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Question 1 [16 marks]
A 50.0 g object connected to a spring with a force constant at 35.0 N/m oscillates on a horizontal
frictionless surface with an amplitude of 4.00 cm. Find:
(a) the total energy of the system
(b) the kinetic energy when the object is 3.0 cm from its equilibrium position.
(c) the potential energy when the object is 3.0 cm from its equilibrium position.
Question 2 [16 marks]
When an open metal pipe is cut into two pieces, the lowest resonance for the air column in one piece is
256 Hz and that for the other is 440 Hz.
(a) What resonant frequency would have been produced by the original pipe?
(b) How long was the original pipe?
Note: Assume that the speed of sound is v = 343 m/s.
Question 3 [16 Marks]
A thin sheet of mica (n = 1.58) is used to cover one slit of a double-slit arrangement. The central
point on the screen is now occupied by the fringe that corresponds to the m = 7 fringe in the absence
of the mica. If λ = 550 nm, what is the thickness of the mica?
Question 4 [16 Marks]
Silicon has a refractive index of n = 3.5 for visible light. To minimize reflective losses at the surface,
a silicon solar cell is coated with a thin layer of silicon monoxide (n = 1.45).
Determine the minimum thickness of this layer that will produce the least reflection at a wavelength
of 550 nm.
