15. A string of length L and linear density λ is stretched to a tension T. What is the expression of its resonance frequencies of standing waves?
(A)
(B)
(C)
(D)
(E),where n is any positive integer. (Hint: Wave equation of small displacement y is )

11. Same setting as problem 10, what is the work done by the piston during the expansion process?(A) 24 J； (B) 21 J； (C)18 J； (D) 16 J； (E) o J.

12. Same initial condition as in problem 10, but this time we insulate the system from the environment such that the expansion process is quasi-static and adiabatic. Starting with 20℃ and 10 liter, what is the volume of the chamber when the pressure reaches 1 atm? Assuming the specific heat are and (A) 24 liter； (B) 22.1 liter； (C)18.4 liter； (D) 16.9 liter； (E) 12.3 liter.

13. Same as problem 12, what is the change of entropy during this process?(A) 24 J/K； (B) 21 J/K； (C)18 J/K； (D) 16 J/K；(E)0 J/K.

14. In electrostatic equilibrium, the electric field just outside any charged con- ductor is(A) always zero； (B) always perpendicular to the surface of the conductor； (C)always parallel to the surface of the conductor, along the gra- dient of the surface charge distribution； (D) always parallel to the surface, but perpendicular to the gradient of the surface charge distribution, (E) of no particular direction.

16. Two parallel infinite wires 2cm apart carry currents of 1A and 8A, separately. What is the force per meter between them?(A) (B) N/m； (C)(D) (E)

17. A 1.2 mF capacitor is connected across a generator whose output is V = Vosin(2πft), with Vo = 20 V, f = 60 Hz, and t in seconds. Find the peak current and absolute value of the current at t = 5ms.(A) 9.05A, 2.80A； (B) 9.05A, 1.80A； (C)1.44A, 0.45A； (D) 1.44A, 0.25A； (E) 9.05A, 8.61A.

18. The deBroglie wavelength of a non-relativistic particle with mass m and speed u is:(A)(B)(C) (D) (E) . Here h is the Planck constant and c is the speed of light.

19. A solenoid of 10cm in diameter and 2.0m in length carries 25 Amperes current. It produces an internal magnetic feld of 100 mT. How many turns of wire does this solenoid have?(A) 3183；(B) 32； (C)6366； (D) 64； (E) 12732. 

20. The following fgure shows a conductive sphere with a spherical cavity in the center. The total charge on the conductor is zero, but a point charge Q is placed at the center of the cavity. How does the electric potential (V) as a function of the distance from the center (r) looks like?(A)(B) (C)(D)(E)

複選題21. Two balls of masses my = 1 kg and mo = 100 kg, with initial speed 1 m/s and 10 m/s, respectively, collide inelastically in space. They stick together after the collision. Which of the following is true in the Center of Mass Frame? (A) The total momentum does not change； (B) The total kinetic energy does not change； (C)The magnitude of velocity change of me is less than that of mi； (D) The magnitude of momentum change of me is less than that of my； (E) The magnitude of kinetic energy change of me is less than that of my.