MikaStars39/nano-eval huggingface dataset:
In a centrifugal tachometer, two homogeneous thin rods with lengths $a$ and $b$ are connected perpendicularly at point $O$, and point $O$ is hinged to a vertical axis. The vertical axis rotates at a constant angular velocity $\omega$, and the rod of length $a$ forms an angle $\varphi$ with the vertical line. What is the relationship between $\omega$ and $\varphi$ ?

Options:
A. $$
\omega^{2}=2 g \frac{b^{2} \operatorname{s i n} \varphi-a^{2} \operatorname{c o s} \varphi} {( a^{3}+b^{3} ) \operatorname{s i n} 2 \varphi}.
$$
B. $$
\omega^{2}=5 g \frac{a^{2} \operatorname{c o s} \varphi-b^{2} \operatorname{s i n} \varphi} {( a^{3}-b^{3} ) \operatorname{s i n} 2 \varphi}.
$$
C. $$
\omega^{2}=6 g \frac{b^{2} \operatorname{c o s} \varphi+a^{2} \operatorname{s i n} \varphi} {( a^{3}-b^{3} ) \operatorname{c o s} 2 \varphi}.
$$
D. $$
\omega^{2}=4 g \frac{a^{2} \operatorname{s i n} \varphi-b^{2} \operatorname{c o s} \varphi} {( b^{3}+a^{3} ) \operatorname{s i n} 2 \varphi}.
$$
E. $$
\omega^{2}=6 g \frac{a^{2} \operatorname{c o s} \varphi+b^{2} \operatorname{s i n} \varphi} {( b^{3}-a^{3} ) \operatorname{c o s} 2 \varphi}.
$$
F. $$
\omega^{2}=2 g \frac{a^{2} \operatorname{s i n} \varphi+b^{2} \operatorname{c o s} \varphi} {( a^{3}+b^{3} ) \operatorname{s i n} 2 \varphi}.
$$
G. $$
\omega^{2}=4 g \frac{b^{2} \operatorname{s i n} \varphi-a^{2} \operatorname{c o s} \varphi} {( b^{3}-a^{3} ) \operatorname{c o s} 2 \varphi}.
$$
H. $$
\omega^{2}=3 g \frac{b^{2} \operatorname{s i n} \varphi+a^{2} \operatorname{c o s} \varphi} {( b^{3}+a^{3} ) \operatorname{c o s} 2 \varphi}.
$$
I. $$
\omega^{2}=5 g \frac{b^{2} \operatorname{c o s} \varphi-a^{2} \operatorname{s i n} \varphi} {( a^{3}-b^{3} ) \operatorname{s i n} 2 \varphi}.
$$
J. $$
\omega^{2}=3 g \frac{b^{2} \operatorname{c o s} \varphi-a^{2} \operatorname{s i n} \varphi} {( b^{3}-a^{3} ) \operatorname{s i n} 2 \varphi}.
$$
Answer: J
To measure the radioactivity of a sample with a Geiger-Müller counter, the count rate is 800 pulses per minute. At this time, the background count is 40 pulses per minute. To achieve a measurement accuracy of ±4%, how much time must be measured?

Options:
A. Ten minutes
B. One cycle
C. Two hours
D. Six seconds
E. An interval
F. Two minutes
G. 1 minute
H. Four seconds
I. Five minutes
J. A half-hour
Answer: G
Use a Geiger-Müller counter with a bell-shaped probe to measure a $\mathbf{C}^{14}$ sample placed on an aluminum tray with a thickness of 10 mg/cm$^{2}$. During the measurement, the distance is 15 mm, and the diameter of the counter's window is 20 mm, with a thickness of 3 mg/cm$^{2}$. The measured radioactivity is $3.95 \times 10^{3}$ counts per minute. Calculate the absolute radioactivity of the sample.

Options:
A. 0.8 milliCurie
B. 3.0 milliCurie
C. 0.1 milliCurie
D. 0.4 milliCurie
E. 0.05 milliCurie
F. 0.5 milliCurie
G. 1.5 milliCurie
H. 0.3 milliCurie
I. 0.2 milliCurie
J. 2.0 milliCurie
Answer: I
When studying the radioactivity of $\mathrm{C o^{62}}$, it was found that the $\beta$ rays with the maximum energy on the $\beta$ energy spectrum can be absorbed by an aluminum layer of 1120 mg/cm$^{2}$. For the $\gamma$ rays of Co$^{62}$, the half-reducing thickness is 12 g/cm$^{2}$. Try to determine the energy of a) β particles, and b) γ photons of Co$^{62}$.

Options:
A. a) 1.8 million electron volts, b) 1.2 million
B. a) 5.1 million electron volts, b) 0.9 million
C. a) 2.5 million electron volts, b) 1.1 million
D. a) 2.0 million electron volts, b) 2.5 million
E. a) 3.2 million electron volts, b) 1.9 million
F. a) 2.3 million electron volts, b) 2.7 million
G. a) 4.0 million electron volts, b) 3.2 million
H. a) 1.5 million electron volts, b) 3.0 million
I. a) 3.6 million electron volts, b) 1.4 million
J. a) 4.8 million electron volts, b) 2.3 million
Answer: C
Measuring an isotope with a half-life of 30 minutes, from 10:03 AM to 10:13 AM, a total of 34,650 pulses were recorded in ten minutes. Calculate the radioactivity of this sample at 10:00 AM in pulses per minute.

Options:
A. $$
3 2 1 8 pulses/min
$$
B. $$
3 6 0 5 pulses/min
$$
C. $$
4 8 2 7 pulses/min
$$
D. $$
4 2 3 1 pulses/min
$$
E. $$
3 4 4 4 pulses/min
$$
F. $$
4 9 9 7 pulses/min
$$
G. $$
3 7 5 6 pulses/min
$$
H. $$
3 9 0 2 pulses/min
$$
I. $$
4 5 3 0 pulses/min
$$
J. $$
4 1 5 9 pulses/min
$$
Answer: J
A $\alpha$ particle beam with a current of 200 microamperes passes through 1 cubic centimeter of nitrogen at 76 cmHg and 0°C. If all the nitrogen nuclei in 1 cubic centimeter are concentrated on a 1 square centimeter surface, the number of nuclear reactions is $\mathbf{6.2 \times 10^{8}}/$ second. Calculate the effective cross-section (expressed in barns).

Options:
A. 7.3 barns
B. 3.1 barns
C. 9.1 barns
D. 5.2 barns
E. 0.04 bar
F. 8.0 barns
G. 6.5 barns
H. 1.8 barns
I. 4.7 barns
J. 2.9 barns
Answer: E
When exposed to slow neutrons, $Ir^{193}_{77}$ produces the radioactive isotope $Ir^{194}$ with a half-life of 19 hours. Calculate the radioactivity of an iridium target with a thickness of 0.1 millimeters and a cross-sectional area of 1 cm$^2$. If the target is irradiated with a neutron flux of intensity $10^{10}$ neutrons/cm$^2$ for 1 minute, and the reaction has an effective cross-section of 15 barns.

Options:
A. Approximately 2 microcuries
B. Approximately 8 microcuries
C. Approximately 7 microcuries
D. Approximately 4 microcuries
E. Approximately 10 microcuries
F. Approximately 1 microcurie
G. Approximately 6 microcuries
H. Approximately 9 microcuries
I. Approximately 3 microcuries
J. Approximately 5 microcuries
Answer: D
To prepare 10 mL of $Na_3$P $^{32}$ $O_{4}$ aqueous solution with a specific radioactivity of $3 \times 10^{4}$ pulses/min·mL, how much $Na_3$P $^{32}$ $O_{4}$ solution with a specific radioactivity of 2.7 millicurie/mL is needed? The counting efficiency is 0.005.

Options:
A. $2.5 \times 10^{-3}$ milliliters
B. $7 \times 10^{-3}$ milliliters
C. $10^{-3}$ milliliters
D. $1.8 \times 10^{-2}$ milliliters
E. $8.5 \times 10^{-3}$ milliliters
F. $1.5 \times 10^{-2}$ milliliters
G. $6 \times 10^{-4}$ milliliters
H. $5 \times 10^{-4}$ milliliters
I. $4 \times 10^{-3}$ milliliters
J. $9.5 \times 10^{-3}$ milliliters
Answer: C
Tracer atoms have gained widespread application in geology. Among these, deuterium is used to ascertain the distribution of underground water and the rapidity of watercourses, and to determine the reserves of oil in oil fields. Suppose the quantity of underground water is approximately 10 $^{6}$ cubic meters, and it is measured with a gas counter in the form of hydrogen. If the minimum detectable radioactivity is 10 pulses per minute, what should be the minimum radioactivity of the tritiated water sample added to the well for it to be detectable?

