Physics 120 Christmas Exam

Physics 120 Christmas Exam - 1993

1.

``QUICKIES''

(a): [2 marks] For an ideal gas the pressure and temperature are directly related to one of the following velocities of the gas molecules (underline the correct one): (i) most probable velocity; (ii) average velocity; (iii) root-mean-square velocity; (iv) maximum velocity.
(b): [2 marks] In 1947 Estermann, Simpson & Stern carried out an experiment whose purpose was:
(c): [2 marks] Shining laser light on a multiple slit system you count eleven little maxima in between the principal maxima. The number of slits in the system is:
(d): [2 marks] You have a pair of sound sources of nearly the same frequency. The average frequency you hear is 264 Hz and, in addition, you hear six beats per second. The frequencies of the two sources are Hz and Hz.
(e): [2 marks] Much of the energy from the fusion reactions in the Sun's interior escapes from the Sun not in the form of light or heat (photons), but rather in the form of elusive particles called .
(f): [2 marks] In British Columbia we average 625 deaths per year from a certain kind of cancer. For any given year the number of deaths would be expected to lie within $\pm$ % of this average nineteen times out of twenty.
(g): [2 marks] You have a mass oscillating on a spring with a period of 0.4 s. You now remove half the mass. The new period of oscillation is then seconds.
(h): [2 marks] The escape velocity from the earth's surface is $1.12 \times 10^{4}$ m/s. If the earth were squashed, without loss in mass, to a sphere whose radius is 100 times smaller, the escape velocity from the surface would then be m/s.

2.

EXPONENTIALS

(a): [8 marks] If I have 40 rabbits and they double their number every 69 days, how many will I have after $1{1\over2}$ years? (Assume 1 year = 365 days.)
(b): [8 marks] What is the birthrate per day at the end of that time?

3.

SIMPLE HARMONIC MOTION

We have a mass of 2.0 kg oscillating on a spring with spring constant 120 N/m.

(a): [5 marks] What is the period of oscillation of the system?
(b): [10 marks] You observe that at t=0 the mass has a displacement of 0.10 m from its equilibrium position and a velocity of 2.0 m/s. What are the maximum displacement and maximum velocity of the mass?

4.

WAVES

You have an organ pipe of length 3.3 m which is open at one end and closed at the other. The speed of sound is 331 m/s.

(a): [6 marks] What are the frequencies of the fundamental mode and the next harmonic?
(b): [6 marks] The sound intensity scale is defined relative to a reference intensity, $I_0 \equiv 10^{-12}$ W/m², for which the decibel reading is zero. If, at a certain position, our organ pipe produces $2.3 \times 10^4$ W/m² of sound intensity, what decibel reading do we record?
(c): [6 marks] Explain in a few sentences why blowing at the open end of the organ pipe produces a mixture of all the harmonics of the pipe.

5.

DIFFRACTION

$\begin{figure} \epsfysize 2.0in \mbox{\epsfbox{/home/jess/P120/PS/line_source.ps} } \end{figure}$

You have a sound source emitting a frequency of 1260 Hz. The emitter has a width of $\ell = 1.5$ m from which sound emerges uniformly and in phase. If, as shown, you have a bank of sound receivers at a distance D=40 m from the source, with the line of receivers parallel to the source line, then . . .

(a): [6 marks] Give a qualitative drawing of how the sound intensity varies along the line of receivers.
(b): [6 marks] What is the distance, along the receiver line, from the central maximum to the first minimum? (Assume that the speed of sound is 331 m/s.)
(c): [8 marks] What is the ratio of the intensity at the third maximum to that of the central maximum? Give a numerical value and a phasor diagram.

6.

THIN FILM INTERFERENCE

$\begin{figure} \epsfysize 0.25in \mbox{\epsfbox{/home/jess/P120/PS/newtons_rings.ps} } \end{figure}$

You have a circular glass lens (cut from a sphere of radius 21.2 m) resting on top of a piece of perfectly flat glass. Viewing the lens with green light of wavelength 525 nm, incident normally from above, you see alternate bright and dark circular bands which are closer and closer together as their distance from the point of contact increases.

(a): [5 marks] Do you see a dark or bright circle at the centre (point of contact)? Explain why.
(b): [10 marks] Viewed from the top, what is the radius of the 17 $^{\hbox{\rm th}}$ dark circular band?

7.

PROBABILITY

(a): [10 marks] In a normal full deck of playing cards there are 52 cards, all different, with 13 cards (2,3,4,5,6,7,8,9,10,J,Q,K,A) in four different suits ( $\clubsuit, \diamondsuit, \heartsuit \hbox{\rm ~and } \spadesuit$ ). What is the probability that when you pull 7 cards at random from the deck, without replacing any card, you have a ``Royal Flush"? Having a ``Royal Flush" means that your 7 cards include A,K,Q,J & 10, all of the same suit, plus any two other cards.
(b): [10 marks] You have a bucket full of buttons (thousands and thousands of them) all identical except for colour. There are many different colours. You take out a cupful (containing very many buttons) and spill them on a table, counting only the red buttons. You repeat this many times, each time returning to the pail the buttons spilled on the previous trial and mixing the buttons in the pail well. After many such trials you notice that a cupful contains, on average, 6 red buttons. What is the probability that the next cup will contain three or less red buttons?

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