﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  133 
  

  

  the 
  writer's 
  judgment 
  that 
  the 
  resonance 
  was 
  distinctly 
  

  

  sharper 
  for 
  the 
  3^4 
  fork 
  than 
  for 
  the 
  128 
  fork. 
  Indeed, 
  a 
  

   shift 
  of 
  the 
  water-level 
  of 
  a 
  centimetre 
  or 
  more 
  for 
  the 
  lower 
  

   fork 
  seemed 
  to 
  correspond 
  to 
  a 
  shift 
  of 
  2*5 
  mm. 
  for 
  the 
  

   higher 
  fork. 
  

  

  Reviewing 
  now 
  the 
  last 
  four 
  experiments, 
  we 
  deduce 
  the 
  

   important 
  result 
  that 
  if 
  either 
  Melde's 
  or 
  Helmholtz's 
  ex- 
  

   periment, 
  or 
  that 
  with 
  the 
  adjustable 
  water- 
  resonator, 
  is 
  

   used 
  for 
  a 
  determination 
  of 
  the 
  pitch 
  of 
  a 
  fork, 
  then, 
  ceteris 
  

   •paribus, 
  the 
  work 
  is 
  susceptible 
  of 
  higher 
  accuracy 
  for 
  high 
  

   pitches 
  than 
  for 
  low 
  ones; 
  since 
  at 
  the 
  higher 
  pitches 
  the 
  

   resonance 
  is 
  sharper. 
  

  

  Brass 
  Instruments. 
  — 
  Let 
  us 
  now 
  consider 
  the 
  behaviour 
  of 
  

   the 
  air 
  in 
  the 
  brass 
  instruments 
  used 
  in 
  orchestral 
  and 
  other 
  

   bands. 
  The 
  phenomena 
  in 
  question 
  form 
  an 
  important 
  

   illustration 
  of 
  the 
  theory 
  here 
  advanced. 
  The 
  air 
  contained 
  

   in 
  such 
  instruments 
  vibrates 
  in 
  response 
  to 
  the 
  appropriate 
  

   impressed 
  forces 
  applied 
  at 
  the 
  cupped 
  mouthpiece 
  by 
  the 
  

   player's 
  lips 
  and 
  breath. 
  Further, 
  this 
  column 
  of 
  air, 
  like 
  

   the 
  thread 
  in 
  Melde's 
  experiment, 
  can 
  give 
  a 
  series 
  of 
  tones 
  

   according 
  to 
  the 
  number 
  of 
  vibrating 
  segments 
  into 
  which 
  it 
  

   is 
  divided. 
  Again, 
  the 
  vibrations 
  of 
  the 
  air 
  in 
  these 
  in- 
  

   struments 
  may 
  be 
  expected 
  to 
  have 
  a 
  very 
  large 
  value 
  of 
  the 
  

   damping 
  coefficient 
  (^/2), 
  for 
  the 
  whole 
  mass 
  of 
  this 
  air 
  is 
  

   very 
  small, 
  yet 
  the 
  activity 
  of 
  its 
  output 
  is 
  very 
  great. 
  

   Thus 
  we 
  may 
  anticipate 
  that 
  such 
  instruments 
  will 
  show 
  

   very 
  plainly 
  a 
  range 
  of 
  resonance 
  and 
  a 
  difference 
  in 
  this 
  

   range 
  from 
  note 
  to 
  note, 
  as 
  in 
  Melde's 
  experiment. 
  And 
  so 
  

   they 
  do, 
  but 
  they 
  have 
  also 
  complications 
  of 
  their 
  own 
  which 
  

   are 
  not 
  present 
  in 
  the 
  vibrating 
  thread. 
  

  

  These 
  complications 
  involve 
  a 
  disturbance 
  of 
  the 
  pitch 
  of 
  

   the 
  prime 
  and 
  arise 
  as 
  follows. 
  As 
  is 
  well 
  known, 
  an 
  ope?i 
  

   parallel 
  pipe 
  of 
  given 
  length 
  and 
  width 
  has 
  a 
  certain 
  funda- 
  

   mental 
  tone 
  and 
  the 
  full 
  harmonic 
  series 
  of 
  other 
  tones. 
  A 
  

   stopped 
  pipe 
  of 
  the 
  same 
  dimensions 
  has 
  a 
  fundamental 
  

   nearly 
  an 
  octave 
  lower 
  and 
  only 
  the 
  odd 
  series 
  of 
  harmonics. 
  

   A 
  pipe 
  in 
  the 
  form 
  of 
  a 
  complete 
  cone 
  with 
  open 
  base 
  and 
  

   closed 
  vertex 
  of 
  the 
  same 
  length 
  and 
  base 
  diameter 
  as 
  the 
  

   foregoing, 
  has 
  a 
  fundamental 
  in 
  agreement 
  with 
  the 
  open 
  

   parallel 
  pipe, 
  and 
  has 
  also 
  the 
  full 
  harmonic 
  series 
  of 
  other 
  

   tones. 
  

  

  The 
  brass 
  instruments 
  now 
  under 
  consideration 
  may 
  be 
  

   regarded 
  as 
  derived 
  from 
  the 
  cone 
  by 
  

   (i.) 
  the 
  opening 
  of 
  the 
  vertex, 
  

   (ii.) 
  the 
  introduction 
  of 
  a 
  mouthpiece? 
  at 
  that 
  end, 
  and 
  

  

  (iii.) 
  the 
  provision 
  of 
  a 
  bell 
  at 
  the 
  other 
  end. 
  

  

  