1 Conceptual Physics Review (Chapters 25, 26, 27 & 28) Solutions Chapter 25 Describe the period of a pendulum. Describe the characteristics and properties of waves. Describe wave motion. Describe factors that affect the speed of a wave. Distinguish between transverse and longitudinal waves, and be able to give an example of each. Distinguish between constructive and destructive interference. Describe how a standing wave occurs. Describe the Doppler effect for sound. Describe sonic booms. Be able to define all vocabulary words in bold from the chapter. Chapter 26 Describe the relationship between a sound wave s frequency and pitch. Describe the movement of sound through air. Compare the transmission of sound through air with that through solids, liquids, and a vacuum. Describe factors that affect the speed of sound. Describe loudness and sound intensity. Know the range of frequencies that a human can hear Determine the relative intensities of two sounds from their respective decibel levels. Describe natural frequency. Describe resonance. Describe beats. Be able to define all vocabulary words in bold from the chapter. Chapter 27 Describe the dual nature of light. What produces light (electromagnetic waves)? Define photons and identify which theory of light they provide evidence for. Explain why it is difficult to measure the speed of light. Know what a light-year is Know the different portions of the electromagnetic spectrum and how they each relate to each other in terms of wavelength and frequency. Describe opaque materials. Describe solar and lunar eclipses. Distinguish between umbra and penumbra. Describe polarization. Know the speed of light in meters per second and kilometers per second. Explain why sound waves move faster through steel than through air, while light waves travel more slowly in any medium than through a vacuum.
2 Chapter 28 Explain why white and black are not true colors. Describe what factors affect the color of an object. Describe what determined whether a material reflects, transmits, or absorbs light of a certain color, in terms of the frequency of that color of light. Identify the three primary colors of light, and what secondary colors are formed by combining any two of them in equal proportions. Describe white light. Define complementary colors. Identify the three primary pigments by name, and identify which of the primary colors of light each pigments absorbs and reflects. Describe the difference between color mixing by addition and color mixing by subtraction. Labs Review the Pendulum Lab. Review the Mechanical Waves Lab. Review the Speed of Sound Lab. Homework Assignments Review all written assignments out of your textbook. Review all reading quizzes. Review all worksheets. Review all class notes and challenge problems worked during class.
3 Sample Calculations 1. What is the frequency, in hertz, that corresponds to each of the following periods? a) 0.10 sec f = = = 10Hz T 0.10s b) 5 secs f = = = 0. Hz T 5s 2 1 c) 60 sec f = = = T 1 s 60Hz 60 5 d) 24 hours f = = = 1.16x10 Hz T ' 60min $ ' 60sec $ 24hr% "% " & 1hr #& 1min # 3 e) 12 mins f = = = 1.39x10 Hz T ' 60sec $ 12 min% " & 1min # 2. What is the period, in seconds, that corresponds to each of the following frequencies? a) 10 Hz T = = = 0.1sec f 10Hz b) 0.2 Hz T = = = 5sec f 0.2Hz c) 60 Hz T = = = 0.017sec f 60Hz d) x 10-5 Hz T = = = 86,400sec 5 f x10 Hz 7 e) 2.3 MHz T = = = 4.35x10 sec 6 f 2.3x10 Hz 3. A metronome is set so that it makes ten complete vibrations in 12 seconds. Find the frequency of the metronome. The problem gives information that tells us the period of the vibration of the metronome is 12/10 or 1.2 seconds. Frequency and period are reciprocals of each other, so the frequency of the metronome is 10/12 or 8.3 x 10-1 Hz. 4. While sitting on a pier, Carlos notices that incoming waves are 2.0 m between crests. If the waves lap against the pier every 5.0 s, find the a) frequency of the waves Frequency is the number of waves passing a given point per second. Here, the waves lap against the pier every 5.0 sec, meaning the period of the wave is 5.0 sec. The frequency is the reciprocal of period, which is 0.2 Hz. b) speed of the waves v = λf = ( 2.0m) ( 0.2Hz) = 0.4 m s 5. Light travels at a speed of 3 x 10 8 m/s in a vacuum, and for practical purposes, through air as well. The wavelength of a shade of yellow light is 5.80 x m. Find the frequency of this light. v = λf, so f = v λ = 3.00x108 m s 5.80x10 11 m = 5.17x1018 Hz
