Name: Date: MIDTERM 1 Physics 2306 Fall 2012 FORM A BEFORE YOU BEGIN: 1. Fill in CORRECTLY your ID number in the Scantron, as well as which FORM of the test you have. 2. Write the course number (2306) 3. Write down your name on the test and scantron; fill in the appropriate bubbles 4. Assume MKS units unless specified otherwise. 5. Take the speed of sound in air to be 340 m/s, and the acceleration of gravity, g = 9.8 m/s 2 ; e=1.6x10-19 C; k=9.0x10 9 Nm 2 /C 2 For problems where you are asked to rank items, items of different magnitudes should be separated by commas, while those of the same magnitude should have no comma between them. For example: Rank the following numbers from highest to lowest A) 7 B) 5 C) 5 D) 3 Answer: A,BC,D
1 A heavy weight is connected to the end of a light string to form a pendulum. You hear that the frequency of the string when plucked varies as a function of time as the pendulum swings. Suppose the swinging amplitude is 20 degrees from the vertical. Relative to what you would hear if the pendulum were at rest and not swinging, the frequency of the fundamental at maximal angular displacement is: 1) 6% lower 2) 3% lower 3) the same 4) 3 % higher 5) 6 % higher 2 A traveling wave on a horizontal vibrating string has wavelength 2.0 m and vertical amplitude 5.0 cm. The string has a wave speed 5.0 m/s. A light insect with mass 6.0 mg holds tight to the top side of the string. What is the maximal normal force on the insect exerted upwards by the string (do not ignore gravity)? 1) 0.13 mn 2) 0.022 mn 3) 0.74 mn 4) 0.61 mn 5) 1.5 mn
3 A string displacement ( exp is the natural exponential): y(x,t) = exp( (kx t) 2 ) exp( (kx + t) 2 ) is best described as being: 1) a standing wave 2) a right traveling wave 3) a left traveling wave 4) a left and right travelling wave 5) all of the above 4 The third harmonic of a vibrating string is 300 Hz. If the wave speed is 100 m/s, what is the length of the string? 1) 0.5 m 2) 0.2 m 3) 10 m 4) 4 m 5) 0.8 m
5 A mass of 1.0 kg is suspended from a string, and another mass of 2.0 kg is suspended from the first mass by a separate but otherwise identical string. The wave velocity in the bottom string divided by the wave velocity in the upper string is: 1) 1.2 2) 1.4 3) 0.6 4) 0.2 5) 0.8 6 One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column? 1) 256 Hz 2) 32 Hz 3) 128 Hz 4) 88 Hz 5) 64 Hz
7 Raptors, having a much more advanced ability to hear, can detect sound with an intensity level as low as 4.0 db. When you walk, the resulting sound has an intensity level of 40 db at a distance of 0.5 m. Assuming you are downwind from the raptor (so it won t pick up your scent), how close to the raptor can you walk without being detected? 1) 96 m 2) 79 m 3) 32 m 4) 65 m 5) 43 m 8 A person is hearing two sound waves simultaneously. One has a period of 1.50 ms and the other has a period of 1.54 ms. What is the period of the beat due to these two waves? 1) 58 ms 2) 330 ms 3) 1.5 ms 4) 0.040 ms 5) 3.0 ms
9 As you stand by the side of the road, a car approaches you at a constant speed, sounding its horn, and you hear a frequency of 80.0 Hz. After the car goes by, you hear a frequency of 60.0 Hz. What is the speed of the car? The speed of sound in the air is 343 m/s. 1) 25.0 m/s 2) 36.0 m/s 3) 49.0 m/s 4) 16.0 m/s 5) 64.0 m/s 10 The sound from two in phase point sources reach point O by two different paths. One path is 20.0 m long and the second path is 21.0 m long. The sound destructively interferes at point O. What is the minimum frequency of the sources if the speed of sound is 340 m/s? 1) 6800 Hz 2) 340 Hz 3) 520 Hz 4) 170 Hz 5) 680 Hz
