SCIENCE 1 PHYSICS

Christmas Exam - 1998

- 2.5 hours -

Instructors: Jess H. Brewer & Domingo Louis-Martinez

1.
``QUICKIES''   [24 marks -- 4 each]
(a)
A particle has a position (x) as a function of time (t) given by   $x = b \, t^3$  where  b = 2  m/s3. What is the acceleration of the particle at  t = 1 s?
(b)
If you have a thousand radioactive atoms with a half-life of 3 hours, how many would you expect to decay in the first six hours?
(c)
A hailstone of mass m falling from the sky over Vancouver experiences a drag force given by Fd = k v2 where k is a constant and v is the hailstone's airspeed. What is the terminal airspeed of the hailstone in terms of m, g and k?
(d)
Two sound emitters have frequencies $\nu_1$ and $\nu_2$ whose average is 400 Hz. Their combined intensity exhibits 2 beats per second. What are $\nu_1$ and $\nu_2$?
(e)
One organ pipe (A) is open at both ends; another (B) is open at one end and closed at the other. If both have the same fundamental frequency, what is the ratio of their lengths,  LA / LB?   Hint: A sketch should help.
(f)
Suppose that you want to make a glass camera lens with a nonreflective coating of a transparent material whose index of refraction is higher than that of the glass. What is the optimum thickness of the coating?

2.
Right Hemisphere - Left Hemisphere   [15 marks]

Match up each of the following situations with one or more of the graphs shown: for each match, draw a connecting line and label the axes on the graph.

\epsfbox{graphs.ps}

3.
Falling Rod   [15 marks] A thin, uniform rod 1 m long is pivoted about a frictionless pin at one end. The rod is released from a vertical position with an infinitesimal angular velocity. Find the angular velocity and angular acceleration of the rod at the instant when it is horizontal.

\epsfbox{thin_rod.ps}

4.
Interference and/or Diffraction   [15 marks]

\epsfbox{6slit_grating.ps}

Blue-green light of wavelength $\lambda = 500$ nm passes normally through a planar array of parallel slits and makes the above intensity pattern on a screen D = 1.0 m away. Describe the array of slits in as much quantitative detail as you can.

5.
Thermal Physics   [16 marks]

Use words to define any mathematical symbols you use in answering the questions on this page.

(a)
[5 marks] What is the definition of the ENTROPY of a system?
(b)
[5 marks] What is the definition of the TEMPERATURE of a system?
(c)
[6 marks] A very simple organism has only two possible states: asleep (zero energy) and awake (energy $\varepsilon = 4.14 \times 10^{-21}$ J). If this organism is in thermal equilibrium with a heat reservoir at room temperature (300 K), what is the probability that it will be asleep?
Hint: The probabilities of the two possible states must add up to 1.
Boltzmann's constant: $k_{\scriptscriptstyle{\rm B}} = 1.38 \times 10^{-23}$ J/K.  

6.
YOUR CHOICE of DERIVATIONS   [15 marks]

Answer EITHER this question OR the one on the next page!

(a)
Power in a Wavy String

If a continuous transverse sinusoidal wave of amplitude A is propagating down a taut string of linear mass density $\mu$ at velocity v with frequency $\omega$, show that the power transmitted in the wave is   $P = {1\over2} \mu \, \omega^2 A^2 \, v$.

(b)
Doppler Effect

-- Answer EITHER this question OR the one on the previous page!

Sound waves emitted by a source moving directly toward a stationary observer at a speed v (less than the speed of sound c) will be detected at a frequency f which is different from the frequency f0 at which they are emitted in the rest frame of the source.

Show that f / f0 = c / (c - v).

\epsfbox{doppler.ps}

Hint: Think in terms of wave crests, as illustrated in the sketch above. How much does the source ``catch up'' with one wave crest before it emits the next one?



Jess H. Brewer
1998-12-18