Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 3861. (January 2006)

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 pont)

Deadline expired on February 13, 2006.

### Statistics:

 73 students sent a solution. 4 points: Almási 270 Gábor András, Dajka Attila Norbert, Dudás János, Elekes Csaba, Engedy Balázs, Gresits Iván, Hegyi Ádám, Hotzi Bernadette, Karai Róbert, Kónya 495 Gábor, Molnár 811 Kristóf, Nagy 224 Csaba, Nagy 317 Péter, Pálovics Róbert, Pásztor Attila, Rácz 206 György, Szaller Dávid, Széchenyi Gábor, Takács 484 Marcell, Tűri Balázs, Werner Miklós. 3 points: 31 students. 2 points: 9 students. 1 point: 8 students. 0 point: 1 student. Unfair, not evaluated: 3 solutions.

Problems in Physics of KöMaL, January 2006