As you probably know, sound is a wave, and more specifically, a pulse wave. This simply means that it is formed by areas of higher and lower pressure in the atmosphere through which it travels. Terms such as "amplitude," when used in reference to sound, are actually referring to the plot of the air pressure versus time on a graph. Now, it is difficult to believe that such (extremely small) fluctuations in air pressure could have any effect on a plant's growth. There is very little difference, to a plant, in music and ambient noise.

However, you might want to consider this question from another perspective. It is possible that in an experiment, plants which are exposed to music may grow more than plants that are not. Why? Because even though it is unlikely that the plants themselves respond to the music, their /caretakers/ do! Maybe the plants which are exposed to music receive better care than those which do not. Might be worth looking into!

Whether music affects plant growth has been the subject of many, many science fair projects. It seems as though it is uncertain whether music really does have an effect. Sound is a wave traveling through air and it may be possible that changes in air pressure may affect plant growth (thus even ambient noise may contribute to plant growth.) However, it's difficult to test this because there a lot of variables that need to be controlled i.e. soil composition, water, light, etc. Then how would you treat your negative control? Would you grow the plant in some kind of sound proof box such that a minimal amount of sound gets to it? It is definitely an interesting idea, but difficult to test rigorously.

There is no evidence to suggest that music has any effect on plant growth. Some people believe that it does in a mystical sense, but it has never been verified scientifically. Moreover, there is no reason, scientifically, to believe that plants should be affected by music either.