Options:
A. $2 \times 10^{4}$ curies
B. $8 \times 10^{1}$ curies
C. $7 \times 10^{6}$ curies
D. $5 \times 10^{2}$ curies
E. $9 \times 10^{5}$ curies
F. $10^{3}$ curies
G. $4 \times 10^{3}$ curies
H. $1 \times 10^{8}$ curies
I. $3 \times 10^{4}$ curies
J. $6 \times 10^{7}$ curies
Answer: F
The absorption cross-section of materials in the X-ray region generally increases monotonically as photon energy decreases, except for sharp drops at certain photon energies. For zinc $(Z=30)$, the photon energies with sharp drops are 9.678 keV, 1.236 keV, 1.047 keV, and 1.024 keV. Determine the X-ray energies of zinc that are higher than 5 keV, and specify the corresponding transitions. Calculate the ionization energy of $\mathrm{Zn}^{+29}$ (where $\mathrm{Zn}^{+29}$ denotes a zinc atom with 29 electrons removed).
is____.

Options:
A. $$
9. 4 7 6 ( \mathrm{k e V} ) ( \mathrm{L}_{2} \to\mathrm{M} )
$$
$$
7. 3 6 9 ( \mathrm{k e V} ) ( \mathrm{M}_{1} \to\mathrm{K} )
$$
$$
1 2. 3 8 ( \mathrm{k e V} )
$$
B. $$
8. 6 5 4 ( \mathrm{k e V} ) ( \mathrm{L}_{2} \to\mathrm{K} )
$$
$$
8. 6 3 1 ( \mathrm{k e V} ) ( \mathrm{L}_{1} \to\mathrm{K} )
$$
$$
1 1. 4 4 ( \mathrm{k e V} )
$$
C. $$
8. 7 6 4 ( \mathrm{k e V} ) ( \mathrm{L}_{1} \to\mathrm{K} )
$$
$$
7. 2 9 4 ( \mathrm{k e V} ) ( \mathrm{M}_{2} \to\mathrm{K} )
$$
$$
9. 5 1 ( \mathrm{k e V} )
$$
D. $$
7. 9 4 3 ( \mathrm{k e V} ) ( \mathrm{L}_{3} \to\mathrm{K} )
$$
$$
8. 9 6 2 ( \mathrm{k e V} ) ( \mathrm{M}_{1} \to\mathrm{K} )
$$
$$
1 0. 8 4 ( \mathrm{k e V} )
$$
E. $$
9. 1 5 6 ( \mathrm{k e V} ) ( \mathrm{N}_{2} \to\mathrm{K} )
$$
$$
7. 8 6 3 ( \mathrm{k e V} ) ( \mathrm{L}_{3} \to\mathrm{M} )
$$
$$
1 0. 9 2 ( \mathrm{k e V} )
$$
F. $$
8. 1 2 3 ( \mathrm{k e V} ) ( \mathrm{L}_{3} \to\mathrm{K} )
$$
$$
9. 0 0 8 ( \mathrm{k e V} ) ( \mathrm{M}_{1} \to\mathrm{K} )
$$
$$
1 1. 2 0 ( \mathrm{k e V} )
$$
G. $$
7. 8 5 4 ( \mathrm{k e V} ) ( \mathrm{L}_{3} \to\mathrm{K} )
$$
$$
9. 6 3 2 ( \mathrm{k e V} ) ( \mathrm{L}_{1} \to\mathrm{M} )
$$
$$
1 0. 4 9 ( \mathrm{k e V} )
$$
H. $$
8. 8 4 5 ( \mathrm{k e V} ) ( \mathrm{M}_{3} \to\mathrm{K} )
$$
$$
9. 5 1 3 ( \mathrm{k e V} ) ( \mathrm{N}_{1} \to\mathrm{K} )
$$
$$
1 0. 0 6 ( \mathrm{k e V} )
$$
I. $$
8. 2 9 6 ( \mathrm{k e V} ) ( \mathrm{L}_{2} \to\mathrm{K} )
$$
$$
9. 7 4 3 ( \mathrm{k e V} ) ( \mathrm{M}_{2} \to\mathrm{K} )
$$
$$
1 1. 3 9 ( \mathrm{k e V} )
$$
J. $$
9. 9 6 2 ( \mathrm{k e V} ) ( \mathrm{L}_{1} \to\mathrm{K} )
$$
$$
7. 5 3 4 ( \mathrm{k e V} ) ( \mathrm{L}_{2} \to\mathrm{M} )
$$
$$
9. 8 7 ( \mathrm{k e V} )
$$
Answer: B
Assuming the existence of the meson as suggested by Hideki Yukawa to explain nuclear forces, based on the uncertainty principle, provide the relationship between the range of nuclear force and the mass of the meson, and estimate the mass of the meson is____.

Options:
A. $$
1 0 0 \mathrm{M e V}
$$
B. $$
5 0 0 \mathrm{M e V}
$$
C. $$
1 5 0 \mathrm{M e V}
$$
D. $$
3 5 0 \mathrm{M e V}
$$
E. $$
6 0 0 \mathrm{M e V}
$$
F. $$
1 2 5 \mathrm{M e V}
$$
G. $$
2 0 0 \mathrm{M e V}
$$
H. $$
2 5 0 \mathrm{M e V}
$$
I. $$
3 0 0 \mathrm{M e V}
$$
J. $$
4 0 0 \mathrm{M e V}
$$
Answer: G
Which type of Fangchao layer should be selected for an 8-degree seismic fortification intensity?

Options:
A. Use a 20-thick plaster layer with $1 : 1$ lime-cement mix under the ceiling.
B. Prepare a 40-thick layer of $2 : 1$ mud plaster behind interior panels.
C. Implement a 30-thick asphalt layer of $1 : 5$ ratio on basement walls.
D. Form a 10-thick layer of $1 : 6$ clay mortar beneath outdoor pavement.
E. Spread a 50-thick gravel mixture of $1 : 9$ concrete on pathway edges.
F. Deploy a 25-thick layer of $1 : 4$ sand-cement mix on exterior walls.
G. At a brick below the indoor floor, apply a 20-thick layer of $1 : 2$ cement mortar with 5% waterproofing agent.
H. Install a 5-thick fibreglass mat with $1 : 7$ adhesive on attic surfaces.
I. Apply a 35-thick coating of $1 : 8$ polyurethane on garage flooring.
J. Construct a 15-thick layer of $1 : 3$ gypsum plaster above the roof tiles.
Answer: G
The effective value of the breakdown voltage of a sphere gap during a power frequency AC voltage test is $500 \mathrm{kV}$, with an air pressure of $100 \mathrm{kPa}$, a temperature of 20°C, and a humidity of $20 \mathrm{g/cm}^{3}$. What is the power frequency breakdown voltage of this sphere gap under standard atmospheric pressure?

Options:
A. $$ U_{0}=5 0 5. 2 0 $$
B. $$ U_{0}=4 6 0. 6 4 $$
C. $$ U_{0}=4 7 5. 7 5 $$
D. $$ U_{0}=4 6 5. 0 5 $$
E. $$ U_{0}=4 8 0. 8 8 $$
F. $$ U_{0}=4 8 9. 9 0 $$
G. $$ U_{0}=4 3 0. 0 0 $$
H. $$ U_{0}=4 7 0. 3 0 $$
I. $$ U_{0}=4 9 0. 1 0 $$
J. $$
U_{0}=4 6 9. 7 0
$$
Answer: J
The total length of a certain ultra-high voltage line is $500 \mathrm{km}$. Given: the source leakage reactance is $X_{\mathrm{S}} = 115 \Omega$, the lossless conductor wave impedance is $Z = 309 \Omega$, and there is a shunt reactor at the midpoint of the line with $X_{\mathrm{L}} = 1210 \Omega$. What is the ratio of the midpoint and endpoint voltage to the source voltage when the line is unloaded at the endpoint?

