Bauhaus-Universität Weimar

Sound and Music. A Non-Mathematical Treatise on the Physical Constitution of Musical Sounds and Harmony
Taylor, Sedley
V. §51.] 
is represented slightly below the other, though, in 
fact, the two are strictly coincident. 
Let the waves abdf...z be moving from left to 
right, the waves zt's'n...a from right to left. The 
crest him meets the trough pnm at m. After these 
have crossed each other, the trough ghk and the crest 
rqp will also meet at m, since km and pm are equal 
distances. Similarly the crest efg and the trough 
ts'r will meet at m. Accordingly the point m is a 
node, and, by exactly the same reasoning, so are a, c, 
e, g, k, p, r, t, àc. The distances between pairs of 
consecutive nodes are all equal, each being a single 
pulse-length, i.e. half a wave-length, of either series. 
Two pulse-lengths, as gk and km, give three nodes 
g, k, and m ; three pulse-lengths four nodes, and so on. 
There is thus always one node in excess of the num¬ 
ber of pulses. On the other hand, the fixed ends of 
the tube, which are the origins of the systems of re¬ 
flected waves, occupy two of these nodes. Deducting 
them we arrive at this result. 
The number of nodes is one less than the number 
of the pulse-lengths {or half wave-lengths), which 
together make up the length of the vibrating tube.


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