86 Mr. W. Baily on the Vibrations of a Film 



Hitherto we Lave dealt only with infinite films ; we will 

 now consider what forms of vibration can be maintained in 

 films of limited size, the waves undergoing reflection from the 

 boundaries of the film. 



When the film is an equilateral triangle, suppose a set of 

 waves to be started having their fronts J_ to one of the sides 

 of the triangle. These waves will be reflected so as to have 

 their fronts J_ to another side, and again reflected so as to 

 have their fronts _|_ to the remaining side, and by another 

 reflection they will assume their first direction. If the wave- 

 length is such that the time a wave takes to return to the same 

 position is an integral number of wave-periods, we shall have 

 the case of three sets of equal waves meeting each other at 

 angles of 120°. Fig. 8 shows the form of vibration when the 

 wave-length is -^ of the side of the triangle (no allowance 

 being made for the change of phase at the reflections). The 

 thin lines show the position of the maximum displacement due 

 to each wave at one of the instants at which these lines all 

 pass through certain points, and the numerals 1, 1 show the 

 ventral segments which are then at their maximum displace- 

 ment, the ventral segments 2, 2 and 3, 3 come to their maxi- 

 mum at different times, as already explained. 



Again, suppose two sets of waves to be started in opposite 

 directions, each set having the front J_ to a side of the tri- 

 angle, and the phases of both sets being the same along a per- 

 pendicular from an angle on the opposite side ; we shall with 

 a suitable wave-length have six sets of waves meeting each 

 other in pairs, the directions of the pairs making with one 

 another angles of 120°, and all the phases being the same at 

 certain points. 



Again, suppose waves to start simultaneously from each of 

 the sides of the equilateral triangle; the waves will be reflected 

 so as to produce other three sets of waves also with their fronts 

 parallel to the sides, by having their direction of motion reversed. 

 Here we again get the six sets of waves above considered, but 

 in a different position. See fig. 6, in which this form of vibra- 

 tion is shown, without allowing for any change of phase at the 

 reflections. The continuous lines show the coincidence of the 

 maximum displacement in one direction due to the waves meet- 

 ing ; and the dotted lines show the same coincidence in the 

 opposite direction. At the black spots we get the coincidence 

 of all the maximum displacements in the same direction ; so 

 that these spots show the ventral segments. The wave-length 



x/3 

 is equal to the distance between the ventral segments x — — . 



"With the number of ventral segments shown in the figure the 