Options:
A. $$0.961,\ 1.013$$
B. $$0.973,\ 1.064$$
C. $$1.035,\ 0.989$$
D. $$0.912,\ 1.056$$
E. $$0.984,\ 1.089$$
F. $$1.027,\ 0.942$$
G. $$1.081,\ 0.953$$
H. $$0.998,\ 1.072$$
I. $$1.015,\ 0.996$$
J. $$0.947,\ 1.102$$
Answer: B
Two $110/220 \ \mathrm{kV}, \ \mathrm{Y0}/\mathrm{Y0}$ connected three-phase transformers, each with a capacity of 120 MVA. The first transformer has an excitation current of 4% and per-phase winding-to-ground capacitance of $5000 \ \mathrm{pF}$; the second transformer has an excitation current of 0.5% and per-phase winding-to-ground capacitance of $20000 \ \mathrm{pF}$. What is the expected overvoltage factor when these two no-load transformers are disconnected on the 110 kV side?

Options:
A. $$2.057$$
B. $$1.623$$
C. $$2.476$$
D. $$1.762$$
E. $$1.884$$
F. $$2.208$$
G. $$1.945$$
H. $$2.331$$
I. $$1.496$$
J. $$1.735$$
Answer: E
Given the conditions of measurement, where $p = 0.1013 \mathrm{MPa}$ and $t = 20^{\circ}\mathrm{C}$, we have coaxial cylindrical electrodes with an inner electrode diameter of 0.5 cm and an outer electrode diameter of 50 cm; the electrode surfaces are smooth. Upon applying a sinusoidal alternating voltage, the current sharply increases at a particular voltage level. What is the effective value of this voltage?

Options:
A. $$
3 9. 9 8 k V
$$
B. $$
3 0. 8 5 k V
$$
C. $$
3 4. 1 4 k V
$$
D. $$
4 6. 2 5 k V
$$
E. $$
4 1. 2 9 k V
$$
F. $$
5 4. 1 7 k V
$$
G. $$
4 8. 3 7 k V
$$
H. $$
5 0. 7 3 k V
$$
I. $$
4 9. 5 2 k V
$$
J. $$
5 2. 6 0 k V
$$
Answer: E
The experimental AC breakdown voltage (RMS) obtained for the rod gap is 300 kV, with the air pressure at 99.8 kPa, temperature at $25^{\circ} \mathrm{C}$, and humidity at $20 \, \mathrm{g/m}^{3}$. What will the breakdown voltage be under standard conditions?

Options:
A. $$
2 9 3. 4 7 k V
$$
B. $$
2 9 0. 8 2 k V
$$
C. $$
2 8 7. 0 5 k V
$$
D. $$
2 8 2. 7 4 k V
$$
E. $$
2 8 8. 5 1 k V
$$
F. $$
2 8 1. 3 9 k V
$$
G. $$
2 9 5. 2 3 k V
$$
H. $$
2 9 1. 6 8 k V
$$
I. $$
2 8 5. 9 0 k V
$$
J. $$
3 0 0. 0 0 k V
$$
Answer: E
For $\mathrm{SF}_{6}$ gas at a pressure of 0.1 MPa, if its $E/p$ value is 10% greater than the critical value $(E/p)_{\mathrm{crit}}$, what is the effective electron ionization coefficient $\bar{α}$ at this time?

Options:
A. $$
1 5 6. 9 2 {\mathrm{c m}}^{-1}
$$
B. $$
2 3 1. 5 7 {\mathrm{c m}}^{-1}
$$
C. $$
2 9 6. 0 2 {\mathrm{c m}}^{-1}
$$
D. $$
2 4 5. 1 4 {\mathrm{c m}}^{-1}
$$
E. $$
1 8 5. 2 7 {\mathrm{c m}}^{-1}
$$
F. $$
2 6 4. 4 4 {\mathrm{c m}}^{-1}
$$
G. $$
2 7 0. 8 5 {\mathrm{c m}}^{-1}
$$
H. $$
2 1 3. 9 8 {\mathrm{c m}}^{-1}
$$
I. $$
1 9 9. 5 1 {\mathrm{c m}}^{-1}
$$
J. $$
2 0 8. 6 3 {\mathrm{c m}}^{-1}
$$
Answer: D
When the parallel plate electrodes are in a vacuum, the capacitance is $0.1 \mu\mathrm{F}$. Now, a solid dielectric with a relative permittivity of 3.18 is inserted. After applying an AC voltage of 50 Hz and 5 kV, the dielectric loss is 25 W. What is the $\tan\delta$ of the inserted solid dielectric?

Options:
A. $$0.7$$
B. $$0.6$$
C. $$0.4$$
D. $$0.1$$
E. $$0.5$$
F. $$0.9$$
G. $$0.3$$
H. $$0.8$$
I. $$1.0$$
J. $$0.2$$
Answer: D
Under standard conditions, the densities of air, oxygen, and nitrogen are $\rho = 1.293 \ \mathrm{kg} \cdot \mathrm{m}^{-3}$, $\rho_{0} = 1.429 \ \mathrm{kg} \cdot \mathrm{m}^{-3}$, and $\rho_{\mathrm{N}} = 1.251 \ \mathrm{kg} \cdot \mathrm{m}^{-3}$, respectively. Assume air contains only oxygen and nitrogen. What are the partial pressure of nitrogen and the mass fraction of nitrogen in the air ?

Options:
A. 0.076 MPa,74%
B. 0.081 MPa,68%
C. 0.088 MPa,76%
D. 0.067 MPa,79%
E. 0.095 MPa,71%
F. 0.080 MPa,75%
G. 0.099 MPa,70%
H. 0.070 MPa,78%
I. 0.063 MPa,80%
J. 0.073 MPa,72%
Answer: A
At a certain moment, there are $N$ molecules of oxygen that have just collided with other molecules. How much time will pass before half of them have not collided with other molecules?
( Assume that the oxygen molecules move at an average speed, the temperature of the oxygen is 300 K, and the mean free path of the oxygen molecules is 2.0 cm at the given pressure. )

Options:
A. $$
=5. \ 7 \times1 0^{-5} \ \mathrm{s}
$$
B. $$
=4. \ 8 \times1 0^{-5} \ \mathrm{s}
$$
C. $$
=2. \ 7 \times1 0^{-5} \ \mathrm{s}
$$
D. $$
=3. \ 5 \times1 0^{-5} \ \mathrm{s}
$$
E. $$
=1. \ 0 \times1 0^{-5} \ \mathrm{s}
$$
F. $$
=2. \ 1 \times1 0^{-5} \ \mathrm{s}
$$
G. $$
=1. \ 8 \times1 0^{-5} \ \mathrm{s}
$$
H. $$
=2. \ 2 \times1 0^{-5} \ \mathrm{s}
$$
I. $$
3. \ 1 \times1 0^{-5} \ \mathrm{s}
$$
J. $$
=4. \ 5 \times1 0^{-5} \ \mathrm{s}
$$
Answer: I
The mean free path of a nitrogen molecule under standard conditions is $\overline{{{\lambda}}} = 7.0 \times 10^{-8} \mathrm{~m}$. When the air has no overall motion, how far does a nitrogen molecule actually travel when it moves 1 cm?

Options:
A. $$
7. \, 9 \, \times\, 3 0^{8} \mathrm{m}
$$
B. $$
4. \, 0 \, \times\, 5 0^{5} \mathrm{m}
$$
C. $$
1. \, 5 \, \times\, 3 0^{3} \mathrm{m}
$$
D. $$
9. \, 6 \, \times\, 4 0^{9} \mathrm{m}
$$
E. $$
2. \, 1 \, \times\, 1 0^{5} \mathrm{m}
$$
F. $$
3. \, 5 \, \times\, 1 0^{6} \mathrm{m}
$$
G. $$
5. \, 3 \, \times\, 1 0^{5} \mathrm{m}
$$
H. $$
8. \, 4 \, \times\, 2 0^{6} \mathrm{m}
$$
I. $$
6. \, 8 \, \times\, 2 0^{7} \mathrm{m}
$$
J. $$
1. \, 2 \, \times\, 1 0^{4} \mathrm{m}
$$
Answer: E
The cylinder surrounded by an adiabatic wall is divided into chambers A and B by an adiabatic piston. The piston can slide freely without friction inside the cylinder. Each of chambers A and B contains 1 mol of diatomic ideal gas. Initially, the gas is in a state of equilibrium with pressure, volume, and temperature of $p_{0},V_{0} ,T_{0}$ respectively. An electric heater in chamber A gradually heats it until the pressure in chamber A becomes $2 p_{0}$. What are the total entropy change in both chambers A and B?

