Motion in one transverse plane

The piano string is under tension, which causes transverse (at right angles to the string's length) forces to appear when the string is displaced. This enables the string to act as a medium for carrying waves. The hammer strike transfers energy to the string and creates travelling waves moving in both directions away from the position of hammer strike. An analogous effect can be seen when a pebble is dropped in a pond, except that in the pond waves move in all horizontal directions, in concentric circles, away from the pebble's entry position in the water.

When the waves on the piano string reach the boundaries at the ends of the string's speaking length (between the two bridges, or between a bridge and an agraffe), they are reflected or partially reflected back along the string, in the opposite direction.

There are then two sets of waves moving along the string, in opposite directions, being continuously reflected at the boundaries, and moving back again in the opposite direction.

As the two waves pass each other, they create a new kind of wave called a standing wave, which does not travel along the string, but nonetheless moves the string in a transverse wave motion.

The vibration of the string is the motion of standing waves. This may be difficult to imagine - so to see how two travelling waves moving in opposite directions along a string, combine to form standing waves.

click here.

Motion in two transverse planes

Real piano strings in situ move in two transverse planes. The motion is still essentially standing wave motion, but the general behaviour is more complicated than waves in one plane can describe. There are some important aspects of piano tuning that can only be described when motion in two planes is accounted for.