4 6. A gamma ray is high-frequency light. Find the wavelength of a gamma ray with a frequency of Hz. c = λf, so λ = c f = 3.00x108 m s 1x10 22 Hz = 3x10 14 m or 30 femtometers 7. If the speed of a longitudinal sound wave is 340 m/s, and the frequency is 1000 Hz, what is the wavelength of the wave? v = λf, so λ = v f = 340 m s 1000Hz = 0.34m 8. The Sears Building in Chicago sways back and forth at a frequency of about 0.1 Hz. What is its period of vibration? p = 1 f = 1 0.1Hz =10sec 9. If a train of freight cars, each 10 m long, rolls by you at the rate of 2 cars each second, what is the speed of the train? Conceptually, 2 cars of 10 meters each pass by a given point in one second. Therefore, the speed must be 2x10=20 meters per second. Or, using a wave speed equation, v = λf = ( 10m) ( 2Hz) = 20m s 10. If a wave with wavelength 10 m has a frequency of 2 Hz, what is the wave speed? v = λf = ( 10m) ( 2Hz) = 20m s 11. If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 meters, find each of the following: a) the frequency of the wave Frequency is the number of vibrations or cycles per second. Since we are told that this wave vibrates up and down (one cycle) two times each second, the frequency is 2 Hz. b) the wavelength of the wave Wavelength is the distance between successive identical parts of a wave. Since we are told that the distance between successive crests is 1.5 meters, the wavelength is 1.5 meters. c) the speed of the wave v = λf = ( 1.5m) ( 2Hz) = 3m s 12. Is it possible for one wave to cancel another wave so that the combined amplitude is zero? Explain your answer. Yes, this phenomenon is called destructive interference. When the crest of one wave completely overlaps with the trough of another wave of identical amplitude, the crest of the first completely fills in the trough of the other, resulting in zero amplitude. 13. Is the Doppler effect an apparent change in speed or frequency of a wave, due to the motion of the source relative to the receiver? The Doppler effect is an apparent change in frequency of a wave. While the wave source creates waves of a constant speed, the motion of either the source or the receiver causes a change in the frequency with which the waves reach the receiver.
5 14. Find the frequency of a sound wave that has a wavelength of 1.5 meters. Could you hear this sound? v = λf, so f = v λ = 340m s 227Hz Yes, I could probably hear this sound, since most 1.5m humans can hear any sounds between 20 Hz and 20,000 Hz. 15. Your teacher says Hello to you from across the gym, 34 m away. How long does it take the sound to reach you? This problem gives a distance that sound travels, which is NOT a wavelength, as far as we know. I will NOT use the formula involving wavelength and frequency. Instead, I will use the familiar equation d = vt. d = vt, so t = d v = 34m 340m s = 0.1sec 16. Imagine a hiker camping in the mountains. Just before going to sleep he yells WAKE UP, and the sound echoes off the nearest mountain, returning 8 hours later. How far away is that mountain? The sound the hiker makes travels to the nearest mountain and back to the hiker s position, which takes a total time of 8 hours. This means that the sound travels the distance TO the mountain in 4 hrs, and spends the other 4 hrs traveling back again. To find the distance to the mountain, use 4 hrs as the time. " d = vt = ( 340 m s) 4hrsx 60min x 60sec % $ ' = 4,896,000m OR 4.9Mm # 1hr 1min & 17. Suppose that you put your left ear down against a railroad track, and your friend one kilometer away strikes the track with a hammer. How much sooner will the sound get to your left ear than to your right ear? The speed of sound is about 5950 m/s in steel and 340 m/s in air. The question asks how much sooner, which means we need to find the two different times for the sound to travel through the steel railroad track and through the air, both for a distance of 1 km. Once we have these two times, we will subtract in order to answer the question. Time for sound to travel through the track: d = vt, so t = d v = 1x103 m 5950m s = 0.168sec Time for sound to travel through the air: d = vt, so t = d v = 1x103 m = 2.94 sec 340 m s So, the difference is 2.94 sec sec = 2.77 sec. It will take 2.77 sec longer for the sound to get to my right ear. 18. Radio station WKLB in Boston broadcasts at a frequency of 99.5 MHz. What is the wavelength of the radio waves emitted by WKLB? c = λf, so λ = c f = 3.00x108 m s 99.5x10 6 Hz = 3.01m 19. How much more intense is the average factory (90 db) to normal speech (60 db)? 10 3 = 1000 times more intense
6 20. A pendulum s natural frequency is one full back-and-forth swing every 2 seconds. For maximum amplitude, how often should the pendulum bob be pushed? Express your answer in terms of time and also as a frequency, in Hz. For maximum amplitude, the frequency of the forced vibration (the push) should exactly match the natural frequency of the pendulum. This means that the bob should be pushed once every 2 seconds, or with a frequency of 0.5 Hz. a) Would the pendulum continue to swing at this natural frequency if it were pushed only half as frequently? If it were pushed only half as frequently, each push would still coincide with a natural swing of the pendulum. It would continue to swing, but would not achieve maximum amplitude. b) What about if it were pushed with twice the frequency? If it were pushed with twice the frequency, every other push would be in a direction opposed to the natural swing of the pendulum, meaning it would not continue to swing (vibrate) at its natural frequency. 