I am following the lessons from the website "www.studybass.com". I stumbled upon this exercise and i think that the time signature 2/2 is wrong. It is impossible for 2 half notes to fit in a bar that has 2 beats. So should I mentally change the time signature? Or is the exercise right?
The exercise is correct.
The numerator of the time signature does indicate the number of "beats." However, just as important is the denominator of the time signature, which tells you what note value receives one beat. Thus the 2/2 time signature means that there are two beats in the measure, where each beat is one half note in length. Thus a measure with two half notes fits 2/2 time exactly.
This time signature is also known as "cut time," or alla breve.
The trick is to recognize that a quarter note is not always one beat. It's only worth one beat where the time signature has a 4 in the denominator.