AP Waves/Optics ~ Learning Guide Name: Instructions: Using a pencil, answer the following questions. The guide is marked based on effort, completeness, thoughtfulness, and neatness (not accuracy). Do your best! General Waves: 1. Is a rattle in a car ever a resonance phenomenon? Explain. 2. Why can you make water slosh back and forth in a pan only if you shake the pan at a certain frequency? 3. Explain the difference between the speed of a transverse wave travelling down a cord and the speed of a tiny piece of the cord. Repeat with a longitudinal wave. 4. What kind of waves will travel down a horizontal metal rod if you strike its end i. vertically from above ii. horizontally parallel to its length 5. Give TWO reasons why circular water waves decrease in amplitude as they travel away from the source. (hint: look up Inverse Square Law on the internet) 6. When a sinusoidal wave crosses the boundary between two sections of cord where one side is a thick cord (like a rope) and the other is thin (like a string), the frequency of the wave does not change (although the wavelength and velocity do change). Explain why. What do we call this phenomenon?
7. When a standing wave exists on a string, the vibrations of the incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Justify your answer. 8. AM radio signals have frequencies between 550 khz and 1600 khz. i. With what speed do radio waves travel at? ii. What is the range of wavelengths associated with these frequencies? 9. The speed of sound in water is 1560 m/s while it is only 343 m/s in air. Provide an explanation for the higher speed in water. 10. A sailor strikes the side of his ship just below the surface of the water. He hears he echo of this wave 3.0 s later. How deep is the ocean floor at this point? (ans. 2340m) 11. Sketch the resulting wave pattern when the waves below overlap as shown (principle of superposition)
12. A particular string vibrates in four loops at a frequency of 280Hz. Name at least three other frequencies at which it will resonate. 13. If two successive overtones of a vibrating string are 280Hz and 350Hz, what is the frequency of the fundamental? How many nodes would be present in the 280Hz standing wave? 14. A closed pipe is considered to be a pipe that is open on one end and closed on the other. An open pipe is one that is open on both ends. A pipe in air produces two successive overtones at 240Hz and 280Hz. How long must the pipe be and what is the fundamental frequency if i. it is open (ans: 4.3m, 40Hz) ii. it is closed (ans: 4.3 m, 20Hz)
15. The human ear canal is approximately 2.5cm long. Estimate the frequencies found in the audible range that will produce standing waves in the ear canal. (ans: 3430Hz, 10290Hz, 17150Hz) 16. A particular organ pipe can resonate at 264Hz, 440Hz, and 616Hz, but not any frequencies in between. i. Is this an open or a closed pipe? Justify. ii. What is the fundamental frequency of this pipe? (ans: 88Hz)
17. A vibrating tuning fork is held above a column of air, as shown in the diagrams below. The reservoir is raised and lowered to change the water level, and thus the length of the column of air. The shortest length of air column that produces a resonance is L 1 = 0.25 m, and the next resonance is heard when the air column is L 2 = 0.80 m long. The speed of sound in air at 20 C is 343 m/s and the speed of sound in water is 1490 m/s. (a) Calculate the wavelength of the standing sound wave produced by this tuning fork. (ans: λ actual = 1.1 m) (b) Calculate the frequency of the tuning fork that produces the standing wave, assuming the air is at 20 C. (ans: f = 312 Hz) (c) Calculate the wavelength of the sound waves produced by this tuning fork in the water, given that the frequency in the water is the same as the frequency in air. (ans: λ water = 4.8 m) (d) The water level is lowered again until a third resonance is heard. Calculate the length L 3 of the air column that produces this third resonance. (ans: 1.3m)
(e) The student performing this experiment determines that the temperature of the room is actually slightly higher than 20 C. Is the calculation of the frequency in part (b) too high, too low, or still correct? Too high Too low Still correct Justify your answer. 18. Water waves approach an underwater shelf where the velocity changes from 2.8m/s to 2.1m/s. If the incident wave makes an angle of 34º with the shelf, what is the angle of refraction. Sketch the waves and label the given information before you proceed. (ans: 25 º) Light: 1. How can you determine the speed of light in a solid, rectangular, transparent object? Draw a sketch of your method. 2. How can you see a round drop of water on a table even though water is colourless and transparent? 3. The speed of light in a certain substance is found to be 89% of its value in water. What is the index of refraction of this substance? (ans: n = 1.49) 4. An aquarium filled with water has flat glass sides whose index of refraction is 1.52. A beam of light from outside the aquarium strikes the glass at an angle of 43.5º to the perpendicular as shown.
a. What is the angle of this light ray when it enters the glass? (ans: 26.9º) b. What is the angle when it then enters the water? Sketch the path that the light follows. (ans: 31.2º) 5. Light is incident on an equilateral glass prism at Ө = 45º as shown below.
a. Sketch the path that the light follows as it passes through the glass prism (n = 1.58) b. Calculate the angle at which the light emerges on the opposite face. (ans: 60.5º to the normal) 6. **What must be the minimum index of refraction of the prism above is replaced by one whose apex angle is 90º and the light is be totally internally reflected at the opposite side?
Lenses/Mirrors: 1. An object O is placed 18 centimeters from the center of a converging lens of focal length 6 centimeters as illustrated below: a. On the illustration above, sketch a ray diagram to locate the image. b. Is the Image real or virtual? Explain your choice. c. Using the lens equation, compute the distance of the image from the lens. (ans: 9 cm) A second converging lens, also of focal length 6 centimeters is placed 6 centimeters to the right of the original lens as illustrated below. d. On the illustration above, sketch a ray diagram to locate the final image that now will be formed. Clearly indicate the final image.
