The Dynamical Theory of Sound
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The result may be deduced from (27), or more directly from (15). We find » = Hm J P - J, (ct) (29) For example, in the special problem above considered, where 4>o (r) = 0, whilst Xo ( r ) = c\ or according as r $ a, we find = c\t or according as t $ a/c. The consequent value of 8 at is s for t a/c, whilst at the instant t = a/c it is negative infinite. To escape this result we must slightly modify the data, replacing the original distribution of density by a continuous one. The figure is an ...attempt to GENERAL THEORY OF SOUND WAVES 211 shew an initial distribution of s which varies rapidly but continuously from s to in the neighbourhood of r = a, together with the consequent time-variation of s at 0.
i Oh- 1 -cb Fig. 66.
The problem which we have discussed exhibits a marked contrast with the theory of plane waves, in that the wave resulting from an arbitrary disturbance contains both con- densed and rarefied portions, even when there is no initial velocity and the initial disturbance of density has everywhere the same sign.
What to read after The Dynamical Theory of Sound?
You can find similar books in the "Read Also" column, or choose other free books by Lamb, Horace, Sir, 1849-1934 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The result may be deduced from (27), or more directly from (15). We find » = Hm J P - J, (ct) (29) For example, in the special problem above considered, where 4>o (r) = 0, whilst Xo ( r ) = c\ or according as r $ a, we find
i Oh- 1 -cb Fig. 66.
The problem which we have discussed exhibits a marked contrast with the theory of plane waves, in that the wave resulting from an arbitrary disturbance contains both con- densed and rarefied portions, even when there is no initial velocity and the initial disturbance of density has everywhere the same sign.
What to read after The Dynamical Theory of Sound?
You can find similar books in the "Read Also" column, or choose other free books by Lamb, Horace, Sir, 1849-1934 to read onlineMoreLess
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