1887.] On some measurements of the notes of a whistle. 91 
very roughly approximate in consequence of the narrowness of the 
pipe in which the resonance takes place. 
At Mr Horace Darwin’s request we undertook to attempt some 
measurements of the pitch of the notes sounded by such whistles 
by a method which would be independent of the calculation of 
the pitch from the pipe-length, and in this way to test the 
accuracy of the calculation of pitch by that method. The plan 
which seemed most promising was to obtain the true wave- 
lengths of the notes in free air by the use of a sensitive flame in 
the way suggested by Lord Rayleigh, “Acoustical Observations”, 
IL., Phil. Mag. [5] vir. p. 153*. The formula of p. 90 could then 
be safely employed to calculate the vibration frequency of the note. 
A number of observations were taken on this plan, details 
of which are given below. 
The wave-length measured in this way was always considerably 
greater than four times the length of the whistle-pipe, and it 
varied appreciably with the pressure of the air with which the 
whistle was blown: and here a difficulty as to the interpretation 
of the results should be mentioned. In order to obtain the nodes 
the whistle must be blown continuously; this was done by means 
of a heavily loaded gas-bag, the pressure being measured in the 
usual way by a U-tube; but when the whistle is used for testing 
the limit of audibility it is blown by the sudden puffs at an 
uncertain and doubtless varying pressure, obtained by compressing 
the rubber bladder. Fora particular length of pipe one particular 
pressure gives the clearest note, and it is possible that this is 
the note which the ear regards as the note sounded when the 
bladder is squeezed, and that the different lengths of whistle 
should be compared at those particular pressures. This however 
is matter of speculation rather than of experimental evidence. 
An interesting point is suggested by the occurrence of nodes 
for very short wave-lengths. The flame could be made to flare by 
the whistle however short the length of the pipe might be, but 
the shortest wave-length for which we have been able to obtain 
nodes is 1584 mm. corresponding to a vibration frequency of 
21,517 complete vibrations per second. This value was obtained 
with the reading 3 mm. of the length of the whistle-pipe, and 
with the same whistle the extreme limit of audibility for our own 
ears was as follows 
F. M. T. shortest length of whistle-pipe 3°38 mm. 
BVPI N iS aio cents at ermesrs cine < Ste «ious 3°7 mm. 
so that distinct nodes were obtained when the sound was inaudible. 
It is however very difficult to get them satisfactorily and no good 
* Reproduced in Glazebrook and Shaw’s Practical Physics, p. 180. 
