BVHS Physics: Waves Unit - Targets Part A: General Wave Properties: Students should be able to 1) describe waves as traveling disturbances which transport energy without the bulk motion of matter. In transverse waves, the disturbance is perpendicular to the direction of travel. In longitudinal (compressional) waves, the disturbance is parallel to the direction of travel. 2) calculate the velocity, distance traveled by or time traveled by a wave given the other two variables. 3) calculate the velocity, frequency or wavelength of a wave given the other two variables. 4) describe the consequences of the interference of two waves including descriptions of constructive and destructive interference. 5) describe the phenomena of reflection including the use of the law of reflection. 6) describe refraction qualitatively (it will be addressed quantitatively later in the semester) 7) describe diffraction as the bending of a wave around an obstacle or an edge. This can be described in conjunction with interference to describe diffraction patterns. Part B: Sound waves and Light waves. Students should be able to 1) identify the source of electromagnetic radiation as accelerating charges and the source of sound waves as oscillating objects. 2) identify sound waves as longitudinal waves and light waves as transverse waves. 3) relate the speed of sound to the medium through which it travels. Specifically they should know that sound travels fastest (not necessarily better) through a solid than a liquid and a liquid than through a gas. Sound cannot travel through a vacuum. Speeds above the speed of sound are known as supersonic. 4) relate the speed of light to the medium through which it travels. Light travels fastest through a vacuum. This speed has a value of 3 x10 8 m/s and is known as c. Light travels more slowly through any medium other than a vacuum. No matter or information may travel at superluminal velocities. 5) describe that sound waves have a spectrum of different frequencies. Humans perceive differences in frequency as pitch with higher frequency as higher pitch. Frequencies too high for humans to perceive are known as ultrasonic and those that are too low are infrasonic. 6) sort the electromagnetic spectrum (including the colors of the visible spectrum) in order from high to low or vice versa by frequency or wavelength. 7) students should be able to give a qualitatively give a description of the Doppler effect for light or sound.
1. What are waves? Waves Unit: Worksheet 1 Topics A1, A2, A3 2. Draw a transverse waveform in the space below and label the amplitude, crest, trough and wavelength. 3. Draw a longitudinal waveform in the space below and label the compression, rarefaction and wavelength. 4. The two primary types of waves are transverse and longitudinal. In which type do the particles that make up the wave move perpendicular to the wave? What do the particles do in the other type of wave? Each type of wave travels at a constant velocity as long as the medium stays the same. For instance, at standard pressure and 20 C, sound travels in air at about 343 m/s. The speed of sound increases with increasing temperature in air and changes if the sound wave is transmitted through liquids or solids. No matter what the speed of a wave though, if the speed stays constant then the distance traveled by a sound wave can be calculated by d = v * t. (distance = velocity * time elapsed) 5. Mr. Halberstadt is 200 meters away from the school when the 1 st hour tardy bell rings. How long does it take the sound to travel from the school to him? (Use v sound = 343 m/s) 6. A hiker determines the distance across a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. How large is the lake if the echo arrives 1.5 seconds after her shout? (Use v sound = 343 m/s) 7. Two submarines are on exercises in the Atlantic. One sends out a sonar wave pulse that reflects off of the other sub. It takes 5 seconds for the pulse to leave, reflect and return. In seawater the speed of sound is about 1560 m/s. a. How far is the other sub? b. If the subs are each moving towards each other at 20 m/s, how long will it be until they collide if no action is taken?
In the vacuum of space, light waves travel at a constant speed regardless of frequency. This speed is approximately 3 x 10 8 m/s. 8. How long does it take for radio signals to get from Mars to Earth when they are at their closest (about 54,000,000,000 meters)? This is how the rovers and landers send data to the Earth. 9. It takes light about 500 seconds to get to the Earth from the Sun. Approximately how far away is the Sun? All waves (light, sound, water) follow this simple equation: speed = wavelength * frequency v = λ * f In this equation, wavelength is in meters and frequency is in Hz so v is in m/s. 10. A tuning fork plays a frequency of 320 Hz. What is the wavelength of these sounds if the speed of sound is 343 m/s? 11. The speed of sound in iron is about 5100 m/s. A train traveling on iron rails creates a 200 Hz tone when braking. a. How long will it take the sound to travel 1000 m? b. What wavelength will this sound have in the iron rail? c. What wavelength will this same sound have in air? d. How long does it take for this sound to travel 1000 m in air at 343 m/s? 12. 96.5 FM broadcasts on a frequency of 96.5 Megahertz. Radio waves travel at the speed of light (3.0 x 10 8 m/s). What is the wavelength of this funky frequency? 13. 610 Sports (home of the 2009 Royals) broadcasts on a frequency of 610 kilohertz. What is the wavelength of these radio waves? 14. A fisherman notices that wave crests pass the bow of his anchored boat every 3.0
seconds. He measures the distance between two crests to be 8.5 meters. How fast are the waves traveling? Waves Unit: Worksheet 2 Topics A4, A5 Review: 1. Mr. Merlenbach points his laser pointer at a building 1 mile (1,610 meters) away. How long will it be before she can see the red dot on the building? (v light = 3 x 10 8 m/s) 2. It takes light about 4.3 years to get here from the 2 nd closest star to Earth, Proxima Centauri. How far away is Proxima Centauri in meters? Your answer should suggest why we use light-years as a distance measurement in astronomy. 3. Red light in that has a wavelength of about 7 x 10-7 meters. What is the frequency of this light? When two or more waves come together at the same location, the resulting disturbance is the sum of the disturbances from the individual waves. This fact is known as the principle of linear superposition. 4. Two boats travel past a swimmer in a lake. The waves from boat 1 have an amplitude of 40 cm while the waves from boat 2 have an amplitude of 30 cm. a. If the swimmer gets hit by a crest from both boats at the same time, what will the displacement of the resulting wave (include a sign indicating if the displacement is up or down)? What kind of interference is this? b. What is the resulting displacement if a crest from boat 1 arrives at the same time as a trough from boat 2? What kind of interference is this? 5. Two speakers are connected to a signal generator such that the same tone leaves each speaker at the same time in phase. What would a listener hear if they placed their ear at a position that was a. equidistant from both speakers b. ½ wavelength further from one speaker than the other. c. 7 wavelengths further from one speaker than the other. d. 15 wavelengths from one speaker and 16.5 wavelengths from the other. 6. If you are sitting at the point described in problem 5d and one of the speakers was turned off, what would you hear? 7. Describe the law of reflection. 8. The diagram to the right is shows two mirrors that
meet at an angle of 135. If a light ray hits the first mirror at an angle of 40, use the law of reflection to find the angle φ at which it leaves the 2 nd.
