The answer is yes, you can tighten it up but only in the short term. If you've done nothing else to engine recently this is an indication that the belt has started to get brittle so will not be as flexible as usual (unless you've somehow manged to get oil on it) In most cases tightness is achieved by moving alternator. Normally one or two pivot bolts and a securing bolt. As to cost and how of a new belt, depends on model, type and age of car.........£!5 for a haynes manual will be cheaper than any garage for something as simple as this....providing you've got some tools!
strevs
October 2007