Annoying click when cutting off a note

There's an annoying click that I can hear on my Lenovo laptop when notes are played.  I'm sure it's caused by the hard truncation of the sine wave that I use to produce each note (I generated the notes using the Linux open source tone program).  But then the click doesn't seem to go away even after I attenuate each note to zero volume before turning it off.  Wonder if it's some other artifact?

SA