2. A marine archaeologist looks out the port of a research submarine, as shown. The port is spherically shaped with center of curvature at point C and radius of curvature r. It is made of a material that has an index of refraction of n w, the same as the index of refraction of seawater, which is greater than n a, the index of refraction of air. The archaeologist is located to the left of point C and some equipment in the submarine is located behind the archaeologist. The archaeologist can see through the port, but the port also acts as a mirror so the archaeologist can see the reflection of the equipment. a. What is the focal length of the mirror? b. On the following figure, sketch a ray diagram to locate the position of the image of the equipment formed as a result of the mirror effect.
c. Based on your ray diagram, check the appropriate spaces below to describe the image of the equipment formed as a result of the mirror effect. i. Image is: upright inverted ii. Image is: real virtual iii. Image is: larger than the equipment smaller than the equipment The archaeologist also observes a seahorse located outside the port directly in front of the archeologist. Due to refraction of light at the inner surface of the port, the seahorse does not appear to the archaeologist to be at its actual location. d. On the figure above, sketch a ray diagram to locate the position of the image of the seahorse formed by the refraction of light at the port. e. Based on your ray diagram, check the appropriate spaces below to describe the image of the seahorse, as seen by the archaeologist, formed by the refraction of light at the port. i. Image is: upright inverted ii. Image is: real virtual iii. Image is: larger than the seahorse smaller than the seahorse
Double Slit: 1. Is the double-slit experiment more convincing for the wave theory of light or the particle theory? Be sure to back up your answer by describing what would happen if the other were true (what would be observed?). 2. Research. When white light passes through a prism, it breaks down into the colours of the rainbow. a. Sketch the pattern below labelling the colours in the correct order: b. Explain why this happens (this phenomenon is known as dispersion). 3. Why do we get nodes and antinodes when light passes through two slits? One Slit? 4. Compare and contrast the pattern produced by a single slit to that produced by a double slit. Use sketches and label any variables found in the equation appropriately.
5. White light falls onto a double slit. The center of the pattern is observed to be white (but bright), while rainbows appear at intervals on either side. Use the equation to explain what side of the rainbow is blue and what side is red (closer to the center or further from the centre). 6. Why doesn t the light from the headlights of a car in the distance produce an interference pattern? Provide two reasons. 7. What happens to the diffraction pattern of a single slit if the whole apparatus is immersed in water instead of air? A vacuum instead of air? 8. Two small speakers S are positioned a distance of 0.75 m from each other, as shown in the diagram below. The two speakers are each emitting a constant 2500 Hz tone, and the sound waves from the speakers are in phase with each other. A student is standing at point P, which is a distance of 5.0 m from the midpoint between the speakers, and hears a maximum as expected. Assume that reflections from nearby objects are negligible. Use 343 m/s for the speed of sound. (a) Calculate the wavelength of these sound waves. (ans: λ = 0.1372 m)
(b) The student moves a distance Y to point Q and notices that the sound intensity has decreased to a minimum. Calculate the shortest distance the student could have moved to hear this minimum. (ans: 0.459 m) (c) Identify another location on the line that passes through P and Q where the student could stand in order to observe a minimum. Justify your answer. (d) i. How would your answer to (b) change if the two speakers were moved closer together? Justify your answer. (ans: Y would increase) ii. How would your answer to (b) change if the frequency emitted by the two speakers was increased? Justify your answer. (ans: Y would decrease)
9. Your teacher gives you a slide with two closely spaced slits on it. She also gives you a laser with a wavelength λ = 632 nm. The laboratory task that you are assigned asks you to determine the spacing between the slits. These slits are so close together that you cannot measure their spacing with a typical measuring device. a. From the list below, select the additional equipment you will need to do your experiment by checking the line next to each item. Meterstick Ruler Tape measure Light-intensity meter Large screen Paper Slide holder Stopwatch b. Draw a labeled diagram of the experimental setup that you would use. On the diagram, use symbols to identify carefully what measurements you will need to make. c. On the axes below, sketch a graph of intensity versus position that would be produced by your setup, assuming that the slits are very narrow compared to their separation.
d. Outline the procedure that you would use to make the needed measurements, including how you would use each piece of the additional equipment you checked in (a). e. Using equations, show explicitly how you would use your measurements to calculate the slit spacing.
10. In a classroom demonstration, a beam of coherent light of wavelength 550 nm is incident perpendicularly onto a pair of slits. Each slit has a width w of 1.2 x 10 6 m, and the distance d between the centers of the slits is 1.8 x 10 5 m. The class observes light and dark fringes on a screen that is a distance L of 2.2 m from the slits. Your notebook shows the following setup for the demonstration. a. Calculate the frequency of the light. (ans: f = 5.45x10 14 Hz) b. Calculate the distance between two adjacent dark fringes on the screen. (ans:.067 m) The entire apparatus is now immersed in a transparent fluid having index of refraction 1.4. c. What is the frequency of the light in the transparent fluid? (ans: f = 5.45x10 14 Hz) d. Does the distance between the dark fringes increase, decrease, or remain the same? Explain (ans: decrease) Increase Decrease Remain the same Explain your reasoning.