21. In order to create beats, should two sound waves be of the same frequency or of different frequencies? Why? Beats result from interference of two waves of slightly different frequencies. As they interfere, the vibrations will sometimes reinforce as they undergo constructive interference, and then they will undergo destructive interference. What humans hear, is a single pitch that alternates between loud (constructive interference) and soft (destructive interference). 22. Two notes of frequencies of 110 Hz and 140 Hz are sounded together. What is the resulting beat frequency? Would you be able to hear the beats? If not, why not? If so, what would they sound like? The resulting beat frequency is 30 Hz. You probably would not be able to hear them because most humans cannot distinguish beat frequencies greater than 10 Hz. 23. If a baby cries at a db level of 110 db and a firecracker has a db value of 150, how many babies would have to be crying to be as intense as the sound from a firecracker? 150 db is 10 4 times more intense than 110 db, therefore, 10,000 babies would have to be crying! 24. If you owe me $50, and you only pay me $45, by how much money were you short? What percentage is this of the amount you owed me? This percentage is equivalent to a percent error. You were ($50-$45) = $5 short. (5/50) *100 = 10% 25. Assume that the actual speed of sound at a given temperature is 340 m/s and that you do an experiment to calculate the speed of sound using echo reflection. If your experimentally determined speed of sound is 335 m/s, what is your percent error in the experiment? Show your work!!! 340m /s 335m /s *100% =1.5% 340m /s
7 26. For each of the following pairs, identify which has the longer wavelength and identify which has the higher frequency: a. radio waves vs. gamma rays Radio waves have longer wavelength and gamma rays have higher frequency. b. ultraviolet radiation vs. microwaves Microwaves have longer wavelengths and UV radiation has higher frequency. c. microwaves vs. X-rays Microwaves have longer wavelengths and X-rays have higher frequency. d. visible light waves vs. infrared radiation IR radiation has longer wavelengths and visible light has greater frequency. e. gamma rays vs. visible light waves Visible light has longer wavelengths and gamma rays have higher frequency. f. X-rays vs. radio waves Radio waves have longer wavelengths and X-rays have higher frequency. 27. How long does it take for light from the sun to reach Earth if the sun is 1.50 x m away? Show your calculation!! d = vt, so t = d/v. t = 1.5x1011 m 3.00x10 8 m /s = 500s 28. When you look at a distant star or planet, you are looking back in time. How far back in time are you looking when you observe Pluto through the telescope from a distance of 5.91 x m? t = d/v t = 5.91x1012 m 3.00x10 8 m /s = 1.97 x 104 s 29. If a person could travel at the speed of light, it would still take 4.3 years to reach the nearest star, Proxima Centauri. How far away, in meters, is Proxima Centauri? (Ignore any relativistic effects.) d = vt d = 3.00x10 8 m s 3600s 1hrs 24hrs 1day 365days 1yr 4.3yrs = 4.07x10 16 m OR d = 9.46 x m/yr * 4.3yrs = 4.07 x m 30. The wavelength of green light is about 500 nm. What is the frequency of this light? f = v λ 500nm x 10-9 m/nm = 5.00x10-7 m 3.00x10 8 m /s 5.00x10 7 m = 6.00x1014 Hz
8 31. When electromagnetic waves travel through a medium such as glass, what happens to the speed of the waves? What happens to the frequency? What happens to the wavelength? The speed of the wave slows down in glass, but the frequency remains constant. This means the wavelength must get shorter, because speed = wavelength x frequency. 32. Draw a sketch (not necessarily to scale) of the sun, moon, and Earth in their relative positions for a solar eclipse. Then draw a sketch with the relative positions for a lunar eclipse. Throughout your life, which type of eclipse would you probably be able to see more often? Explain why. Sun Earth Moon Lunar Eclipse (Moon goes dark, passing into Earth s shadow) There s no particular reason why one type of eclipse should necessarily occur more frequently than another, although total lunar eclipses occur more frequently than total solar eclipses, because the earth casts a larger shadow than the moon does. 33. I have a bright red umbrella. What do I actually mean when I say the umbrella is red? Explain in terms of frequencies of light that are reflected or absorbed by the umbrella. A red umbrella is made of material that has a red pigment. This means that the umbrella will absorb other frequencies (green, blue) of light, and only reflect red wavelengths of light. (Note that the red umbrella can also be thought of as being composed of magenta and yellow pigments. In this analysis, magenta and yellow pigments both reflect the red frequencies, magenta absorbs green, and yellow absorbs blue, leaving only the red color reflected.) 