For multiple choice click on the correct answer for the solution.
 

1) The equation for a certain standing wave on a string is:
 

y = 5X10^-3(cos 2t)sin 16x
 

What is the approximate length of the shortest string that could be used? The amplitude and x are in metres and t is in seconds.
 

A) 0.5 m

B) 0.6 m

C) 0.4 m

D) 0.3 m

E) 0.2 m
 

2) Two travelling waves,
 

y = 0.10 sin(3t + 4px) metres
 

and
 

y = 0.20 sin(3t - 5px) metres
 

meet at t = 0. What is the displacement at x = 4.5 m?
 

A) 0.14 m

B) 0 m

C) -0.20 m

D) -0.14 m

E) 0.20 m
 

3) The intensity level 5.0 m from a speaker is 75 db. What acoustical power would pass through a rectangular opening (2.0 m x 1.0 m) in a wall at this distance from the speaker? Assume that the speaker is a point source radiating in all directions.
 

A) 6.32 x 10^-5 W

B) 7.98 x 10^-5 W

C) 4.85 x 10^-4 W

D) 1.36 x 10^-6 W

E) 1.78 x 10^-6 W
 

4) A whistle is emitting a frequency of 1000 Hz. You approach it at a speed of 4.00 m s^-1. What frequency will you hear?
 

A) 1012 Hz

B) 980 Hz

C) 1020 Hz

D) 1000 Hz

E) 1004 Hz
 

5) A black body at 800 K sits in a room at 27º C. Its surface area is 3.00 m². What net power does it radiate? (Stefan's constant is 5.62X10^-8 WK^-4m^-2)
 

A) 3.65 x 10³ W

B) 4.98 x 10³ W

C) 2.63 x 10⁴ W

D) 6.83 x 10⁴ W

E) 3.95 x 10⁵ W
 

6) A city is at 50º south latitude. At noon on a certain day, the Earth's axis of rotation is tilted 10º towards the Sun (i.e., the N pole is closer to the Sun than the S pole). What is the angle q you would use to calculate the average solar intensity at this city at this time?
 

A) 20 º

B) 30º

C) 40º

D) 50º

E) 60º
 

7)

A beam of light enters side 1 of a triangular piece of plastic (a prism) of index of refraction 1.5 as shown. The three sides of the prism are of equal length. Which of the following statements is correct?

 

A) The beam will emerge from side 1.

B) The beam will emerge from side 2.

C) The beam will emerge from side 3.

D) The beam will not emerge.

E) The problem cannot be solved because the wavelength of the light has not been given.
 

8)

A glass hemisphere of radius 5 cm is placed over a spot on a table and viewed from above. Where does the spot appear to be?

 

A) 5 cm below the top of the hemisphere.

B) At the top surface of the hemisphere.

C) 2.5 cm above its real position.

D) 5 cm above the top of the hemisphere.

E) At infinity.
 

9) Determine the wavelength of an n = 3 electron in a linear conjugated p-system of length 1.05 nm.
 

A) 0.4 nm

B) 0.7 nm

C) 2.1 nm

D) 2.8 nm

E) 4.5 nm
 

10) If the chromophore of question 9 contained 8 carbon atoms, what is the probability density of the n = 3 electron at the 2^nd or the 7^th carbon atom.
 

A) 2.4 nm^-1

B) 1.8 nm^-1

C) 3.2 nm^-1

D) 0.6 nm^-1

E) 4.8 nm^-1
 

11) A toaster is rated at 700 watts when plugged into a 115 volt (rms) circuit. Determine the resistance of the toaster.
 

A) 11.3 W

B) 0.16 W

C) 18.9 W

D) 2.80 W

E) 5.11 W
 

12) The radioactive decay product of ¹⁵₈O is (¹⁵₈O decays by beta-decay):
 

A) ¹⁵₉F

B) ¹⁶₈O

C) ¹⁴₉F

D) ¹⁴₇N

E) ¹⁵₇N
 

13) Determine the maximum kinetic energy of the -ray in the radioactive decay of ³¹₁₄Si. The mass of the electron is 0.000550 amu.
 

A) 7.3 x 10^-11 J

B) 2.4 x 10^-13 J

C) 1.6 x 10^-13 J

D) 4.9 x 10^-14 J

E) 9.2 x 10^-12 J

Atomic number Z	Element symbol	Mass number A	Atomic mass
12	Mg	24	23.985045
13	Al	27	26.981541
14	Si	28	27.976928
14	Si	31	30.975364
15	P	31	30.973763
15	P	32	31.973908
16	S	32	31.972072

 

14) Suppose that 2 years after a spill of radioactive tritium ( ³₁ T) into Lake Ontario a count rate of 670 counts/hour is obtained from a 10 ml sample of lake water. After another 2 years, the count rate from a similar sample is 410 counts/hour. If all the non-radioactive clearance processes (river outflow, evaporation, absorption into lake mud, etc.) can be assumed to have a half-life T_x, determine T_z. (Assume that complete mixing of the tritium throughout the lake has occurred. The radioactive half life of tritium is 12.33 yr)
 

A) 0.7 yrs

B) 1.7 yrs

C) 2.7 yrs

D) 3.7 yrs

E) 4.7 yrs
 

15) Which one of the following statements is false?
 

A) The light radiated by the Earth is primarily in the infrared region of the electromagnetic spectrum.
 

B) The greenhouse effect is due to the fact that the atmosphere is clear to incoming radiation in the ultraviolet and visible, but opaque to outgoing radiation in the infrared.
 

C) The main problem with excess CO₂ is that it increases atmospheric absorption in the near-ultraviolet region of the electromagnetic spectrum.
 

D) Determination of the Earth's albedo (the fraction of sunlight reflected to that absorbed) can be made by examining the moon at first or third quarter.
 

E) Some anthropogenic gases such as the chlorofluorocarbons can contribute to the greenhouse effect.
 
 
 

16) A crude telescope is constructed of 2 thin lenses of focal length 50 cm and 15 cm (the eyepiece) in air. The lenses are of glass of index of refraction 1.6. The front surface of the objective is placed just under the surface of a remarkably clear lake. What now will be the new separation between the lenses if both object viewed and the final image are at infinity? (Assume both surfaces of the objective have the same magnitude of radius of curvature. The index of refraction of water is 1.33)

ANSWER
 

17) A spring is suspended vertically from the ceiling. When a mass of 2.0 kg is hung on the end of the spring, the mass lowers 25 cm before it reaches its new equilibrium position. The mass is then raised 20 cm above the equilibrium position and released. Find the velocity of the mass the second time it is 10 cm below the equilibrium position.

ANSWER
 

18) A manufacturer of plastics needs to make a light filter which will absorb 80% of the photons (l = 488 nm) striking it. A measurement on a sample piece of the plastic 1.0 cm thick indicated that 30% of the photons striking it were absorbed.
 

(a) Determine the pathlength (thickness) required to absorb 80% of the photons.

ANSWER
 

(b) Determine absorbance of the plastic which absorbs 80% of the photons.

ANSWER

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