most likely exaust leak, as stated. if its a front engine mounted ride, get underneath it and follow the exaust pipe from the enigne to the tail and see if there is a hole. muffler broken? not sure, but check it out. If the muffler was totaly broke it would sound worse than a bear under the hood, more like mini-nukes going off each time the cylinders fire, and the sound would be coming from the rear of the car.
not sure why putting the clutch in makes it worse, unless you're pumping the gas at the same time.
good luck.