We have already explained that, in a medium such as air, a wave of compression is propagated at a speed which is measured by the square root of the quotient of the air-pressure, or elasticity, by its density. In exactly the same way the hump that is formed on a rope by giving one end of it a jerk, runs along at a speed which is measured by the square root of the quotient of the stretching force, or tension, by the density. The propagation of a pulse or wave along a string is most easily shown for lecture purposes by filling a long indiarubber tube with sand, and then hanging it up by one end. The tube so loaded has a large weight per unit of length, and accordingly, if we give one end a jerk a hump is created which travels along rather slowly, and of which the movement can easily be watched. We may sometimes see a canal-boat driver give a jerk of this kind to the end of his horse-rope, to make it clear some obstacle such as a post or bush. If we do this with a rope fixed at one end, we shall notice that when the hump reaches the end it is reflected and returns upon itself. If we represent by the letter _l_ the length of the rope, and by _t_ the time required to travel the double distance there and back from the free end, then the quotient of 2_l_ by _t_ is obviously the velocity of the wave. But we have stated that this velocity is equal to the square root of the tension of the rope (call it _e_) by the weight per unit of length, say _m_. Hence clearly— 2_l_/_t_ = √(_e_/_m_); or _t_ = 2_l_ · √(_m_/_e_) Supposing, then, that the jerks of the free end are given at intervals of time equal to _t_, or to the time required for the pulse to run along and back again, we shall find the rope thrown into so-called _stationary waves_. If, however, the jerks come twice as quickly, then the rope can accommodate itself to them by dividing itself into two sections, each of which is in separate vibration; and similarly it can divide itself into three, four, five, or six, or more sections in stationary vibration. The rope, therefore, has not only one, but many natural free periods of vibration, and it can adapt itself to many different frequencies of jerking, provided these are integer multiples of its fundamental frequency. The above statements may be very easily verified by the use of a large tuning-fork and a string. Let a light cord or silk string be attached to one prong of a large tuning-fork which is maintained in motion electrically as presently to be explained. The other end of the cord passes over a pulley, and has a little weight attached to it. Let the tuning-fork be set in vibration, and various weights attached to the opposite end of the cord.