Options:
A. $$1.75R$$
B. $$6.90R$$
C. $$2.89R$$
D. $$4.25R$$
E. $$0.65R$$
F. $$5.00R$$
G. $$1.20R$$
H. $$2.00R$$
I. $$3.50R$$
J. $$4.10R$$
Answer: C
There are two rods, $A$ and $B$, each with a linear expansion coefficient of $\alpha_{1}$ and $\alpha_{2}$ respectively. To ensure that rod $A$ is longer than rod $B$ by $\Delta l$ at any temperature, what are the lengths $l_{0 1}$ and $l_{0 2}$ of rods $A$ and $B$ at 0°C?

Options:
A. $$
\begin{array} {l} {{{{\frac{\alpha_{1}} {\alpha_{2}-\alpha_{1}}} \Delta l}}} \\ {{{{\frac{\alpha_{2}} {\alpha_{1}-\alpha_{2}}} \Delta l}}} \\ \end{array}
$$
B. $$
\begin{array} {l} {{{{ \frac{\alpha_{2}} {\alpha_{2}-\alpha_{1}}} \Delta l}}} \\ {{{{\frac{\alpha_{1}} {\alpha_{2}-\alpha_{1}}} \Delta l}}} \\ \end{array}
$$
C. $$
\begin{array} {l} {{{{\frac{\alpha_{1}} {\alpha_{1}-\alpha_{2}}} \Delta l}}} \\ {{{{\frac{\alpha_{2}} {\alpha_{2}-\alpha_{1}}} \Delta l}}} \\ \end{array}
$$
D. $$
\begin{array} {l} {{{{\frac{\alpha_{1}} {\alpha_{2}}} \Delta l}}} \\ {{{{\frac{\alpha_{2}} {\alpha_{1}}} \Delta l}}} \\ \end{array}
$$
E. $$
\begin{array} {l} {{{{\frac{\alpha_{2}} {\alpha_{1}-\alpha_{2}}} \Delta l}}} \\ {{{{\frac{\alpha_{1}} {\alpha_{1}-\alpha_{2}}} \Delta l}}} \\ \end{array}
$$
F. $$
\begin{array} {l} {{{{\frac{\alpha_{1}} {\alpha_{1}+\alpha_{2}}} \Delta l}}} \\ {{{{\frac{\alpha_{2}} {\alpha_{1}+\alpha_{2}}} \Delta l}}} \\ \end{array}
$$
G. $$
\begin{array} {l} {{{{\frac{\alpha_{2}} {\alpha_{1}+\alpha_{2}}} \Delta l}}} \\ {{{{\frac{\alpha_{1}} {\alpha_{1}+\alpha_{2}}} \Delta l}}} \\ \end{array}
$$
Answer: B
After coating the surface of a steel needle with density $\rho=7.8 \times 10^{3} \ \mathrm{kg/m}^{3}$ with a thin layer of oil that cannot be wetted by water, it is gently placed horizontally on the surface of still water. To ensure that the needle does not sink into the water at 0°C, disregarding Archimedes' buoyancy, what is the maximum diameter the steel needle can have?

Options:
A. $$ 0. 1 6 \times1 0^{-3} \mathrm{~ m}
$$
B. $$
= 0. 0 9 \times1 0^{-3} \mathrm{~ m}
$$
C. $$
= 0. 0 5 \times1 0^{-3} \mathrm{~ m}
$$
D. $$
= 0. 2 8 \times1 0^{-3} \mathrm{~ m}
$$
E. $$
= 0. 3 5 \times1 0^{-3} \mathrm{~ m}
$$
F. $$
= 0. 1 9 \times1 0^{-3} \mathrm{~ m}
$$
G. $$
= 0. 2 0 \times1 0^{-3} \mathrm{~ m}
$$
H. $$
= 0. 3 1 \times1 0^{-3} \mathrm{~ m}
$$
I. $$
= 0. 0 7 \times1 0^{-3} \mathrm{~ m}
$$
J. $$
= 0. 2 4 \times1 0^{-3} \mathrm{~ m}
$$
Answer: A
Design specifications and parameters for a certain low-pass digital filter are as follows:
The digital filter features a Butterworth-type amplitude-frequency response and is designed using the bilinear transformation method.
When $0 \mathrm{Hz} \leqslant f \leqslant 2.5 \mathrm{Hz}$, the filter gain attenuation is less than $3 \mathrm{dB}$.
When $f \geq 50 \mathrm{Hz}$, the filter gain attenuation is greater than or equal to $40 \mathrm{dB}$.
The sampling frequency of the digital system is $200 \mathrm{Hz}$.
Determine the system function $H(z)$ of the digital LPF and find its cascade form system function with each stage not exceeding second order.

Options:
A. $$
\frac{1 6 5 0} {s^{4}+2 8 \sqrt{2} s+1 6 5 0}
$$
$$
\frac{3+1 z^{-1}-z^{-2}} {1 0 8. 1 4-1 5 5 z^{-1}+8 2. 8 6 z^{-2}}
$$
B. $$
\frac{1 7 0 0} {s^{3}+3 9 \sqrt{2} s+1 7 0 0}
$$
$$
\frac{1-2 z^{-1}+z^{-2}} {1 1 8. 1 4-1 1 8 z^{-1}+8 9. 8 6 z^{-2}}
$$
C. $$
\frac{1 2 0 0} {s^{2}+3 7 \sqrt{3} s+1 8 0 0}
$$
$$
\frac{3+6 z^{-1}-z^{-2}} {1 3 0. 1 4-1 6 8 z^{-1}+9 7. 8 6 z^{-2}}
$$
D. $$
\frac{1 9 0 0} {s^{4}+4 0 \sqrt{1} s+1 8 0 0}
$$
$$
\frac{2+4 z^{-1}+z^{-2}} {1 1 0. 1 4-1 9 3 z^{-1}+8 4. 8 6 z^{-2}}
$$
E. $$
\frac{1 4 0 0} {s^{2}+3 5 \sqrt{3} s+1 9 0 0}
$$
$$
\frac{3+5 z^{-1}-z^{-2}} {1 0 5. 1 4-1 8 8 z^{-1}+7 6. 8 6 z^{-2}}
$$
F. $$
\frac{1 5 0 0} {s^{2}+3 0 \sqrt{5} s+1 6 5 0}
$$
$$
\frac{2-5 z^{-1}-z^{-2}} {1 2 0. 1 4-2 1 8 z^{-1}+9 6. 8 6 z^{-2}}
$$
G. $$
\frac{1 7 5 0} {s^{3}+4 5 \sqrt{2} s+1 7 5 0}
$$
$$
\frac{1+1 z^{-1}+z^{-2}} {1 0 6. 1 4-1 5 8 z^{-1}+8 3. 8 6 z^{-2}}
$$
H. $$
\frac{1 3 5 0} {s^{4}+3 9 \sqrt{1} s+1 3 5 0}
$$
$$
\frac{4+5 z^{-1}+z^{-2}} {1 3 5. 1 4-1 9 9 z^{-1}+8 8. 8 6 z^{-2}}
$$
I. $$
\frac{1 6 0 0} {s^{2}+4 0 \sqrt{2} s+1 6 0 0}
$$
$$
\frac{1+2 z^{-1}+z^{-2}} {1 1 5. 1 4-1 9 8 z^{-1}+8 6. 8 6 z^{-2}}
$$
J. $$
\frac{1 8 0 0} {s^{2}+5 0 \sqrt{4} s+1 5 0 0}
$$
$$
\frac{2+3 z^{-1}-z^{-2}} {1 0 5. 1 4-1 7 8 z^{-1}+8 2. 8 6 z^{-2}}
$$
Answer: I
A 1m long copper rod with a cross-sectional area of $1 \times 10^{-4}$ m² is free at both ends. Find: the fundamental frequency of the rod's free longitudinal vibration, and the position in the rod where the displacement amplitude is minimal. If a weight of 0.18 kg is added to one end of the rod, what would the new fundamental frequency of the rod's longitudinal vibration be, and where would the position of minimal displacement amplitude be located at that time? (Density of copper: 8.9 × 10³ kg/m³)

