Plucking vs Bowing

There are 2 main ways that you can produce sound on a string instrument, you can either pluck the string or use a bow.
                                 
                             Fig. 1. sketch of what happens when a string
                              is plucked, from Joe Wolfe Strings, Standing
                              Waves and Harmonics; 2016.

Plucked

As shown in fig.1, when a string is plucked it has "pulse wave that propagate[s]" in both directions from where it was plucked (Rossing, 2014). The resulting vibration is what we hear, and it can be considered as a "combination of several modes of vibration" (Rossing, 2014). What is meant by that is, if the string is plucked from the center, the vibration is a mix of "the fundamental plus the odd-numbered harmonics" (Rossing, 2014); and if the string is plucked from any where other than the center it will have a mix of the modes it is made of, and thus will sound different to us. Since there are so many options, we can find the speed (corresponding to the sound we hear) of the resulting sound wave using this equation:
           
                                        Vsound,string = sqrt(T/µ)
                       
where T is the tesion and µ is the mass per unit length (sqrt mean square root) (McGill, 2017).

 Bowed

When one uses a bow, instead of just plucking, a few things about our waves change. Fisrt off, the string now has "continuos energy" so now it can continue it's motion indefinitely (lets pretend we will never run out of bow) (Wolfe, 2016). Also, the shape of the string that is required to match the uniformely moving bow is different as well.

                          
                           Fig. 2. A sketch of the reflection of travelling kinks caused by bowing a
                           string, from Joe Wolfe, Strings, Standing Waves and Harmonics; 2016.

Another intersting thing is that a string actually doesn't just vibrate back and forth. In actuality, the string "forms two straight lines with a sharp bend at the point of intersection", as seen in fig. 2, and the bend moves around that curved path we see (Rossing, 2014).