of: 
  load 
  decrease 
  

   the 
  forced 
  vibration 
  till 
  it 
  finally 
  vanishes 
  in 
  the 
  limit. 
  

  

  3. 
  If, 
  however, 
  the 
  point 
  at 
  which 
  the 
  load 
  is 
  fixed 
  is 
  not 
  

   the 
  same 
  as 
  that 
  at 
  which 
  the 
  impressed 
  force 
  acts 
  on 
  the 
  

   system, 
  the 
  treatment 
  is 
  not 
  equally 
  simple. 
  The 
  expression 
  

   for 
  the 
  forced 
  vibration 
  then 
  obtained 
  from 
  the 
  Lagrangian 
  

   equations 
  has 
  the 
  determinant 
  for 
  the 
  free 
  periods 
  as 
  its 
  

   denominator; 
  but 
  the 
  numerator 
  contains 
  some 
  additional 
  

   terms, 
  the 
  magnitude 
  of 
  which 
  is 
  proportional 
  to 
  the 
  applied 
  

   load. 
  If 
  these 
  terms 
  are 
  ignored, 
  the 
  sequence 
  of 
  changes 
  

   with 
  increasing 
  load 
  would 
  be 
  exactly 
  the 
  same 
  as 
  that 
  

   stated 
  in 
  the 
  preceding 
  paragraph. 
  

  

  4. 
  There 
  is 
  no 
  difficulty 
  in 
  verifying 
  the 
  foregoing 
  indi- 
  

   cations 
  of 
  theory 
  experimentally. 
  In 
  the 
  case 
  of 
  the 
  violin 
  

   or 
  'cello, 
  at 
  least 
  the 
  first 
  three 
  of 
  the 
  natural 
  modes 
  of 
  

   vibration 
  of 
  the 
  instrument 
  have 
  to 
  be 
  taken 
  into 
  account 
  to 
  

   explain 
  the 
  phenomena 
  produced 
  by 
  the 
  mute 
  within 
  the 
  

   ordinary 
  range 
  of 
  tone 
  of 
  the 
  instrument. 
  The 
  two 
  first 
  

   resonance-frequencies 
  are 
  those 
  mentioned 
  by 
  Helmholtz 
  in 
  

   his 
  work. 
  The 
  pitch 
  of 
  the 
  first 
  is 
  only 
  slightly 
  lowered 
  by 
  

   the 
  mute. 
  The 
  second 
  is 
  the 
  well-known 
  " 
  wolf-note/' 
  and 
  

   the 
  pitch 
  of 
  this 
  is 
  depressed 
  by 
  about 
  450 
  cents 
  by 
  the 
  mute. 
  

   The 
  pitch 
  of 
  the 
  third 
  resonance 
  is 
  about 
  an 
  octave 
  higher 
  

   than 
  that 
  of 
  the 
  second, 
  and 
  this 
  also 
  gives 
  a 
  marked 
  

   " 
  wolf-note." 
  The 
  mute 
  lowers 
  the 
  pitch 
  of 
  this 
  by 
  about 
  

   700 
  cents. 
  The 
  mass 
  of 
  an 
  ordinary 
  brass 
  mute 
  is 
  sufficient 
  

   to 
  make 
  the 
  second, 
  third, 
  and 
  higher 
  resonance-frequencies 
  

   approximate 
  to 
  their 
  limiting 
  values. 
  The 
  effect 
  of 
  the 
  mute 
  

   should 
  accordingly 
  be 
  to 
  increase 
  the 
  intensity 
  of 
  the 
  graver 
  

   tones 
  and 
  harmonics 
  of 
  the 
  instrument, 
  and 
  to 
  decrease 
  those 
  

   of 
  high 
  pitch. 
  This 
  is 
  exactlj' 
  what 
  has 
  been 
  found 
  experi- 
  

   mentally 
  by 
  Edwards 
  (Physical 
  Review, 
  Jan. 
  1911). 
  

  

  5. 
  Mr. 
  Griltay's 
  criticisms 
  may 
  now 
  be 
  easily 
  disposed 
  of. 
  

  

  Experiment 
  shows 
  that 
  he 
  is 
  incorrect 
  in 
  saying 
  " 
  I 
  suppose 
  

  

  that 
  the 
  change 
  of 
  pitch 
  of 
  the 
  note 
  of 
  maximum 
  resonanc 
  e 
  

  

  of 
  bridge, 
  belly, 
  &c. 
  will 
  practically 
  be 
  the 
  same 
  whether 
  the 
  

  

  bridge 
  be 
  loaded 
  at 
  its 
  highest 
  point 
  or 
  as 
  low 
  as 
  possible 
  

  

  and 
  near 
  to 
  its 
  left 
  foot." 
  As 
  a 
  matter 
  of 
  fact, 
  trial 
  shows 
  

  

  that 
  the 
  lowering 
  of 
  the 
  pitch 
  of 
  either 
  of 
  the 
  two 
  " 
  w 
  r 
  olf- 
  

  

  notes 
  " 
  is 
  three 
  to 
  five 
  times 
  as 
  much 
  in 
  the 
  former 
  case 
  as 
  

  

  in 
  the 
  latter. 
  As 
  the 
  observed 
  mule-effect 
  is 
  less 
  when 
  the 
  

  

  load 
  is 
  placed 
  at 
  the 
  foot 
  of 
  the 
  bridge, 
  the 
  experiment 
  

  

  actually 
  furnishes 
  a 
  strong 
  confirmation 
  of 
  the 
  correctness 
  of 
  

  

  my 
  views, 
  and 
  shows 
  also 
  that 
  the 
  interpretation 
  given 
  by 
  

  

  