True-false questions are worth 2 points each, three-choice multiple
choice questions are worth 3 points each, five-choice multiple choice
questions are worth 6 points each. The maximum possible score is 114;
the average score was 80.1; the median score was 81. The exam period
was 90 minutes. Click here to see page1
page2 of the formula sheet that came
with the exam.
Unless told otherwise, you should assume that the acceleration of
gravity near the surface of the earth is 9.8 m/s2
downward and ignore any effects due to air resistance.
Choose the closest number to the correct answer when a numerical
answer is required>.
Assume that a pendulum is near the earth's surface.
A sound wave of frequency f travels from water (speed of sound
is 1500 m/s) to steel (speed of sound is 5600 m/s). What is the ratio
of the wavelength of this sound in water λwater
to that in steel λsteel ?
(a) λsteel / λwater = 0.25
(b) λsteel / λwater = 0.73
(c) λsteel / λwater = 1.00
(d) λsteel / λwater = 2.53
(e) λsteel / λwater = 3.73
(a) f = 7 kHz
(b) f = 12 kHz
(c) f = 16 kHz
(d) f = 19 kHz
(e) f = 21 kHz
The number of nodes in the figure is 4 (including both ends).
We now change the block of mass M to another block of mass
m, while keeping the frequency of the transducer the same. This
produces a standing wave with 3 nodes on the string (including both
ends). What is the required mass m of the new block?
(a) m = 9 M / 4
(b) m = 7 M / 4
(c) m = 3 M / 2
(d) m = 5 M / 4
(e) m = 3 M / 4
A siren gives a loudness β7 when it is 7 m
away and β9 when it is 9 m away.
Find the difference β7 -
(a) β7 - β9 = 0.98 dB
(b) β7 - β9 = 1.58 dB
(c) β7 - β9 = 2.18 dB
(a) β = β9 + 4.8
(b) β = 3 β9
(c) β = 4.8 β9
(a) 671 Hz
(b) 690 Hz
(c) 702 Hz
(d) 715 Hz
(e) 740 Hz
(a) ΔA = 5.3 × 10-4 m2
(b) ΔA = 7.8 × 10-4 m2
(c) ΔA = 9.3 × 10-4 m2
(d) ΔA = 11.2 × 10-4 m2
(e) ΔA = 13.5 × 10-4 m2
In a container of volume V = 0.5 m3 is 0.8 kg of an
ideal gas. Its pressure is P = 1. 25 × 105 Pa
at temperature T = 290 K.
What is the molecular mass M of the molecules making the gas?
(a) M = 22.3 amu
(b) M = 30.8 amu
(c) M = 33.5 amu
(d) M = 41.1 amu
(e) M = 49.0 amu
(a) v580 / v290 = 1.21
(b) v580 / v290 = 1.31
(c) v580 / v290 = 1.41
(d) v580 / v290 = 1.71
(e) v580 / v290 = 2.00
An object of mass m is hanging from a vertical spring of spring
constant k (= 20 N/m) near the surface of the earth. In
equilibrium, the spring is stretched by 10 cm relative to the relaxed
length of the spring. The spring is then compressed by 1 cm relative to
the equilibrium position and is released into oscillation at time
t = 0. The height of the object relative to the equilibrium
height oscillates as shown below as a function of time.
Among the three time points marked A and B and C, when is the speed
of the object the greatest?
(a) 0.10 kg
(b) 0.15 kg
(c) 0.20 kg
A pendulum hanging from the ceiling of an elevator is swinging with
the period of 2 seconds when the elevator is at rest. Assume that the
elevator is near the surface of the earth. Suddenly, the elevator
undergoes vertical acceleration and the period of the pendulum has
changed to 2.2 seconds.
What is the direction of acceleration?
(a) 1.4 m/s2
(b) 1.7 m/s2
(c) 2.0 m/s2
(d) 2.3 m/s2
(e) 2.6 m/s2
A container is filled with water to the brim and a uniform block of
unknown density is added to the container. The block floats with 75% of
its volume immersed in water and the amount of water overflowed from the
container is 1 liter (1 liter is 10-3 m3). Assume
that the mass density of water is 1,000 kg/m3.
What is the mass density of the unknown material?
(a) 1,250 kg/m3
(b) 1,100 kg/m3
(c) 900 kg/m3
(d) 750 kg/m3
(e) 600 kg/m3
(a) 9.8 N
(b) 11.2 N
(c) 12.5 N
(d) 15.7 N
(e) 18.2 N
This question and the following one relate to the
A pendulum is made of a small weight of mass 1.5 kg attached to a
string of length 2 m. The mass is released gently with the initial angle
displacement of 5°.
How long does it take for the mass to reach its lowest point for the
(a) 2.84 s
(b) 1.42 s
(c) 0.71 s
(a) 0.33 J
(b) 0.22 J
(c) 0.11 J
An incompressible and non-viscous βfluid flows from left to
right through a circular pipe that changes its radius from
r1 to r2 between regions 1 and 2
(see figure, not to scale). The fluidic velocity in region 1 is
v1 (= 3 m/s) and the fluidic velocity in region 2 is
v2 (= 9 m/s). The density of fluid is 1,300
What is the ratio between r2 and r1?
(a) r2 / r1 =0.58
(b) r2 / r1 =0.44
(c) r2 / r1 =0.33
(a) |P2-P1| = 24,500 Pa
(b) |P2-P1| = 35,300 Pa
(c) |P2-P1| = 46,800 Pa
(d) |P2-P1| = 57,900 Pa
(e) |P2-P1| = 0 Pa
Yuri constructs a barometer as shown below using water as
the fluid in order to measure the atmospheric pressure. He takes it to
the top of a mountain. The column of water reaches the height h
of 9.18 m. The water density is 1,000 kg/m3.
What is the atmospheric pressure measured by the barometer?
(a) 115,000 Pa
(b) 105,000 Pa
(c) 95,000 Pa
(d) 90,000 Pa
(e) 80,000 Pa
Which one of the following statements is true?
(a) The pressure of the fluid is everywhere the same because the
average height of the fluid is the same everywhere the same.
(b) The pressure of the fluid is smallest on the right end of the pipe
because its diameter is the largest.
(c) The pressure of the fluid is the smallest in the narrowed section
because the velocity is the largest there.
(d) The pressure of the fluid is the largest in the narrowed section because
the velocity is the largest there.
(e) None of the above statements is true.
You then blow into another pipe and the output sound is lower in
pitch. Which of these is a possible pressure variation recorded
just outside the pipe as a function of time?