The violin is commonly used for sad music because of its sound and the waves of the music that can be achieved with the violin. Not just the violin, the stringed instruments have a sound that is close to the human voice, so it is a common choice for composers of emotional music.
Keep in mind that violin can also be used to play happy music too because the major keys tend to sound happy and then the minor keys tend to sound sad. Another thing, most people no longer listen to classical were violin can be used to play really nice and happy music. Therefore, there is no much exposure to what the violin can do.
Violins are ideally suited to producing the sad music and expressing the downside of human emotions. The sound of the violin flawlessly captures the raw emotion of the human voice. The tone frequencies that come with a violin resonate from our ears and into our hearts. The sound of the violin also closely matches the characteristics of sadness in the human speech.
The more "sad" instruments can be played more solemnly, slower and with a small gentle range of pitch movements. The violin also has a lower pitch than most instruments, which makes it capable of capturing a wide range of feelings. Also, the violin has extreme levels of vibrato, which makes it sound rather dramatic.