34. What color does my red umbrella appear when it is illuminated with white light? With yellow light? With magenta light? With cyan light? The red umbrella, lit with white light, reflects only the red light, and thus appears red in color. The red umbrella lit with yellow light can be thought of as being lit by red & green light it absorbs the green light, but reflects the red, and still appears red. The red umbrella lit with magenta light can be thought of as lit by red & blue light it absorbs the blue light, but reflects the red, and thus, still appears red. Finally the red umbrella lit with cyan light is being lit by blue & green light, both of which it absorbs. The umbrella will not reflect much light at all, and appear black. 35. My raincoat is bright yellow when illuminated with white light. What color does it appear when illuminated with red light? With green light? With blue light? The yellow raincoat is composed of yellow pigment, which reflects green and red but absorbs blue light. When lit with red light, then, the yellow raincoat will appear red (there is no green in the light to be reflected). When lit with green it reflects green it appears green. When lit with blue light, there is no green or red to be reflected the blue light is absorbed, and the yellow raincoat appears black. Sun green cyan blue Moon Solar Eclipse (Sun goes dark, Moon casts shadow on Earth) Earth yellow red magenta
9 36. When a piece of green glass is held in front of a white light source, what color is the light that is transmitted through the glass? What color light is transmitted through a piece of blue glass held in front of a white light source? What color light is transmitted through the two pieces of glass (blue and green) when they are held one against the other in front of the white light source? Green glass transmits the green frequencies, and absorbs the red and blue frequencies. Blue glass allow blue frequencies to pass through, and absorbs red and green. The two pieces of glass together will absorb all frequencies, and allow no light to pass through. 37. Microwave ovens emit waves of about 2450 MHz. What is the wavelength of this radiation? Show your work!! c = λf, so λ = c f = 3.00x108 m s 2450x10 6 Hz = 0.12m 38. When red light shines on a red rose, why do the leaves become warmer than the petals? Red light shining on a red rose is almost completely reflected by the red petals. The green leaves, however, only reflect green light, so the red light is absorbed by the leaves, and the em wave energy heats up the those leaves. 39. What are the three primary colors of light? For each pair of primary colors, list the color that is produced by mixing that pair of colors of light. Then, note what color is produced by mixing all three primary colors of light in equal proportions. The primary colors of light are Red, Green, and Blue. The secondary colors come from mixing these primary colors: R+G = Yellow, G+B = Cyan, and B+R=Magenta. Mixing all three colors of light results in white light. 40. What are complementary colors? Give three examples of pairs of complementary colors, and describe what happens when light of the two colors in each pair is mixed, and also explain what happens when pigment of the two colors in each pair is mixed. Complementary colors are colors from opposite sides of the color wheel. Mixing complementary colors (of light) Red and Cyan, for example results in White light (Red, Blue, and Green are all present). Mixing complementary pigments Blue and Yellow, for example results in a Black pigment, because all wavelengths of light are absorbed by the pigments. 41. If molecules in the sky scattered low-frequency light more than high frequency light, what color would the sky appear during the majority of the day? What color would it appear at sunrise and sunset? Molecules in the sky currently scatter higher-frequency (blue) light, which allows us to see the sky as blue; during a sunset, more of the sun s green frequencies are scattered, leaving behind a sunset that is red in appearance. Under different conditions, if lower frequency light (red) were scattered, we d see the sky as red. And if lower frequencies of light are scattered more easily than higher, the red frequencies from the sun would be scattered, leaving the sun to be colored blue at sunrise and sunset. 42. You are working in a theater and have three lights available to shine on the actors on stage: red, blue, and green. If the actor is wearing a yellow jumpsuit, what color does the jumpsuit appear when you shine the red light on the actor? What color does the jumpsuit appear when you shine the blue light on the actor? What about when you shine the green light on the actor? What if you shine all three lights simultaneously on the actor? Yellow reflects red and green light, so a yellow jumpsuit lit with red light would only appear red there would be no green light to reflect off the suit. Blue light on a yellow jumpsuit would be completely absorbed (blue is the complementary to yellow), so the suit would reflect little light, and appear very dark. Green light on the yellow suit would be reflected, giving it a green color. Shining R, G, and B on the suit is the equivalent of shining white light on it light of all wavelengths which would allow the red and green light to be reflected, giving it the expected yellow color.
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