**P. 3861.** The internal part of a long-necked vase is a vertical cylinder, the diameter of its base is 3 cm and its volume is 2 dl. The vase is filled with water such that the air column above the water amplifies the sound of a vibrating tuning fork placed above the vase. Interestingly if the water from this vase is poured into another long-necked vase, the air above the water again amplifies the sound of the tuning fork. The internal part of this vase is a cylinder with base diameter 3 cm, and volume 3 dl. The bottoms of both vases are 1.7 cm thick, the speed of sound in air is 342 m/s, and the frequency of the tuning fork is smaller than 1 kHz.

*a*) Find the heights of the vases.

*b*) Find the volume of the water that was poured into the vases.

*c*) What is the frequency of the tuning fork?

(4 points)