Options:
A. $$
f_{1} = 1.80 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{4} = 0.25 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{cos}(kl)}{kl} = 0.5
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{5} \cdot \frac{c}{f_{1}}$.
B. $$
f_{1} = 1.60 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{11} = 0.09 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{tan}(kl)}{kl} = 0.3
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{4}{5} \cdot \frac{c}{f_{1}}$.
C. $$
f_{1} = 1.86 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{2} = 0.5 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{tan}(kl)}{kl} = 0.2
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{4} \cdot \frac{c}{f_{1}}$.
D. $$
f_{1} = 1.90 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{3} = 0.33 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{sin}(kl)}{kl} = 0.1
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{3} \cdot \frac{c}{f_{1}}$.
E. $$
f_{1} = 1.95 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{7} = 0.14 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{cos}(kl)}{kl} = 0.6
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{6} \cdot \frac{c}{f_{1}}$.
F. $$
f_{1} = 2.10 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{9} = 0.11 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{sin}(kl)}{kl} = 0.9
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{2}{3} \cdot \frac{c}{f_{1}}$.
G. $$
f_{1} = 2.00 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{5} = 0.20 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{tan}(kl)}{kl} = 0.4
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{2} \cdot \frac{c}{f_{1}}$.
H. $$
f_{1} = 1.65 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{10} = 0.10 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{cos}(kl)}{kl} = 0.7
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{1}{7} \cdot \frac{c}{f_{1}}$.
I. $$
f_{1} = 1.75 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{6} = 0.16 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{sin}(kl)}{kl} = 0.3
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{3}{4} \cdot \frac{c}{f_{1}}$.
J. $$
f_{1} = 1.70 \times 10^{3} \, \mathrm{Hz}, x_{\mathrm{min}} = \frac{L}{8} = 0.12 \, \mathrm{m}; \operatorname{tr} \frac{\operatorname{tan}(kl)}{kl} = 0.8
$$
derive $f_{1}^{\prime}, x_{\operatorname*{min}} = \frac{5}{6} \cdot \frac{c}{f_{1}}$.
Answer: C
A steel rod is 0.5 m long with a radius of $0.005 \ \mathrm{m}$, and both ends are free. Determine the fundamental frequency of the rod's transverse vibration. If the rod vibrates at the fundamental frequency and the amplitude at the center of the rod is $2 \, \mathrm{cm}$, what is the amplitude at both ends of the rod?

Options:
A. $$ \ f=1 7 5 \ \mathrm{H z} ; 0. 0 2 2 \ \mathrm{m} $$
B. $$ \ f=1 8 0 \ \mathrm{H z} ; 0. 0 4 4 \ \mathrm{m} $$
C. $$ \ f=1 9 0 \ \mathrm{H z} ; 0. 0 7 7 \ \mathrm{m} $$
D. $$
f=1 7 9 \ \mathrm{H z} ; 0. 0 3 3 \ \mathrm{m}
$$
E. $$ \ f=1 7 9 \ \mathrm{H z} ; 0. 0 9 9 \ \mathrm{m} $$
F. $$ \ f=1 9 5 \ \mathrm{H z} ; 0. 0 8 8 \ \mathrm{m} $$
G. $$ \ f=1 7 9 \ \mathrm{H z} ; 0. 0 1 5 \ \mathrm{m} $$
H. $$ \ f=1 8 5 \ \mathrm{H z} ; 0. 0 6 6 \ \mathrm{m} $$
I. $$ \ f=2 0 0 \ \mathrm{H z} ; 0. 0 1 0 \ \mathrm{m} $$
J. $$ \ f=1 7 2 \ \mathrm{H z} ; 0. 0 5 5 \ \mathrm{m} $$
Answer: D
The diaphragm of a telephone headset is a uniform thin circular steel plate with a radius of $0.015 \mathrm{~m}$ and a thickness of 0.0001 m. If the perimeter is rigidly fixed, find the fundamental frequency of symmetric vibration at the center of the diaphragm.

Options:
A. 1895Hz
B. 1295Hz
C. 1795Hz
D. 1495Hz
E. 1395Hz
F. 1195Hz
G. 1095Hz
H. 1995Hz
I. 1595Hz
J. 1695Hz
Answer: G
When the amplitude of the sound pressure exceeds the static pressure in water, cavitation may occur on the surface of the sonar transducer. Question: If the static water pressure is $2.0 \times 10^{5} \, \mathrm{Pa}$, what is the maximum sound intensity at which cavitation does not occur? What is the corresponding sound pressure level (relative to 1 $\mu\mathrm{bar}$)?

Options:
A. $$
8. 1 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 4 \mathrm{~ dB}
$$
B. $$
9. 3 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 2 \mathrm{~ dB}
$$
C. $$
2. 0 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 3 0 \mathrm{~ dB}
$$
D. $$
6. 9 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 5 \mathrm{~ dB}
$$
E. $$
2. 7 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 6 \mathrm{~ dB}
$$
F. $$
1. 6 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 8 \mathrm{~ dB}
$$
G. $$
5. 6 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 1 8 \mathrm{~ dB}
$$
H. $$
7. 2 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 1 6 \mathrm{~ dB}
$$
I. $$
3. 8 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 3 \mathrm{~ dB}
$$
J. $$
4. 5 \times1 0^{4} \mathrm{~ w / m^{2} ~} ; 1 2 0 \mathrm{~ dB}
$$
Answer: E
If the speed of sound in oil abruptly changes from 1350 m/s to 1340 m/s at a horizontal plane at a certain depth, while the oil's density remains constant at 850 $\mathrm{kg/m^{3}}$, try to calculate the sound pressure reflection coefficient and the sound intensity reflection coefficient for plane sound waves incident from above onto the boundary plane where the speed of sound changes at the following angles: (a) normal incidence; $(\mathrm{b}) 70^{\circ}; (\mathrm{c}) 80^{\circ}; (\mathrm{d}) 89.5^{\circ}$.

Options:
A. $$
0. 0 0 9, 0. 1 3, 0. 1 1 3, 0. 3 3 ;1. 9 \times1 0^{-5}, 0. 0 0 3 1, 8. 1 \times1 0^{-3}, 0. 0 5 8
$$
B. $$
0. 0 0 5, 0. 3 0, 0. 0 9 0, 0. 2 2 ;1. 1 \times1 0^{-5}, 0. 0 0 0 7, 8. 8 \times1 0^{-3}, 0. 0 7 2
$$
C. $$
0. 0 2 4, 0. 0 8, 0. 1 9 3, 0. 1 8 ;1. 7 \times1 0^{-5}, 0. 0 0 1 1, 8. 9 \times1 0^{-3}, 0. 0 6 9
$$
D. $$
0. 0 0 3, 0. 2 0, 0. 0 6 3, 0. 3 5 ;1. 3 \times1 0^{-5}, 0. 0 0 1 7, 8. 6 \times1 0^{-3}, 0. 0 5 9
$$
E. $$
0. 0 0 4, 0. 0 3, 0. 0 9 3, 0. 2 8 ;1. 6 \times1 0^{-5}, 0. 0 0 0 9, 8. 7 \times1 0^{-3}, 0. 0 7 7
$$
F. $$
0. 0 0 7, 0. 2 3, 0. 0 7 3, 0. 1 8 ;1. 8 \times1 0^{-5}, 0. 0 0 0 5, 9. 0 \times1 0^{-3}, 0. 0 8 0
$$
G. $$
0. 0 3 2, 0. 0 9, 0. 0 6 3, 0. 2 5 ;1. 2 \times1 0^{-5}, 0. 0 0 0 8, 8. 3 \times1 0^{-3}, 0. 0 6 7
$$
H. $$
0. 1 0 4, 0. 5 3, 0. 2 9 3, 0. 3 8 ;2. 1 \times1 0^{-5}, 0. 0 0 1 9, 9. 2 \times1 0^{-3}, 0. 0 8 4
$$
I. $$
0. 0 1 5, 0. 0 4, 0. 0 8 3, 0. 2 9 ;1. 4 \times1 0^{-5}, 0. 0 0 2 3, 8. 5 \times1 0^{-3}, 0. 0 7 5
$$
J. $$
0. 0 1 0, 0. 0 6, 0. 0 4 3, 0. 1 5 ;1. 5 \times1 0^{-5}, 0. 0 0 2 8, 9. 4 \times1 0^{-3}, 0. 0 6 8
$$
Answer: E
A 1-meter-long pipe with a cross-sectional area of $S_{2}$ is inserted into a main pipe with a cross-sectional area of $S_{1}$. Given that the ratio of the areas $\frac{S_{2}}{S_{1}} = 10$, find the sound intensity transmission coefficient of this expansion pipe for a plane wave with a frequency of 300 Hz?

