If two strings, tuned to give forth the same number of vibrations per second, are struck at the same time, the tone produced will appear to come from a single source; one sweet, continuous, smooth, musical tone.  The reason is this:  The condensations sent forth from each of the two strings occur exactly together; the rarefactions, which, of course, alternate with the condensations, are also simultaneous.  It necessarily follows, therefore, that the condensations from each of the two strings travel with the same velocity.  Now, while this condition prevails, it is evident that the two strings assist each other, making the condensations more condensed, and, consequently, the rarefactions more rarefied, the result of which is, the two allied forces combine to strengthen the tone.

In opposition to the above, if two strings, tuned to produce the same tone, could be so struck that the condensation of one would occur at the same instant with the rarefaction of the other, it is readily seen that the two forces would oppose, or counteract each other, which, if equal, would result in absolute silence.[G]

[G] When the bushing of the center-pin of the hammer butt becomes badly worn or the hammer-flange becomes loose, or the condition of the hammer or flange becomes so impaired that the hammer has too much play, it may so strike the strings as to tend to produce the phenomenon described in the above paragraph.  When in such a condition, one side of the hammer may strike in advance of the other just enough to throw the vibrations in opposition.  Once you may get a strong tone, and again you strike with the same force and hear but a faint, almost inaudible sound.  For this reason, as well as that of preventing excessive wear, the hammer joint should be kept firm and rigid.

If one of the strings vibrates 100 times in a second, and the other 101, there will be a portion of time during each second when the vibrations will coincide, and likewise a portion of time when they will antagonize each other.  The periods of coincidence and of antagonism pass by progressive transition from one to the other, and the portion of time when exactitude is attained is infinitesimal; so there will be two opposite effects noticed in every second of time:  the one, a progressive augmentation of strength and volume, the other, a gradual diminution of the same; the former occurring when the vibrations are coming into coincidence, the latter, when they are approaching the point of antagonism.  Therefore, when we speak of one beat per second, we mean that there will be one period of augmentation and one period of diminution in one second.  Young tuners sometimes get confused and accept one beat as being two, taking the period of augmentation for one beat and likewise the period of diminution.  This is most likely to occur in the lower fifths of the temperament where the beats are very slow.