武汉大学大二上大学物理期末考试题

武汉理工大学考试试题纸 课程名称 大学物理 (双语) 题号 1 I III III-1 III-2 III-3III-4 专业班级 总分 题分 备注: 学生不得在试题纸上答题(含填空题、选择题等客观题) I. Selecting (only one correct answer in each of the problems. Points: 3’×10) 1. 2. 3. 4. Two identical undamped oscillators have the same amplitude of oscillation only if: A) they are started with the same displacement x0 B) they are started with the same velocity v0 22v0C) they are started so the combination 2x0 is the same 22x0D) they are started so the combination 2v0 is the same Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are hoop 1: M = 150g and R = 50 cm hoop 2: M = 200g and R = 40 cm hoop 3: M = 250g and R = 30 cm hoop 4: M = 300g and R = 20 cm hoop 5: M = 350g and R = 10 cm Order the hoops according to the periods of their motions, smallest to largest. A) 1, 2, 3, 4, 5 B) 5, 4, 3, 2, 1 C) 1, 2, 3, 5, 4 D) 1, 2, 5, 4, 3 A source of frequency f sends waves of wavelength  traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are A) 2, v B) /2, v C) , 2v D) , v/2 When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are: A) 50, 100, 150, and 200 Hz B) 50, 150, 250, and 300 Hz C) 100, 200, 300, and 400 Hz D) 25, 50 75, and 100 Hz A source emits sound with a frequency of 1000 Hz. Both it and an observer are moving toward each other, each with a speed of 100 m/s. If the speed of sound is 340 m/s, the observer hears sound with a frequency of: A) 294 Hz B) 545 Hz C) 1000 Hz D) 1830 Hz A \"wave front\" is a surface of constant: A) phase B) frequency C) wavelength D) amplitude 5. 6. 1

7. In a Young's double-slit experiment, a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern (on the screen) shifts by an amount corresponding to 30 dark bands. The wavelength of the light in this experiment is 480 mm and the index of the mica is 1.60. The mica thickness is: A) 0.090 mm B) 0.012 mm C) 0.014 mm D) 0.024 mm 8. A diffraction pattern is produced on a viewing screen by illuminating a long narrow slit with light of wavelength . If the slit width is decreased and no other changes are made: A) the intensity at the center of the pattern decreases and the pattern expands away from the bright center B) the intensity at the center increases and the pattern contracts toward the bright center C) the intensity at the center of the pattern does not change and the pattern expands away from the bright center D) the intensity at the center of the pattern does not change and the pattern contracts toward the bright center 9. Two stars that are close together are photographed through a telescope. The black and white film is equally sensitive to all colors. Which situation would result in the most clearly separated images of the stars? A)Small lens, red stars B) Large lens, blue stars C)Large lens, red stars D) Small lens, blue stars 10. In a stack of three polarizing sheets the first and third are crossed while the middle one has its axis at 45°to the axes of the other two. The fraction of the intensity of an incident unpolarized beam of light that is transmitted by the stack is: A) 1/2 B) 1/3 C) 1/8 D) 1/4 II. Filling in the blanks (Points: 3’×7) 1. A simple harmonic oscillator consists of a mass m and an ideal spring with spring constant k. Particle oscillates as shown in (i) with period T. If the spring is cut in half and used with the same particle, as shown in (ii), the spring constant is the period is 2. A beam of x rays of wavelength 1x10-10m is found to diffract in second order from the face of a LiF crystal at a Bragg angle of 30°. The distance between adjacent crystal planes, in nm, is about 3. A standing wave pattern is established in a string as shown. The wavelength of one of the component traveling waves is 4. Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is _____ that of wave B. 2

5. Red light is viewed through a thin vertical soap film. At the second dark area shown, the thickness of the film, in terms of the wavelength within the film , is 6. A diffraction grating just resolves the wavelengths 400.0 nm and 400.1 nm in first order. The number of slits in the grating is III. Calculating (49’) 1. A wheel is free to rotate about its axel. A spring is attached to one of its spokes a distance r from the axel, as shown in the figure. Assuming that the wheel is a hoop of mass m and radius R, obtain the frequency of a small oscillations of this system in terms of m, R, r and the spring constant k. (12’) 2. A string, tied to a sinusoidal vibrator at P and running over a support at Q, is stretched by a block of mass m. The separation between P and Q is L. The amplitude of the motion at P is small enough for that point to be considered a node. (a) Determine the resonant frequency based on the wave speed v on the string and the length L of the string. (b) If L=1.2 m, the linear density of the string is 1.6g/m, and the frequency f of the vibrator is fixed at 120Hz. what mass m allows the vibrator to set up the fourth harmonic on the string? (14) 3. Monochromatic light of variable wavelength is incident normally on a thin sheet of plastic film in air. The reflected light is a minimum only for =510nm and =680nm in the visible spectrum. What is the thickness of the film? (n=1.58) (10) 4. Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin=0.2 and sin=0.3. The fourth-order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? (c) How many principle maxima are produced by the grating? (13) 3

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武汉理工大学

试题标准答案及评分标准用纸 | 课程名称 大学物理A

I. Selecting (only one correct answer in each of the problems. (3’×10)

1.C , 2.B, 3. B 4.C 5.D 6.A , 7.D, 8. A 9.B, 10.C

II. Filling in the blanks ( 3’×7 )

1. (2K, T/2) 2. (0.2) 3. (4m) 4 (four times) 5 (3/4) 6(4000)

III. Calculating (49’)

1. (12) Ans: Solution: when the wheel rotates an angle  from the equilibrium position, the spring

force is 

Fkxkrsin (2) The torque acts on the wheel is:

FrFrcoskrsinrcoskr2sincos (2)

When  is very small kr2I (2)

IMR2 (2)

kr2kr2Thus the angular frequency is IMR2 (2) The frequency of the system is f1kr222MR2 (2) 2. (14)(a) Suppose we send a continuous sinusoidal wave along the string toward the right

y1ymsinkxt (1)

When the wave reaches the right end, it reflects and begins to travel back to left.

y2ymsinkxt (1)

The principle of superposition gives, for the combined wave

y22ymsinkx/2cos(t/2) (2)

There is a node at position x=l, klmfmv2L (4) (b) For n = 4, v is the speed of the wave

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vmg (2)

m2fl/n221201.2/421.6103g9.80.846kg(4)

3. Solution: because the reflect conditions from bottom surface and top surface are not same. Thus the

path-length difference is

2nt/2 (2)

When the reflected light is a minimum, the path-length difference is

2nt/22m1/2tm/2n (2)

n is the reflective index of the film. Because the reflected light is minimum only for =510nm and =680nm, we can get

tm11/2nm22/2nm1/m22/1680/5104/3 (2)

And m1, m2 must satisfy the conditionm1m21, thus m1=4, m2=3. (2) The thickness of the film is tm11/2n4510nm/(21.58)646nm (2)

4. (a) The location of maxima can be determined by equation of grating.

dsinm (2)

λ is the wavelength, and m is an integer. Let m be the order number for the line with sin θ = 0.2 and m+1 be the order number for the line with sin θ = 0.3.thus the separation of between adjacent slits can be solved out

d0.30.2d106106m (3)

(b) Minima of the single-slit diffraction pattern occur at angles θ given by a sin θ = kλ, (2)

Where a is the slit width. Since the fourth-order interference maximum is missing, it must fall at one of these angles.

sinmadd1.5106dam4m (3) 6