Options:
A. $$
0. 0 7 5
$$
B. $$
0. 4 7 5
$$
C. $$
0. 3 9 5
$$
D. $$
0. 9 2 5
$$
E. $$
0. 2 0 0
$$
F. $$
0. 5 2 5
$$
G. $$
0. 8 5 0
$$
H. $$
0. 6 0 0
$$
I. $$
0. 1 5 0
$$
J. $$
0. 1 0 0
$$
Answer: A
A circular piston-type sound source with an infinite baffle radiates a sound wave of 330 Hz into the air. The piston radius is 0.15 $\mathrm{m}$. If the sound source radiates a power of 0.5 $\mathbf{w}$, what is the amplitude of the vibrational velocity of the piston surface? Given that the piston mass is 0.015 $\mathbf{kg}$, the elastic constant is 2000 N/m, and internal friction is negligible, what is the amplitude of the driving force required to produce the aforementioned velocity amplitude?

Options:
A. $$
0. 1 0 2m / s ; 4. 8N
$$
B. $$
0. 1 1 0m / s ; 3. 3N
$$
C. $$
0. 1 2 3m / s ; 3. 7N
$$
D. $$
0. 0 7 6m / s ; 2. 6N
$$
E. $$
0. 0 5 6m / s ; 3. 9N
$$
F. $$
0. 0 6 8m / s ; 5. 1N
$$
G. $$
0. 0 9 4m / s ; 2. 8N
$$
H. $$
0. 0 4 9m / s ; 4. 0N
$$
I. $$
0. 0 7 3m / s ; 1. 9N
$$
J. $$
0. 0 8 3m / s ; 2. 5N
$$
Answer: J
The known density of glycerol at 20°C is 1260 kg/m$^3$, the speed of sound is 1980 m/s, and the shear viscosity coefficient is 1.2 N·s/m$^{2}$. Try to calculate its viscous relaxation time. If a 10 MHz sound wave propagates through it, what is the viscous absorption coefficient?

Options:
A. 6.2 x 10 $^{-10}$s,4.45 x 10 $^{2}$Np/m = 1.8 x 10 $^{3}$dB/m
B. 2.1 x 10 $^{-10}$s,3.78 x 10 $^{2}$Np/m = 3.0 x 10 $^{3}$dB/m
C. 3.0 x 10 $^{-10}$s,1.78 x 10 $^{2}$Np/m = 2.1 x 10 $^{3}$dB/m
D. 3.1 x 10 $^{-10}$s,4.56 x 10 $^{2}$Np/m = 2.7 x 10 $^{3}$dB/m
E. 3.5 x 10 $^{-10}$s,5.67 x 10 $^{2}$Np/m = 2.3 x 10 $^{3}$dB/m
F. 3.2 x 10 $^{-10}$s,3.23 x 10 $^{2}$Np/m = 2.8 x 10 $^{3}$dB/m
G. 5.3 x 10 $^{-10}$s,1.23 x 10 $^{2}$Np/m = 4.2 x 10 $^{3}$dB/m
H. 2.9 x 10 $^{-10}$s,2.34 x 10 $^{2}$Np/m = 3.5 x 10 $^{3}$dB/m
I. 4.4 x 10 $^{-10}$s,2.23 x 10 $^{2}$Np/m = 1.5 x 10 $^{3}$dB/m
J. 4.2 x 10 $^{-10}$s,3.89 x 10 $^{2}$Np/m = 2.9 x 10 $^{3}$dB/m
Answer: F
The diaphragm of a moving coil microphone has a cross-sectional area of $0.002 \mathrm{~m}^{2}$, a mass of $0.001 \mathrm{~kg}$, a stiffness of $10,000 \mathrm{~N/m}$, mechanical damping of $20 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}$, a voice coil resistance of $3 \Omega$, and a length of $5 \mathrm{~m}$. It operates within a magnetic field of $1.0 \mathrm{~T}$. Calculate the open-circuit voltage sensitivity level at $1000 \mathrm{~Hz}$ (reference value: $1 \mathrm{~V/Pa}$); Calculate the open-circuit voltage sensitivity level at $100 \mathrm{~Hz}$ (reference value: $1 \mathrm{~V/Pa}$).

Options:
A. $$
-6 5 \mathrm{~ d B} ; -6 4 \mathrm{~ d B}
$$
B. $$
-6 3 \mathrm{~ d B} ; -6 2 \mathrm{~ d B}
$$
C. $$
-7 3 \mathrm{~ d B} ; -7 4 \mathrm{~ d B}
$$
D. $$
-6 7 \mathrm{~ d B} ; -7 0 \mathrm{~ d B}
$$
E. $$
-7 0 \mathrm{~ d B} ; -7 1 \mathrm{~ d B}
$$
F. $$
-6 9 \mathrm{~ d B} ; -7 5 \mathrm{~ d B}
$$
G. $$
-6 6 \mathrm{~ d B} ; -6 7 \mathrm{~ d B}
$$
H. $$
-6 8 \mathrm{~ d B} ; -7 0 \mathrm{~ d B}
$$
I. $$
-6 4 \mathrm{~ d B} ; -6 3 \mathrm{~ d B}
$$
J. $$
-6 2 \mathrm{~ d B} ; -6 6 \mathrm{~ d B}
$$
Answer: G
In order to achieve good power transmission to the medium and extend bandwidth for sound radiation, a $\frac{\lambda}{4}$ matching layer (which also serves as a protective layer) can be used between the piezoelectric chip of the transducer and the sound radiating medium. If the acoustic impedance of the piezoelectric chip is $Z_{1}$ and the acoustic impedance of the sound radiating medium is $Z_{2}$, then the best transmission is achieved when the acoustic impedance of the matching layer $Z=\sqrt{Z_{1} Z_{2}}$. Assuming the piezoelectric chip is PZT-4 and the sound medium is water, what should be the acoustic impedance of the matching layer? Also, what material is most suitable for this matching layer?

Options:
A. Z = 8.2 x 10 $^{6}$Pa·s/m
B. Z = 5.1 x 10 $^{6}$Pa·s/m
C. Z = 6.8 x 10 $^{6}$Pa·s/m
D. Z = 7.1 x 10 $^{6}$Pa·s/m
E. Z = 7.9 x 10 $^{6}$Pa·s/m
F. Z = 7.4 x 10 $^{6}$Pa·s/m
G. Z = 9.0 x 10 $^{6}$Pa·s/m
H. Z = 5.7 x 10 $^{6}$Pa·s/m
I. Z = 6.5 x 10 $^{6}$Pa·s/m
J. Z = 8.5 x 10 $^{6}$Pa·s/m
Answer: D
Using equal loudness contours and pure tone masking curves to calculate: the sound pressure level required to hear a 1000 Hz pure tone within a 2000 Hz pure tone at a sound pressure level (relative to 20 μPa) of 80 dB; the sound pressure level required to hear a 5000 Hz pure tone within the same 2000 Hz pure tone.

Options:
A. 20 dB;54 dB
B. 22 dB;53 dB
C. 27 dB;58 dB
D. 23 dB;55 dB
E. 26 dB;57 dB
F. 25 dB;56 dB
G. 21 dB;52 dB
H. 28 dB;59 dB
I. 19 dB;50 dB
J. 24 dB;51 dB
Answer: B
There are two events, $\mathrm{A}$ and $\mathrm{B}$, that occur simultaneously in the inertial frame $\mathrm{K}$, with the locations of the events being $1 \mathrm{m}$ apart. Another inertial frame $\mathbf{K}^{\prime}$ moves relative to $\mathrm{K}$ along the line connecting the locations of events A and B. In the frame $\mathbf{K}^{\prime}$, the distance between the two locations is measured to be $2 \mathrm{m}$. What is the time interval between the occurrences of the two events as measured in the frame $\mathbf{K}^{\prime}$ ?

Options:
A. $$
4. 3 3 \times1 0^{9} \mathrm{s.}
$$
B. $$
9. 4 4 \times1 0^{6} \mathrm{s.}
$$
C. $$
8. 1 1 \times1 0^{8} \mathrm{s.}
$$
D. $$
1. 6 6 \times1 0^{7} \mathrm{s.}
$$
E. $$
3. 2 2 \times1 0^{8} \mathrm{s.}
$$
F. $$
5. 7 7 \times1 0^{9} \mathrm{s.}
$$
G. $$
6. 8 8 \times1 0^{8} \mathrm{s.}
$$
H. $$
2. 5 5 \times1 0^{9} \mathrm{s.}
$$
I. $$
5. 0 0 \times1 0^{8} \mathrm{s.}
$$
J. $$
7. 9 9 \times1 0^{7} \mathrm{s.}
$$
Answer: F
The Princeton Proton Accelerator (PPA) is used to accelerate highly ionized nitrogen ions. If the PPA can produce protons with a total energy of 3GeV, what is the minimum kinetic energy of a $^{14}1 4 \mathrm{N}^{+6}$ ion with 6 positive charges?

