Think and solve!

Since 1974, when the traditional Delta made its first public appearance, over 800 mathematical problems and over 450 problems in physics have occupied our readers' minds, not counting hundreds of problems included in our continuous mathematical and physical leagues. In most cases their solution requires more thinking than computing, and finding an elegant solution can provide much satisfaction.

The problems are always published with a solution, hidden somewhere in the same issue of the journal. However, we will not provide solutions here. Try for yourself. And if you really cannot find anything and you are sure you do not want to continue trying, but you still wish to know the solution, write to pawelst@mimuw.edu.pl or bartol@mimuw.edu.pl and ask for one. In order to make our communication easier, we preserve the original numbers of the problems as they appeared in Delta. You may quote them when asking for a solution. But before you ask, think and solve!

In this issue we offer you two physical problems by Krzysztof Rejmer.


F 399. If you stand close to a waterfall, you can feel the vibration of the Earth's surface. What is the height of the waterfall, if the frequency of these vibrations is f? The velocity of sound in water is taken to be v and we assume the water is falling down vertically.


F 400. Why the pitch of wind instruments becomes higher during an orchestra's warm-up, while the pitch of string instruments becomes lower?