Julius Sumner Miller: Lesson 33 - Vibrating Bars and Strings - The Phenomenon of Beats

Описание: A - We look again more circumspectly at the two bars mounted on a reson¬ating chambers. They are fixed at two very special points. When sounded each alone they sound ALIKE - IDENTICAL. But they are not! One is 440 and the other 441. Hence we hear ONE beat per second. The "beat frequency "is the difference in the natural frequencies.

B - We explore this matter with two mounted tuning forks. They ARE identical. But now we load one with a rubber band - thus in¬creasing its inertia and lowering its pitch.
We now hear beats.

C - A long steel bar is held at a certain place along its length.. .at a point quite like the point where the A-bar is fixed to its resonating chamber. We strike the bar transversely. It vibrates with two nodes.
We ask: How far along the length of the bar is a node? The answer might well appear to be 1/4 the length - that is 0.25 L. But this is not quite right. It is 0.224 L — and this is a very difficult exercise for students of Physics. Look into this some time.

E - Two tuning forks mounted on their resonating chambers are highly responsive to each other. If they are identical we can strike ONE -damp it - that is - stop it - and low and behold - the other is heard.

F - A set of tuned sticks cut to precise lengths - of hard wood - clear -grained - can give rise to the major diatonic scale if dropped in proper sequence on a hard floor.

G - We now look at vibrating strings: A magnetically-driven steel sliver has a string fixed to it. We hold the remote end of the string. With a certain length and a certain tension in the string we can show the fundamental of the string - the first overtone - the second - and so on — called by some the harmonics. What the string does is governed by its length - its tension - its linear density - that is -how fat it is.

And so we see and hear the beautiful things that sounding devices give us. Of all our human faculties and senses that of hearing is a truly remarkable one and it is a pitiful thing for those who cannot hear.