Options:
A. $$
6. 8 9 \, ( \mathrm{G e V} )
$$
B. $$
3. 8 0 \, ( \mathrm{G e V} )
$$
C. $$
1. 9 8 \, ( \mathrm{G e V} )
$$
D. $$
4. 1 2 \, ( \mathrm{G e V} )
$$
E. $$
10. 3 2 \, ( \mathrm{G e V} )
$$
F. $$
5. 6 7 \, ( \mathrm{G e V} )
$$
G. $$
2. 5 7 \, ( \mathrm{G e V} )
$$
H. $$
8. 4 3 \, ( \mathrm{G e V} )
$$
I. $$
7. 9 4 \, ( \mathrm{G e V} )
$$
J. $$
9. 2 5 \, ( \mathrm{G e V} )
$$
Answer: H
Using two accelerators, the neutral intermediate vector boson $\mathrm{Z}^{0}$ is produced through the reaction $\mathrm{e}^{+}+\mathrm{e}^{-} \to \mathrm{Z}^{0}$. The mass of $\mathrm{Z}^{0}$ is $M=91.187\,\mathrm{GeV}$. What is the minimum energy of the electron beam during collision, assuming that $\mathrm{e^{+}}$ collides with a stationary $\mathrm{e^{-}}$ ?

Options:
A. $$
32.1 \mathrm{GeV}
$$
B. $$
10.9 \mathrm{GeV}
$$
C. $$
68.7 \mathrm{GeV}
$$
D. $$
75.2 \mathrm{GeV}
$$
E. $$
27.8 \mathrm{GeV}
$$
F. $$
50.3 \mathrm{GeV}
$$
G. $$
4 5. 6 \mathrm{G e V}
$$
H. $$
60.5 \mathrm{GeV}
$$
I. $$
82.4 \mathrm{GeV}
$$
J. $$
15.6 \mathrm{GeV}
$$
Answer: G
A beam of $\pi^{+}$ mesons with a kinetic energy of $T$ decays to produce some backward-moving $\mu^{+}$ ($\pi^{+} \to \mu^{+}+$ $\mathbf{v}_{\mu}$). What is the maximum value of $T$ ? ( $m_{\pi}=139.57 \mathrm{MeV}/c^{2}$, $m_{\mu}=105.66 \mathrm{MeV}/c^{2}$, and $m_{\mathrm{v}}=0$ )

Options:
A. $$
5. 4 4 ( \mathrm{M e V} )
$$
B. $$
7. 0 0 ( \mathrm{M e V} )
$$
C. $$
6. 3 6 ( \mathrm{M e V} )
$$
D. $$
4. 8 8 ( \mathrm{M e V} )
$$
E. $$
3. 9 9 ( \mathrm{M e V} )
$$
F. $$
6. 5 5 ( \mathrm{M e V} )
$$
G. $$
4. 0 5 ( \mathrm{M e V} )
$$
H. $$
5. 1 2 ( \mathrm{M e V} )
$$
I. $$
5. 8 0 ( \mathrm{M e V} )
$$
J. $$
5. 3 3 ( \mathrm{M e V} )
$$
Answer: A
A particle with mass $m$ and charge $q$ is bound by Coulomb interaction to a particle with infinite mass and charge $-q$. At time $t=0$, the particle's orbit is approximately a circle with radius $R$. After how much time will its orbital radius decrease to $R/2$ ? (assuming $R$ is sufficiently large so that classical radiation theory can be used without needing quantum theory for calculations)

Options:
A. $$
\frac{5 \pi^{2} \varepsilon_{0} c^{3} m^{2} R^{2}} {q^{4}}
$$
B. $$
\frac{7 \pi^{2} \varepsilon_{0}^{2} c^{4} m^{2} R^{3}} {q^{5}}
$$
C. $$
\frac{6 \pi^{2} \varepsilon_{0}^{2} c^{3} m^{3} R^{3}} {q^{5}}
$$
D. $$
\frac{6 \pi^{2} \varepsilon_{0}^{2} c^{3} m R^{4}} {q^{4}}
$$
E. $$
\frac{7 \pi^{2} \varepsilon_{0} c^{3} m^{2} R^{4}} {q^{4}}
$$
F. $$
\frac{3 \pi^{3} \varepsilon_{0}^{2} c^{3} m^{2} R^{3}} {q^{4}}
$$
G. $$
\frac{7 \pi^{2} \varepsilon_{0}^{2} c^{3} m^{2} R^{3}} {2 q^{4}}
$$
H. $$
\frac{8 \pi^{3} \varepsilon_{0}^{3} c^{3} m^{2} R^{3}} {q^{5}}
$$
I. $$
\frac{7 \pi^{2} \varepsilon_{0}^{2} c^{2} m^{3} R^{3}} {q^{4}}
$$
J. $$
\frac{4 \pi^{4} \varepsilon_{0} c^{2} m^{3} R^{3}} {q^{4}}
$$
Answer: G
In conducting a shell model experiment in deep water, the size of the model is 1/1.5 of the actual object. If the speed of the shell in the air is 500 km/h, what should the speed of the model in the water be when measuring its viscous resistance (assuming the temperature $t$ is 20°C)?

Options:
A. 14.89 m/s
B. 17.58 m/s
C. 11.75 m/s
D. 12.87 m/s
E. 13.45 m/s
F. 15.20 m/s
G. 12.11 m/s
H. 13.99 m/s
I. 14.33 m/s
J. 16.04 m/s
Answer: H
Using a ring cutter with an inner diameter of 79.8mm and a height of 20mm, an undisturbed saturated cohesive soil sample was taken. The specific gravity $G_{\mathrm{s}}=2.70$, water content $w=40.3\%$, and wet soil mass $184 g_{\circ}$. Currently, a lateral constrained compression test is being conducted. Under pressures of 100kPa and 200kPa, the total compression amounts of the sample are $s_{1}=1.4 \mathrm{mm}$ and $s_{2}=2.0 \mathrm{mm}$, respectively. Which option is closest to the given compression coefficient $a_{1-2} (\mathbf{MPa}^{-1})$?

Options:
A. 0.71
B. 0.59
C. 0.56
D. 0.75
E. 0.77
F. 0.65
G. 0.62
H. 0.80
I. 0.68
J. 0.53
Answer: G
A cylindrical disturbed saturated clay sample, after being consolidated under a surrounding pressure of 100 kPa, is subjected to axial pressure for undrained shear until the sample fails. The pore water pressure coefficient at failure is measured as $A_{\mathrm{f}}=0.7$. Given that the measured soil properties are $c^{\prime}=0$ and $\varphi^{\prime}=25^{\circ}$, what is the strength parameter $\varphi_{\mathrm{e u}}$ (with $c_{\mathrm{e u}}=0$) of the sample?

Options:
A. 15.4°
B. 11.6°
C. 13.5°
D. 18.9°
E. 17.4°
F. 20.3°
G. 10.2°
H. 19.1°
I. 12.7°
J. 14.2°
Answer: A
An old building uses a strip foundation with a width of 2.0m and a depth of 2.5m. It is planned to add extra floors, revealing silty clay at a 2.0m depth below the foundation base, with $f_{\mathrm{a k}}=90 \mathrm{kPa}$, $E_{n}=3 \mathrm{MPa}$. The known density of the upper soil layer is $18 \mathrm{kN/m}^{3}$, and the average density of the foundation and the soil above it is $20 \mathrm{kN/m}^{3}$. The characteristic value of the foundation bearing capacity is $f_{\mathrm{a k}}=160 \mathrm{kPa}$. Without groundwater, which of the following values is closest to the maximum allowable vertical force $F_{\mathrm{k}}$ on the top surface of the foundation?

Options:
A. 185.12kPa
B. 167.22kPa
C. 200.75kPa
D. 163.44kPa
E. 182.53kPa
F. 160.37kPa
G. 179.63kPa
H. 192.36kPa
I. 175.98kPa
J. 150.89kPa
Answer: G
In a certain frame structure with one basement level, the elevation of the outdoor ground and the interior floor of the basement are 16.2m and 14.0m, respectively. It is planned to use a square foundation beneath the columns, with a foundation width of 2.5m and a foundation embedment depth of 3.0m below the outdoor ground level. Below the outdoor ground level is 1.2m of artificial fill soil, with $\boldsymbol{\gamma}=17 \, \mathrm{kN/m}^3$; below the fill soil is 7.5m of Quaternary silt, with $\gamma=19 \, \mathrm{kN/m}^3$, $c_{k}=18 \, \mathrm{kPa}$, and $\varphi_{k}=24°$. No groundwater has been observed in the area. Which of the following options is closest to the characteristic value of the foundation bearing capacity determined by the soil's shear strength parameters?

