**P. 4286.** Waves are generated from a wave source, (the phase angle is zero when they are started.) and they travel along a straight line at a speed of 1 m/s. When a point, in the wave, has zero displacement, the closest point which has the maximim displacement is at a distance of 1 m.

*a*) Find the wavelength and the frequency.

*b*) What is the distance between those points whose phase difference is 270^{o}?

*c*) Measured from the initiation of the waves, when will the phase of the point 5 m from the wave-source first be 180^{o}?

(3 points)

**P. 4288.** A spring of length , is hang and when an object is attached to it, its length changes to 2. (The extension of the spring is proportional to the force and its mass is negligible.) When the object, attached to the spring, undergoes uniform circular motion along a horizontal path, the length of the spring is *L* What are the radius of the circle and the angular speed of the object?

(4 points)

**P. 4290.** A thin, strong steel cable is stretched horizontally, with a great force, above a street. A rope dancer walks along the cable. When she covers one-fourth of the length of the cable, (she is at point *N*) the trisecting point of the cable (*H*) is 10 cm below its original position. What will the decent of the point *N* be, when the rope dancer is at point *H*? (The mass of the cable is negligible, the deflection of the rope is very small with respect to the length of the cable, and the tension in the cable can be considered constant.)

(5 points)

**P. 4291.** Two soap bubbles are stuck to each other. One half of the gained shape has a radius of *R*=6 cm and the other half has a radius of *r*=2 cm.

*a*) What is the sphere-radius of the spherical cap which separates the two parts?

*b*) What is the difference between the pressures in the two parts? The surface tension of the soap solution is (=0.029 N/m.)

*c*) By what factor is *R* greater than *r* in case of two other bubbles which stick together, if the sphere-radius of the cap separating the two parts is *R*?

(4 points)

**P. 4294.** An initially stationary, charged, pointlike object can move along a horizontal surface, without friction. Not far from the object there is a long vertical solenoid. The current in thee solenoid is uniformly increased from zero to a given value, and then it is decreased also uniformly to zero again. At the end of this process to which direction will the charged object move with respect to the point *P*, shown *in the figure? *

(6 points)