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RESONANCE.
61
of condensation and rarefaction, that is, the intensity of the sound, rapidly increasing to a maximum. To compare this with the ex­periment of the suspended weight:—the vibrations of the fork cor­respond to the properly timed impulses, and the air in the tube to the suspended body: and, just as in that experiment, the essential point was the proper timing of the impulses, so in this case the essential matter is, that the downward journey of the condensation, shall coincide with the downward movement of the prong. In order that this coincidence may occur each time, it is evident that the wave must travel down and up the tube, in exactly the same time that the fork makes one vibration; that is, while the fork makes one vibration the sound must travel twice the length of the tube. Moreover, every vibration of the fork gives rise to one sound wave; therefore, in order that a tube open at both ends may give its maximum resonance when excited by a fork, it must be half as long as the sound wave originated by that fork.
It will be seen that a certain amount of resonance is obtained if the tube is twice this length; for in that case, every alternate descent of the prong will coincide with a condensation below, and each alternate ascent with a rarefaction; but such resonance will evidently be much feebler. For intermediate lengths, the fork will soon be in opposition to the pulses in the tube, and thus no resonance can result.
Tubes closed at one end are termed stopped tubes; with these the case is somewhat different. Let A B, fig 33, represent a stopped tube, the lower prong of the tuning-fork above, being about to descend towards it. As we have already seen, this gives rise to a condensation A C, which travels down to B D. The air particles in B D, having no way of escape, save backwards, press upon those in C D, and thus the condensation is reflected back to C D, and finally to A C. From here some of the condensed particles escape into the external air, leaving the remaining particles slightly wider apart; that is, a slight rarefaction is formed. If while this has been taking place, the prong has reached its lowest position and is just returning, this movement will have the effect of increasing the rarefaction. This latter will then be transmitted down the tube to BD. On reaching this, there will be less pressure in B D than in D C, and Fig. 33.