Problem P. 4342. (April 2011)
P. 4342. There are three vases on the table, none of them is taller than 40 cm. The hole in all of them is a vertical cylinder. The first vase can be filled with 2 dl water, the second one with 3 dl, and the third with more than 6 dl water. The area of the cross section of the first vase is 10 cm^{2}, the area of the cross section of the other two vases is 20 cm^{2}. There is the same amount of water in each vase. It can be observed that if a specific tuning fork is placed just above the vases, its sound is getting louder. The width of the bottom of each vase is 1 cm, the speed of sound in air is 340 m/s, and the frequency of the tuning fork is less than 1 kHz.
a) What is the amount of water in each vase?
b) What is the frequency of the tuning fork?
c) What is the height of the third vase?
(5 pont)
Deadline expired on 10 May 2011.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle a)\) A vázákban 1 dl víz van.
\(\displaystyle b)\) 850 Hz.
\(\displaystyle c)\) 36 cm.
Statistics:
36 students sent a solution.  
5 points:  Antalicz Balázs, Béres Bertold, Bolgár Dániel, Czigány Máté Gábor, Czipó Bence, Filep Gábor, Fonyó Viktória, Hoffmann Hanna, Horicsányi Attila, Horicsányi Krisztina, Koncz Gabriella, Kovács 444 Áron, Maász Máté, Maknics András, Nagy 111 Miklós, Pataki Bálint Ármin, Pázmán Koppány, Pető János, Sárvári Péter, Seress Dániel, Simon Sebestyén, Szabó 928 Attila, Szélig Áron, Szemes Gábor Bence, Szilágyi 585 Dezső, Ürge László, Zsámboki Richárd. 
4 points:  Horváth 721 Klaudia, Kerti Dávid. 
3 points:  4 students. 
2 points:  3 students. 
