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/s^{2} 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 λ_{water} to that in steel λ_{steel} ?

(a) λ_{steel} / λ_{water} = 0.25 (b) λ_{steel} / λ_{water} = 0.73 (c) λ_{steel} / λ_{water} = 1.00 (d) λ_{steel} / λ_{water} = 2.53 (e) λ_{steel} / λ_{water} = 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 β_{7} when it is 7 m away and β_{9} when it is 9 m away.

Find the difference β_{7} - β_{9}.

(a) β_{7} - β_{9} = 0.98 dB (b) β_{7} - β_{9} = 1.58 dB (c) β_{7} - β_{9} = 2.18 dB

(a) β = β_{9} + 4.8 (b) β = 3 β_{9} (c) β = 4.8 β_{9}

(a) 671 Hz (b) 690 Hz (c) 702 Hz (d) 715 Hz (e) 740 Hz

(a) ΔA = 5.3 × 10^{-4} m^{2} (b) ΔA = 7.8 × 10^{-4} m^{2} (c) ΔA = 9.3 × 10^{-4} m^{2} (d) ΔA = 11.2 × 10^{-4} m^{2} (e) ΔA = 13.5 × 10^{-4} m^{2}

In a container of volume V = 0.5 m^{3} is 0.8 kg of an ideal gas. Its pressure is P = 1. 25 × 10^{5} 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) v_{580} / v_{290} = 1.21 (b) v_{580} / v_{290} = 1.31 (c) v_{580} / v_{290} = 1.41 (d) v_{580} / v_{290} = 1.71 (e) v_{580} / v_{290} = 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) A (b) B (c) C

(a) A (b) B

(a) 0.10 kg (b) 0.15 kg (c) 0.20 kg

(a) (b) (c) (d) (e)

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) upward (b) downward

(a) 1.4 m/s^{2} (b) 1.7 m/s^{2} (c) 2.0 m/s^{2} (d) 2.3 m/s^{2} (e) 2.6 m/s^{2}

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} m^{3}). Assume that the mass density of water is 1,000 kg/m^{3}.

What is the mass density of the unknown material?

(a) 1,250 kg/m^{3} (b) 1,100 kg/m^{3} (c) 900 kg/m^{3} (d) 750 kg/m^{3} (e) 600 kg/m^{3}

(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 same situation:

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 first time?

(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 r_{1} to r_{2} between regions 1 and 2 (see figure, not to scale). The fluidic velocity in region 1 is v_{1} (= 3 m/s) and the fluidic velocity in region 2 is v_{2} (= 9 m/s). The density of fluid is 1,300 kg/m^{3}.

What is the ratio between r_{2} and r_{1}?

(a) r_{2} / r_{1} =0.58 (b) r_{2} / r_{1} =0.44 (c) r_{2} / r_{1} =0.33

(a) |P_{2}-P_{1}| = 24,500 Pa (b) |P_{2}-P_{1}| = 35,300 Pa (c) |P_{2}-P_{1}| = 46,800 Pa (d) |P_{2}-P_{1}| = 57,900 Pa (e) |P_{2}-P_{1}| = 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/m^{3}.

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.

(T) True (F) False

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?