General Physics – ph 211



General Physics – ph 202 Name:____________

Midterm III (Ch 11 – 19) Type A

February 27, 2006

• Exam is closed book and closed notes. Use only your note card.

• Write all work and answers in the color papers provided.

• Show all your work and explain your reasoning (No credit will be given for an answer that does not include the necessary solution or explanation, except for true/false or multiple choice questions)

• Partial credit may be awarded for a correct method of solution, even if the answer is wrong.

Part I – True or False (1.5 points each): For questions 1 – 12, state whether each statement is true or false.

0. My test type is ________.

1. False A wave pulse on a string whose end is fixed is reflected without inversion.

2. False Sound waves in air are transverse waves.

3. True Infrasound carries over long distances better than ultrasound.

4. False Bats use infrasound to navigate.

5. True A concave lens always produces a virtual image.

6. False For total internal reflection to take place, light must go from a medium of lower index of refraction to a medium of higher index of refraction.

7. True A convex mirror always produces a virtual image smaller than the object.

8. False Magnification is positive for inverted images.

9. False The index of refraction for a given material is directly proportional to the frequency of light.

10. False A convex lens is known as a diverging lens and a concave lens is known as a converging lens. (reverse is true)

11. False The reflection of light from a rough surface is called specular reflection.

12. True In a concave mirror the inside of the spherical surface is the reflecting surface.

Part II – Multiple Choice (1.5 points each): Choose the one correct answer for each of the following questions that best answers or completes the question.

13. The velocity of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this string?

A) 50 Hz B) 200 Hz C) 100 Hz D) 25 Hz

Use:

[pic]

14. Which of the following is a false statement?

A) Sound can travel through a vacuum.

B) Light travels very much faster than sound.

C) Sound waves are longitudinal pressure waves.

D) The transverse waves on a vibrating string are different from sound waves.

E) "Pitch" (in music) and frequency have approximately the same meaning.

15. An open pipe of length L is resonating at its fundamental frequency. Which statement is correct?

A) The wavelength is L and there is a displacement node at the pipe's midpoint.

B) The wavelength is L and there is a displacement antinode at the pipe's midpoint.

C) The wavelength is 2L and there is a displacement antinode at the pipe's midpoint.

D) The wavelength is 2L and there is a displacement node at the pipe's midpoint.

Note: the waves here are displacement and not pressure waves. So at each end of open pipe, there is a antinode and at its midpointt a displacement node.

16. Two speakers are placed side by side and driven by the same frequency of 500 Hz. If the distance from a person to one speaker is 5.00 m and the person detects little or no sound, which of the following is a possible distance from the person to the other speaker? (The sound speed is 340 m/s.)

A) 7.7 m B) 8.1 m C) 9.1 m D) 8.4 m

[pic]

[pic] the only answer satisfying this equation is for m =4 ( d2 = 8.06=8.1m

17. If one doubles the tension in a violin string, the fundamental frequency of that string will increase by a factor of

A) 2. B) 1.4. C) 1.7. D) 4.

18. Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?

A) increases the energy by a factor of three

B) increases he energy by a factor of four

C) produces no change

D) increases the energy by a factor of two

19. Resonance in a system, such as a string fixed at both ends, occurs when

A) its frequency is greater than the frequency of an external source.

B) its frequency is smaller than the frequency of an external source.

C) its frequency is the same as the frequency of an external source.

D) it is oscillating in simple harmonic motion.

20. A string of mass m and length L is under tension T. The speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m, with no change in length?

A) 0.5v B) 2v C) 0.71v D) 1.4v

21. When sound passes from air into water

A) its frequency does not change.

B) its wavelength does not change.

C) its velocity does not change.

D) all of the above

22. A sound source approaches a stationary observer. The frequency heard by the observer is

A) lower than the source.

B) equal to zero.

C) the same as that of the source.

D) higher than the source.

23. A concave spherical mirror has a focal length of 20 cm. An object is placed 10 cm in front of the mirror on the mirror's axis. Where is the image located?

