7. The transverse displacement of a standing wave on a string is given by

y(x,t) = 4 sin(0.5x) cos(30t), where x and y are in centimeters (cm). 

What is the wave speed of component waves?
(A) 10 cm/s
(B) 15 cm/s
(C) 30 cm/s
(D) 60 cm/s
(E) 120 cm/s.

8. For an ideal gas undergoing an adiabatic process, both its volume (V) and temperature (T) change. Which one of the following would remain constant? (γ = Cp/Cv) (A) (B) TVγ-1 (C) TγV (D) TγV-1 (E) None of the above.

9. One mole of monatomic ideal gas is used as the working substance of an engine that operates the reversible cycle abcd shown in the figure. What is the efficiency of this engine? (A) 1/2 (B) 1/4 (C) 2/11 (D) 2/13 (E) None of the above.

10. Continued from problem 9. Suppose there is a Carnot engine operating between the highest and the lowest temperature in the cycle abcd. What is the efficiency of this Carnot engine? (A) 1/4 (B) 1/2 (C) 5/8 (D) 3/4 (E) 4/5.

11. Two flat metal plates are a distance d apart, where d is small compared with the plate size. If the plates carry surface charge densities σ and -σ, what is the magnitude of the potential difference between them? (A) σd/ε₀ (B) σ/dε₀ (C) σd/2ε₀ (D) 2σd/ε₀ (E) σ/ε₀.

12. A conducting sphere is charged with a total charge Q (Q ＞ 0) and in electrostatic equilibrium. Which of the following statement is true? (The electric potential at infinity is defined zero.) (A) The potential is the lowest, but not zero, at the center of the sphere. (B) The potential at the center of the sphere is zero. (C) The potential at the surface is higher than the potential at the center. (D) The potential at the center is the same as the potential at infinity. (E) The potential at the center of the sphere is the same as the potential at the surface.

13. A particle of mass m and charge q is circling on an orbit of radius R normal to an external magnetic field Bext. This moving charge would create a new magnetic field. What is this new magnetic field at the center of the orbit? (A) (B)(C)(D)(E) None of the above.

14. What is the time constant τ for the combination shown in the figure? (A) 3RC/8 (B) 3RC/4 (C) 4RC/3 (D) 8RC/3 (E) None of the above.

15. A long conductive rod of radius R carries a nonuniform current density J(r) = J₀r/R, where J₀ is a constant and r is the radial distance form the rod axis. What is the expression for the magnetic field strength inside this rod? (A) μ₀J₀r (B) μ₀J₀r²/3R (C) μ₀J₀r²/R (D) μ₀J₀r²/5R (E) None of the above.

16. Suppose the magnetic field ( B ) in a plane electromagnetic (EM) wave is given by B = Byĵ, where By = 2×10⁻⁷sin(0.5×10³x + 1.5×10¹¹t) Tesla, ĵ is the unit vector along the y direction, and the SI unit is adopted. What is the expression for the electric field vector E(x,t) (in the SI unit) of this EM wave? (A) 60sin(0.5×10³x + 1.5×10¹¹t) î, where î is the unit vector along the x direction. (B) -60sin(0.5×10³x + 1.5×10¹¹t) î, where î is the unit vector along the x direction. (C) 60sin(0.5×10³x + 1.5×10¹¹t) k̂, where k̂ is the unit vector along the z direction. (D) -60sin(0.5×10³x + 1.5×10¹¹t) k̂, where k̂ is the unit vector along the z direction. (E) None of the above.

17. The reason why viruses can be seen using electron microscope is that the wavelength of electron can be smaller than the size of viruses. Assume an electron microscope has an accelerating voltage of 40 kV. What is the wavelength of the electron? (A) 0.006 nm (B) 0.003 nm (C) 0.06 nm (D) 0.03 nm (E) 0.6 nm.

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