Chapters 16-17, 34-36, and Midterm, Tuesday, June 28

Q1. You are holding one end of a light string. The other end is attached to a vertical post. The string is under tension so that the speed of waves is 0.72 m/s. You find several frequencies at which you can oscillate your end of the string so that a point 45.0 cm from the post doesn’t move. a) What are the three lowest values of these frequencies? b) What is the general expression for these frequencies?

Q2. A train is traveling at 25.0 m/s. The frequency of the locomotive whistle is 400 Hz. What is the wavelength of the sound waves in still air a) in front of the locomotive? b) behind the locomotive? What is the frequency of the sound heard by a listener c) in front of the locomotive? d) behind the locomotive?

Q3. A thin layer of ice (n = 1.309) floats on the surface of water (n = 1.333) in a glass container. A ray of light from the bottom of the glass container travels upward through water. a) What is the largest angle with respect to the normal that the ray can make at the water/ice interface and still pass out into the air above the ice? b) What is this angle after the ice melts? (Hint: there are two interfaces involved here --- water/ice and ice/air).

Q4. An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. a) What is the focal length of the lens? Is the lens converging or diverging? b) If the object is 8.0 mm tall, how tall is the image? Is it erect or inverted? c) Draw a principle-ray diagram.

Q5. A ray of light contains two colors: red with wavelength of 660 nm and blue with wavelength 470 nm. The ray passes through two narrow slits separated by 0.30 mm and the interference pattern is observed on a screen 5.0 m from the slits. What is the distance on the screen between the first-order bright fringes for each wavelength?

Q6. Monochromatic light with wavelength λ from a distance source passes through a single slit. The diffraction pattern is observed on a screen 2.50 m from the slit. If the width of the central maximum is 6.0 mm, what is the slit width a if the wavelength is a) 500 nm (visible light)? b) 50.0 μm (infrared light)? c) 0.50 nm (x-ray)?

Q7. (5 points) Two 2.00  C charged particles are located on x axis. One is at x = 0.50 m, and the other is at x = m. Determine the electric field on the y axis at y = 0.25 m. (k e =1/4  0 = 9.0 x 10 9 N. M 2 /C 2 )

Q8. (25 points) A thin, square, conducting plate 25.0 cm on a side lies in the xy plane. A total charge of 1.00 x C is placed on the plate. Find (a) the charge density on the plate, (b) the electric field just above the plate, and (c) the electric field just below the plate. The charge density is uniform.