A) 20 cm behind the mirror C) 6.7 cm in front of the mirror

B) 20 cm in front of the mirror D) 6.7 cm behind the mirror

24. A light ray, traveling obliquely to a concave mirror's surface, crosses the axis at the mirror's focal point before striking the mirror's surface. After reflection, this ray

A) travels parallel to the mirror's axis.

B) passes through the mirror's focal point.

C) travels at right angles to the mirror's axis.

D) passes through the mirror's center of curvature.

25. For all transparent material substances, the index of refraction

A) is less than 1.

B) is equal to 1.

C) is greater than 1.

D) could be any of the given answers; it all depends on optical density.

26. An object in simple harmonic motion obeys the following position versus time equation: y = (0.50 m) sin (π/2 t). What is the maximum speed of the object?

A) 0.39 m/s B) 0.79 m/s C) 0.13 m/s D) 0.26 m/s

27. Consider two pipes of the same length: one is open and the other is closed on one end. If the fundamental frequency of the open pipe is 300 Hz, what is the fundamental frequency of the closed pipe?

A) 300 Hz B) 450 Hz C) 150 Hz D) 600 Hz

28. What is the intensity level of a sound with intensity 10-3 W/m2?

A) 60 dB B) 90 dB C) 30 dB D) 96 dB

29. The decibel is a unit of

A) amplitude. C) wavelength.

B) loudness. D) frequency.

30. How tall must a plane mirror be in order for you to be able to see your full image in it?

A) the same height as you C) 3/4 of your height

B) twice your height D) half of your height

Part III – Problems (8 points each): Show your work clearly and completely for each of the following problems.

31. In an experiment similar to the one you did in class, one end of a string was fastened to a secured rod, and then passed over a pulley. A 0.50 kg hanging mass was attached to the other end of the string. A speaker vibrating at frequency 250 Hz was placed under the string at a distance of 1.2m from the pulley. In the segment of the string between pulley and speaker top, a standing wave of 2.5 wavelength was observed. (a) What is the speed of the wave in the string? (b) What is the mass density of the string?

m = 0.50kg 1.2m = 2.5λ ( λ= 0.48m

f = 250Hz v = λf ( v = 0.48m(250 Hz)

L=1.2m v = 120m/s

n = 5

[pic]

[pic]

32. If the intensity level of one trombone is 70 dB and that of one cornet is 65 dB, which is louder: 76 trombones or 110 cornets? Show your calculations.

βt = 70 dB First need to find the sound intensity (w/m2) of each instrument:

βc = 65dB β = 10 log70 dB

βt = 70 dB

[pic]

Sound intensity for Trombone: [pic]

And for cornet: [pic]

Solution to Problem 32 (continued)

Now total sound intensity from 76 trombone is [pic]

And total sound intensity for 110 cornet is: [pic]

Now recalculate the sound level β for each case.

[pic]

And the total sound level of cornets:

[pic]

Therefore 76 trombone will be louder than 110 cornets.

33. A well with vertical sides and water at the bottom resonates at 7.00 Hz and no lower frequency. If the temperature of the air in the well is 15 oC, how deep is the well.

f = 7.00Hz

T = 15 oC Since there is no frequency lower than 7.00Hz, then

L = ? fundamental frequency is 7.00 Hz.

Well acts like a closed-open tube where:

L = ¼ λ and v = f λ

Unless otherwise specified, you should assume the speed of sound in air is 343 m/s at 20 oC and is described by:

[pic] where TC is air temperature in oC

[pic]

[pic]

L = 12.1 m

34. Kwang stands beside the tracks as a train rolls slowly past. He notes the frequency of the train whistle is 442 Hz when the train is approaching him and 441 Hz when the train is receding from him. Speed of sound in air to be 345 m/s. What is the speed of the train?

Given:

frequencies: [pic]

f1=442 Hz where f ′ is the shifted frequency observed by stationary Kwang, and f

f2=441 Hz is frequency emitted by moving source. Use the –vs when the source

v = 345 m/s is moving toward the observer and +vs when the source is moving

away from the observer

There are two Doppler effects: With the train approaching at speed vs , the observed frequency is f1.

