In this movie, you will visualize the vibrations of the string (at the top), of the soundboard (in the horizontal plane), and the propagation of the sound in the surrounding air (in the vertical crossing planes), when the C2 key is played.

The string is at the top of the picture. The left hand side is the agraffe while the right hand side is the bridge. It is attached to the soundboard at the crossing point of the vertical planes. The transversal displacement is magnified while the longitudinal displacement is represented in a color scale (see legend on the right). The hammer strikes at a point located on the left (0.12 times the length of the string). It can be seen that the longitudinal wave propagates much faster than the transversal wave. So it arrives first at the bridge (right end point). Because the string forms a small angle from horizontal (see the first image of the movie), the longitudinal displacement is transmitted to the soundboard at the attached point. This is why the soundboard begins its motion with a negative (blue) displacement, which is represented with an arbitrary color scale. Then, when the transversal wave arrives at the bridge, it pulls the soundboard towards positive displacements, changing the color to red (positive values).

Meanwhile, the soundboard radiates into the surrounding air. The scale is changing along time, so that the precursor phenomenon can be seen although it is much smaller than the main phenomena occurring afterwards. The piano’s cabinet is an obstacle to the sound propagation, which can be seen in the movie. The computational domain is artificially bounded with PML in order to let out the acoustic waves.

In the following movie, you will visualize the (magnified) vibrations of the soundboard with no change of scale along time.