11 The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude than charge q. In which of the line segements X, Y, Z will there be a point at which the net electric field due to these two charges is zero? 1. only region Y 2. only region Z 3. only region X 4. only regions X and Z 5. all three regions 12 In the figure, a small sphere of mass 6.00 x 10 2 kg and charge +0.400 μc is hung by a thin wire of negligible mass. A charge of 0.220 μc is held 0.290 m away from the sphere and directly to the right of it, so the wire makes an angle with the vertical, as shown. What is the angle (in degrees)? 1. 30.9 2. 5.70 3. 0.10 4. 6.30 5. 0.92
13 A line of uniform charge is extended from x = 5.0 m to x = 4.0 m, and has a linear charge density of 7.0 x 10 6 C/m. What is the magnitude of the resulting electric field at x = 0 m? x 1. 1.2 kn/c 2. 2.2 kn/c 3. 3.2 kn/c 4. 4.2 kn/c 5. 5.2 kn/c 5 4 0 14 Three point charges q, q and q are placed at the corners of a square of side d as shown. What is the magnitude of the net electric field at the center of the square? q 1. 2. 3. 4. 5. 20kq / d 2 2 2 30kq / d 2kq / d 6kq / d 2 2 40kq / 2d 2 q q
15 Two identical small charged spheres are a certain fixed distance apart, and each one initially experiences an electrostatic force of magnitude 90 N due to the other. With time, charge gradually leaks off of both spheres. When each of the spheres has lost one third of its initial charge, the magnitude of the electrostatic force between the spheres will be 1. 90 N 2. 80 N 3. 60 N 4. 40 N 5. 20 N 16 A standard demonstration charges a conducting sphere with small aluminum pie plates on top. When the charge gets large enough, the aluminum pie plates fly (one at a time) from the top. Approximately what charge has to be on the sphere for the last one to fly off? Assume the pie plates had a radius of 5 cm and mass of 1 g, while the sphere has a radius of 15 cm (as in the diagram on the right below). (Hint: the pie plate covered a small fractional area of the sphere, resulting in a fraction of the sphere s total charge being on it. Then, for it to just lift off, the electric field at the surface of the sphere interacts with the surface charge on the plate.) 1. 10 µc 2. 1 µc 3. 0.1 µc 4. 0.01 µc 5. 0.001 µc
17 Two 10cm x 10cm conducting flat plates have a total charge of +1 µc and 1 µc respectively. When they are very close to each other, separated by just an insulating oxide layer about 100 nm thick, what is the force pulling them together? 1. 1.3 N 2. 9.2 N 3. 13 N 4. 5.7 N 5. 20 N 18 A long cylindrical insulator has a uniform charge density,, thoughout its volume. What is the electric field as a function of r, the radial distance away from the center of the cylinder (r<1)? 1. 2. 3. 4. 5.
19 A conducting sphere has a charge +2Q on it, and is located inside a conducting shell with net charge +Q on it. Rank the outgoing electric flux from largest to smallest through centered spherical Gaussian surfaces: A) with 0<r<R1; B) with R1<r<R2; C) R2<r<R3 and D) r>r3. 1) A,B,C,D 2) D,B,AC 3) D,C,B,A 4) AC,BD 5) ABC,D R1 R2 R3 20 A very long uniform line of positive charge (dashed line) is coincident with and runs down the middle the west side of a square box as shown. Rank the net electric flux through each of the six sides of the box (labeled Top, Bottom, North, South, East, West), from largest to least (positive being outwards from the box). (Hint: Consider the lines of electric field coming from the wire when you look down the length of the wire. How many of these lines pass through each of the sides of the box. This number is proportional to the 'flux' through these sides.) 1) TB,E,NSW 2) E,TB,NSW 3) TB,E,NS,W 4) TEB,NSW 5) W,TB,E,NS W T N S E B