Options:
A. 250.3kPa
B. 230.0kPa
C. 195.6kPa
D. 165.8kPa
E. 210.4kPa
F. 175.5kPa
G. 200.7kPa
H. 225.1kPa
I. 180.0kPa
J. 190.2kPa
Answer: E
The plant adopts independent column footings with dimensions of $4 \mathrm{m} \times 6 \mathrm{m}$ and a foundation depth of 2.0m. The groundwater level is at a depth of 1.0m. The bearing stratum is silty clay (with a natural void ratio of 0.8, liquidity index of 0.75, and natural unit weight of 18kN/m³). Three static load tests were conducted on this soil layer, and the measured characteristic values of bearing capacity were 130kPa, 110kPa, and 135kPa, respectively. According to the "Code for Design of Building Foundation" (GB 50007-2002), the foundation bearing capacity characteristic value after deep-width correction is ( ) $kPa$.

Options:
A. 139.5kPa
B. 155.9kPa
C. 134.8kPa
D. 144.0kPa
E. 167.3kPa
F. 145.2kPa
G. 151.0kPa
H. 158.6kPa
I. 171.7kPa
J. 162.4kPa
Answer: H
The column base size of a multi-story factory building is $800 \mathrm{mm} \times 1000 \mathrm{mm}$, using a reinforcement-free spread foundation calculated according to the standard combination of load effects. The vertical force transferred to the ±0.0 position is $F_{\mathrm{k}}=600 \mathrm{kN}$, the moment is $M_{\mathrm{k}}=160 \mathrm{kN} \cdot \mathrm{m}$, and the horizontal force is $H_{\mathrm{k}}=35 \mathrm{kN}$. The base area is $2 \mathrm{m} \times 2.6 \mathrm{m}$, with the designed foundation depth being $1.5 \mathrm{m}$. The foundation material is C15 concrete. The minimum height of the foundation is ( ) m. The design value of the bending moment of the maximum section of the foundation is ( ) kN·m.

Options:
A. 1.1,200.0
B. 0.8,173.2
C. 0.9,190.0
D. 0.4,130.0
E. 0.5,140.0
F. 0.3,120.0
G. 1.2,210.0
H. 0.6,150.0
I. 1.0,180.0
J. 0.7,160.0
Answer: B
In a certain project, the vertical bearing capacity of three test piles was obtained in a vertical static load test for a single pile, measuring 860kN, 880kN, and 890kN, respectively. According to the Chinese "Technical Code for Building Pile Foundations" (JGJ 94-2008), the characteristic value of the vertical bearing capacity $R$ of the single pile used is closest to ( )kN.

Options:
A. 756kN
B. 482kN
C. 459kN
D. 438kN
E. 612kN
F. 523kN
G. 674kN
H. 807kN
I. 912kN
J. 921kN
Answer: D
In a certain soft soil site, the size of the pile cap is $4.0 \mathrm{m} \times 4.0 \mathrm{m}$. Underneath, there are four bored piles with a diameter of 0.5m, a spacing of 3.0m, and a length of 30m. The settlement of the pile foundation calculated by the layer summation method is 50mm. The empirical coefficient for pile settlement calculation $\psi$ is 1.2, resulting in a calculated final pile settlement ()mm.

Options:
A. 22mm
B. 11mm
C. 15mm
D. 21mm
E. 20mm
F. 25mm
G. 18mm
H. 17mm
I. 9mm
J. 13mm
Answer: I
A certain high-rise residential building has a raft foundation, with a foundation depth of $7 \mathrm{m}$. The natural unit weight of the soil above the foundation is $20 \mathrm{kN/m}^{3}$, and the characteristic value of the natural foundation bearing capacity is 180 kPa. A composite foundation with cement fly-ash gravel (CFG) piles is used, and on-site tests measured the characteristic bearing capacity of a single pile as 600 kN. The piles are arranged in a square pattern, with a pile diameter of 400 mm and a spacing of $1.5 \mathrm{m} \times 1.5 \mathrm{m}$. The reduction coefficient for the pile-soil bearing capacity, $\beta$, is taken as 0.95. Which of the following options should the foundation pressure of this building not exceed?

Options:
A. 590kPa
B. 575kPa
C. 480kPa
D. 558kPa
E. 610kPa
F. 555kPa
G. 530kPa
H. 620kPa
I. 600kPa
J. 650kPa
Answer: D
The foundation of a certain building uses independent pile foundations, with the pile dimensions being $6 \mathrm{m} \times 6 \mathrm{m}$. The pile is buried at a depth of 1.5m, with an axial load at the top of the foundation of $F_{\mathrm{k}} = 6000 \mathrm{kN}$. The weight of the foundation and the soil above it is $G_{\mathrm{k}} = 1200 \mathrm{kN}$. The site stratum consists of silty clay, with $f_{\mathrm{a k}} = 120 \mathrm{kPa}$ and $\gamma = 18 \mathrm{kN}/\mathrm{m}^3$. Due to insufficient bearing capacity, it is proposed to use a lime-soil replacement cushion. When the cushion thickness is 2.0m, according to the "Technical Code for Ground Treatment of Buildings" (JGJ 79-2002), the additional pressure at the bottom of the cushion is () kPa.

Options:
A. 88.4kPa
B. 100.7kPa
C. 96.2kPa
D. 89.7kPa
E. 97.1kPa
F. 101.5kPa
G. 94.3kPa
H. 95.8kPa
I. 90.9kPa
J. 92.6kPa
Answer: G
In a homogenous sandy soil site, sand piles are used for treatment with an equilateral triangular layout. The sand pile diameter is 0.5m, and the pile body bearing capacity is 300kPa. The natural soil void ratio is 0.92, with a maximum void ratio of 0.96 and a minimum void ratio of 0.75. The natural foundation bearing capacity is 120kPa. It is required that the relative density of the reinforced sandy soil is not less than 0.7, calculated according to the Chinese "Code for Ground Treatment of Buildings" (JGJ 79-2002). The vibratory sinking pipe construction method is used, with a correction factor $\xi=1.1$. The pile spacing is ( )m. When the relative density of the site's soil layer is 0.7, the bearing capacity is 160kPa, and the composite foundation bearing capacity is ( )kPa.

Options:
A. 2.25m,168.50kPa
B. 2.40m,167.20kPa
C. 2.15m,172.00kPa
D. 2.35m,174.10kPa
E. 2.18m,161.90kPa
F. 2.30m,160.00kPa
G. 2.28m,170.50kPa
H. 2.21m,166.44kPa
I. 2.20m,162.75kPa
J. 2.10m,165.30kPa
Answer: H
Permanent rock bolts are composed of three heat-treated steel bars, each with a diameter of $d = 10 \text{ mm}$ and a tensile strength design value of $f_{y} = 1000 \text{ N/mm}^{2}$. The diameter of the anchorage is $D = 100 \text{ mm}$, and the length of the anchorage section is $4.0 \text{ m}$. The characteristic value of the bond strength between the anchorage and the soft rock is $f_{\mathrm{rb}} = 0.3 \text{ MPa}$. The design value of the bond strength between the steel bar and the anchoring grout is $f_{\mathrm{rd}} = 2.4 \text{ MPa}$, with an anchorage section length of $4.0 \text{ m}$. Given the fixture set force $y = 1000 \text{ kN}$, according to the Chinese "Technical Specifications for Building Slope Engineering" (GB 50330-2002), How much force can a steel bar withstand?

Options:
A. 155.312kN
B. 168.640kN
C. 159.497kN
D. 158.065kN
E. 162.495kN
F. 160.819kN
G. 167.980kN
H. 165.314kN
I. 170.255kN
J. 172.405kN
Answer: E
A gravity retaining wall with a height of 3.0m is used for a certain railway embankment. Both the top and bottom widths are 2.0m, and the wall has a unit weight of 22kN/m³. The horizontal loads at the center of the top and back of the wall are 50kN/m and 70kN/m, respectively. The backfill behind the wall is sandy soil. The base pressure stress at the toe of the retaining wall is ()kPa.

Options:
A. 197.3kPa
B. 188.9kPa
C. 214.8kPa
D. 185.6kPa
E. 205.2kPa
F. 176.4kPa
G. 209.1kPa
H. 194.5kPa
I. 201.9kPa
J. 192.7kPa
Answer: A