**P. 4448.** The speed of sound in carbon dioxide is 1.3 times as much as that of in air. Two children, sitting 2 and 2 metres from the opposite sides of a balloon which is filled with carbon dioxide, and hanged in the height of the heads of the children, found that the balloon ``reinforce'' their whisper the most, exactly at this position.

Estimate the diameter of the balloon.

(5 points)

**P. 4449.** A space probe is to be shot from a point of the interplanetarial space at some speed with respect to the Sun, which is exactly half the speed at which the object would have circular path through the same point.

*a*) With respect to the Sun into which direction must the space probe be launched if it is to move away from the starting point the least?

*b*) With respect to the Sun into which direction must the space probe be launched if it is to move away from the starting point the most?

*c*) By what factor will the greatest distance between the probe and the starting point be greater in case of *b*) than in case of *a*)?

(Any effects except for the gravitation of the Sun are negligible.)

(5 points)

**P. 4451.** A sample of diatomic, ideal gas is taken through a cyclic process. The cyclic process can be composed of such open processes that the specific heat capacity of the gas during the certain processes does not change. The cyclic process is shown in the graph of the *figure.* The algebraic sum of the absorbed and delivered heat by the gas up to an instantaneous state, (*Q*), is shown on the horizontal axis, and the total amount of work done by the gas on its environment up to reaching the certain instantaneous state, (*W*^{*}), is shown on the *y* axis.

*a*) Using the graph, determine the efficiency of the cyclic process.

*b*) What types of processes build up the cyclic process? Reason your statements.

*c*) Let the pressure of the gas at state 1 be *p*_{0}, and its volume be *V*_{0}. Using these parameters plot the cyclic process on the *p*-*V* diagram.

(5 points)

**P. 4452.** In a long thin iron rod uniformly changing magnetic induction can be created. The induced voltage in a wire around the rod is *U*=10 mV. A wire is put around the rod such that into one half of it a resistor of resistance *R*_{1}=10 k, and into the other half a resistor of resistance *R*_{2}=20 k are inserted.

*a*) What is the reading on the ideal voltmeter connected to the *A* and *B *terminals of the resistors?

*b*) What would be the reading on a voltmeter of resistance *R*_{m}=100 k?

Does the measured voltage depend on to which side of the rod the meter is placed?

(5 points)

**P. 4453.** The density of the energy of the electric field inside a straight cylinder shaped metal rod is constant, its magnitude is J/m^{3}; the density of the energy of the magnetic field inside the rod at a distance of *r*=2 cm from the symmetry axis of the rod is J/m^{3}.

*a*) What is the resistivity of the material of the rod?

*b*) What kind of metal was the rod made of?

(5 points)

**P. 4454.** The volume of a cubic aquarium, which is filled with water halfway, is *V*=8 litres. Salt is carefully dissolved in the water such that the refractive index of the water, with respect to light which illuminates the water from below, changes with the height *h* measured from the bottom of the aquarium as a function of *n*(*h*)=*n*_{0}-*kh*^{2}, where *n*_{0}=1.35 is the refractive index at the bottom and *k*=2 m^{-2} is a constant.

The aquarium is illuminated by a light-beam perpendicularly to one of its side. On the other side a screen is moved. The screen always remains parallel to that side of the aquarium which is illuminated by the light. How far is the screen from the aquarium, when only a thin sharp, horizontal line of light can be observed on it?

(6 points)