1. Invent yourself
Develop and construct a device for demonstrating the wave properties of sound in air.

2. Noon
Is it possible to call “noon” the moment in the middle of the time interval between sunrise and sunset? Using a calendar, you will easily notice that throughout the year this moment “drifts” relatively to a certain moment of time. Explain the cause of this effect.

3. Tides
Estimate the heights of the tides in the Black Sea on April 1, 1989.

4. Rolling friction
Investigate how the friction force depends on speed. To be more specific, consider the rolling of a wooden puck on wood (a wooden surface of a table.)

5. Clock
You have visited a planet and you plan to return to it in ten thousand or even in a million years. What clock would you leave on this planet to measure precisely the time of your absence from the planet?

6. Rainbow
Is it possible that three or more rainbows can appear on the sky simultaneously?

7. Sparks
When knives are sharpened on a grinding wheel, sparks fly away. Most often, a single spark bursts apart in all directions at the end of its flight. Explain the phenomenon.

8. Metro
Suggest the methods and measure the speed of a metro electric train midway between two stations. The same is to be done for a bus in which you are going, if there are no reliable distance signs on the route.

9. Astronaut
What maximum travel distance may an astronaut expect

1. at the modern level of technical development?
2. in the far future, when practically all technical difficulties will be overcome?

10. Aqueous planet
What amount of water may form a planet with a constant mass

1. far from the Sun;
2. in a distance of 1 AU from the Sun?

11. Mosquito
At what maximum altitude can a mosquito fly?

12. Sand in a tube
A glass tube is installed vertically and its lower end is tightly closed with a cap. The tube is filled with some sand. During what time T will the sand flow out of the tube, when the cap is opened? Investigate the dependence of T on the following parameters: size of sand grains d, length of the tube L, diameter of the tube D, at a constant degree of packing of sand (you have to introduce and validate this parameter on your own.) We ask you not to consider high degrees of packing for comparability of the results. It is preferred that 10 cm<L<1 m.

13. Electrolytic cell
Prepare some saturated solution of table salt NaCl. Immerse two carbon electrodes (sticks from manganese-zinc battery 373 (R20)) into it so that their metal contacts are not immersed into the solution. Investigate

1. the current-voltage characteristic of the created electrolytic cell in the range of currents from 10 μA to 50 mA;
2. how does the current-voltage characteristic change as the solution is diluted?

14. Fence
A remote large object is separated from you by a picket fence. It happens that you can see the object if you do not stay near the fence, but go along the fence in a car. Explain this phenomenon. What speed is sufficient if a is width of a fence board, b width of the gaps, L is distance to the fence (L>>a, b), γ is angular size of the remote object, γ>>(a+b)/L.

15. Electron
An electron with a velocity of v=3·105 m/s flies with an impact parameter d aside a metal ball with a radius of a few centimeters. The charge of the ball changes with time under a law q(t)=q0cosωt, where q0=10−3 C, ω=108 s−1. Build a dependence plot of the deviation angle φ of the electron on the impact parameter d.

16. Information
How many bits of information did you receive after having read the problems of a YPT? How many bits of information would you receive when looking at a geographic map with the size of a paper sheet?

17. Karlsson
With what rate should Karlsson eat jam not to get thinner during the flight?