Final Practice Problems 1. The figure below shows a snapshot graph at t = 0 s of a sinusoidal wave traveling to the right along a string at 50 m/s. (a) Write the equation that describes the displacement D(x, t) of this wave. Your equation should have numerical values, including units, for all quantities except for x and t. (b) What is the phase of the wave at x = 3 m? (c) Suppose the string s tension is increased by 20%. By what percentage does the wavelength change? Does the wavelength increase or decrease? 2. The 40-cm long tube in the figure below has a 40-cm long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length L is 42.5 cm, 56.7 cm, and 70.9 cm. What is the frequency of the tuning fork? Assume v sound = 343 m/s. 3. Two strings with linear densities of 5.0 g/m are stretched over pulleys, adjusted to have vibrating lengths of 50 cm, and attached to hanging blocks. The block attached to string 1 has a mass of 20 kg and the block attached to string 2 has mass M. Listeners hear a beat frequency of 2.0 Hz when string 1 is excited at its fundamental frequency and string 2 at its third harmonic. What is one possible value for mass M? 1
4. A screen is placed 200 cm behind two narrow slits that are separated by 0.480 mm. The figure below shows the light intensity on the screen. (a) What is the wavelength of the light? (b) Consider point A on the screen. What is l, the difference between the distance from A to one slit and the distance to the other slit? 5. A diffraction grating is placed 1.00 m from a viewing screen. Light from a hydrogen lamp is passed through the grating, and the 656 nm line in the hydrogen spectrum is seen 60.0 cm to one side of the center. Then the hydrogen lamp is replaced with a mercury lamp. (a) Where does the 546 nm line in the mercury spectrum fall on the screen? (b) A spectral line is seen on the screen 36.4 cm away from the center. What is the wavelength? 6. An underwater diver sees the sun 50 above the horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver? Assume that the indices of refraction in water and air are n water = 1.33 and n air = 1.00, respectively. 2
7. Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 2.0 cm tall object is 15 cm in front of the 40 cm focal-length lens. (a) Use graph paper, a ruler, and the ray tracing techniques you ve learned to find the position and height of the image. (b) Calculate the image position and height and compare you answers with what you got in part (a). 8. (a) What is the electric field at the point indicated as a dot in the figure below? (b) What is the acceleration of an electron at that point? magnitude and a direction. Give your answer as a 9. A parallel-plate capacitor is formed of two 10 cm 10 cm plates spaced 1.0 cm apart. The plates are charged to ±1.0 nc. An electron is shot through a very small hole in the positive plate. What is the slowest speed the electron can have if it is to reach the negative plate. 10. A long, thin straight wire with linear charge density λ runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has a net linear charge density 2λ. Assume λ is positive. Find expressions for the electric field strength (a) inside the 3
cylinder, r <R, and (b) outside the cylinder, r > R. In what direction does the electric field point in each of the cases? 11. Five charges are arranged as shown. The figure shows five Gaussian surfaces and the electric flux through each. What are the five charges q 1 to q 5? 12. The electric potential of charge q in the figure below is 3140 V. What is charge q? 13. What is the equivalent resistance between points a and b in the circuit shown below? 4
14. For the circuit shown below, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading. 15. A positive helium ion He + is released from rest from the surface of a +1000 V electrode. It crosses (in vacuum) the gap between the electrodes, passes through a small hole in a 0 V electrode and into a wide magnetic field, then begins to curve as shown. The magnetic field is uniform in the region to the right of the 0 V electrode and is zero to the left of the 0 V electrode. Take the mass of He + to be 6.646 10 27 kg. (a) What is the direction of the magnetic field? Explain your reasoning, then show the field on the diagram. (b) The magnetic field strength is 1.0 T. Does the ion collide with the 0 V electrode? 5
16. The two 10-cm long parallel wires in the figure below are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be 5.4 10 5 N? 6