[pic]

And as the train recedes, the observed frequency is f2:

[pic]

Dividing equation (1) by (2) gives

[pic]

and solving for the speed of the train yields vs = 0/391 m/s = 1.41 km/hr (slow)

35. The light beam in the figure shown strikes surface 2 at the critical angle. Determine the angle incident θi.

β + α + 60ο ’ 180 ( β ’ 90 − 42ο ’ 48ο

α ’ 42ο

α ’90 − θ2

θ2 ’ 18ο

Using Snell’s Law:

n1 sin θ1 ’ n2 sin θ2

You need to find n2 first: use Snell’s law for the refraction from surface 2 (n1 = nair = 1) :

n2 sin 42ο ’ n1 sin 90ο ( n2 = 1.49

n1 sin θ1 ’ n2 sin θ2 ( 1.0 sin θ1 ’ 1.49 sin18ο

θ1 ’ sin–1 (1.49 sin18ο ) ( θ1 ’ 27.5ο

For the following problems show your solution on the color papers. But draw the ray diagrams on the ruler shown for each problem and attach them to your color papers. Verify your numerical results using your scaled drawn ray diagrams.

36. A small object is 12 cm from a thin positive lens of focal length 6 cm. A plane mirror is placed at the second focal length of the lens and crosses the x-axis as shown. The mirror is tilted so the reflected rays do not go back through the lens.

a) Draw a ray diagram to scale showing the final image.

b) Is the image real or virtual?

c) Find the position of the final image.

[pic]

37. Consider a concave mirror with a focal length of 10.0 cm.

a) Find the image distance when the object distance is 10.0 cm.

b) Find the image distance when the object distance is 5.00 cm.

c) Find the magnification of the image for part b).

d) Describe the image for part b).

e) Draw the ray diagram for part b) on the ruler shown below.

a) Since the object is placed at the focal point of the mirror, image is formed at infinity (not visible)

Problem 37 (continued)

b)

[pic]

[pic]

c) The image is virtual, upright, larger and on other side of mirror.

d)

Some questions on Heat and Thermodynamics.

Please explain or show your work clearly for each of the following questions or problems.

1. You are selling your land by square feet. If on a hot day you are measuring a plot of land with a steel tape, will you be making more profit from the land sale? Explain.

Since the tape is metal, it will expand, and for example 100cm of it now may be 101cm. hence the dimensions of actual land are shorter than measured values. Not good!!

2. Consider a cup of tea at room temperature, 24 0C. If it is heated until it has twice the internal energy, what is its new temperature?

When internal energy doubles, the Kelvin temperature of the tea will also double.

Tnew = 2Told where Told = 273 + 24 =297 K

Tnew = 2(297) = 594 K.

Tnew = 598 – 273 = 325 oC (very hot)

3. A 40.0gram sample of water at 22.0o C is held in a 100 gram metal cup. 60.0 grams of water at 65.0o C is stirred into the cool water and the final temperature of the water is 47.0o C. Determine the specific heat of the metal of the cup.

Ti(cup) = Ti(water) = 22.0 oC

m1 (water) = 40.0g

Q (gained by metal cup and cold water) = –Q (lost by warm water)

mcup = 100 g

m2 (warm water) = 60.0g [pic]

T2 = 65.0 oC

Tf = 47.0 oC

cwater = 4.18 J/goC

[pic]

[pic]

4. A cup of coffee is enclosed in an insulated cup ½ cm thick in the shape of a cube 10cm in a side. The temperature of the coffee is 95o C, and the temperature of the surroundings is 21o C. Find the heat loss (in J/s ) due to conduction. The thermal conductivity of the cup is 2 x 10-4 [pic]

5. A heat engine with an efficiency of 24.0% performs 1250J of work. Find (a) the heat absorbed from the hot reservoir, and (b) the heat given off to the cold reservoir.

6. One mole of an ideal gas initially at sea level atmospheric pressure and 0 0C, is taken through a cycle as shown.

a) Calculate the initial volume of the gas?

a) Find the net work done by the cycle.

b) What is the net energy added by heat per cycle?

7. A basketball at 17 0C holds 0.95 mole of air molecules. What is the internal energy of the air in the ball?

[pic]

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