Waves Unit: Worksheet 3 Topics A5 A7 1. The law of reflection is that θ i = θ r? The angles for the law of reflection should always be measured with reference to what other line? 2. The diagram below shows an observer (labeled with an X) and three objects (T, A and U) in the vicinity of the front of a mirror. Draw in the image of each object. 3. Which of the objects from the last problem (T,A and/or U) can be seen by an observer standing at position X? For any that can, show the actual path that the light takes from the
object to the observer. 4. Object A as shown to the right is in front of a mirror. Light rays from object A hit the surface of the mirror and reflect in different directions. Show three different rays that leave A, hit the mirror and how they reflect. 5. Show the path that the light rays indicated will take when reflecting from each of the following reflective surfaces. Refraction: When physicists discuss the refracting ability of a material, they do so utilizing the index of refraction. The index of refraction (n) of a material is defined as the speed of light in a vacuum (represented by the letter c where c = 3 x 10 8 m/s) divided by the speed of light in the material. So the equation is n = c/v. This means that the larger the value of n, the slower light is in a material. For instance, if n = 2 for a substance, light would travel half as fast as it does in a vacuum. It is believed that c is the fastest possible speed, so n can never be less than 1. When light moves into a material in which it travels with a lesser velocity, its path will bend towards a line normal to the boundary between the materials. Thus the angle of refraction will be smaller than the angle of incidence. The opposite happens if the light speeds up. If the light hits perpendicular to the surface, it will go straight through. 6. A material has an index of refraction of 1.82. What is the speed of light in that material? 7. What is the index of refraction of a material if the speed of light through the material is 2.2 x 10 8 m/s? 8. The diagram to the right shows a sunbeam hitting the surface of a lake. Draw a normal line for this incident beam. 9. For the diagram to the right show the path of the light ray
that is reflected from the surface of the lake. Label the angle of incidence θ i and the angle of reflection θ rf. 10. For the diagram to the right, show the refracted ray. Label the angle of refraction θ rr. 11. What is the speed of light in water? 12. Would an observer under the surface of the water (like a fish) observe the sun to be higher or lower in the sky than it actually is? 13. A beam of light moves from air into glass with an angle of incidence of 40. Make a sketch of this situation being sure to indicate the angle of incidence and angle of refraction. Is the angle of refraction larger or smaller than the angle of incidence? (n air = 1.0, n glass = 1.5) In which medium does light move faster? Diffraction: Diffraction refers to the spreading out of waves after passing a barrier. For instance look at the diagram below to the right. You might expect that when the waves pass through the opening in the barrier they would stay as wide as the opening. However, the waves actually spread outward after going through the barrier. 14. Draw the waves after they pass through the barrier on the right. The degree to which the waves spread out past the barrier depends on two main factors; the size of the opening and the wavelength of the waves. In reality these are
really the same factor. For diffraction to occur, the opening can t be much more than a few times the size of the waves. To diffract visible light (with wavelengths around 5 x 10-7 m), the size of the opening must be very small. To diffract x-rays (with wavelengths around 5 x 10-10 m) requires openings about the size of the space between atoms. 14. Visible light has a wavelength that is smaller than the pupil of your eye. Sound waves vary in length but can easily be as long as a person. Which waves will diffract to a greater degree when passing through a aperture, visible light or sound waves? 15. Which sound waves would be diffracted by a greater amount when passing through a door ay those with a frequency in the bass range (~50 Hz) or those in the higher range (~200 Hz)? 16. Why can you hear around corners but you can t see around corners? 17. Light from a laser can be sent through a diffraction grating or what is known as double slit and can create an interference pattern. Explain how this works using both diffraction and interference as a part of your explanation.
Waves Unit: Worksheet 4 Review 1. As the wavelength of sound waves gets longer, what happens to the frequency? 2. Which sound waves would diffract best, those with wavelengths of 5 meters or 0.5 meters? 3. Which light waves would diffract the most, when passed through the same aperture, radio waves with a wavelength of 10 meters or X-rays with a wavelength of 10-10 m. 4. Do waves diffract better through a large aperture or a small one? Topics B1 B4 5. Which of the following particles would create electromagnetic radiation (choose all that apply)? For those that don t, explain why not. a. A neutron accelerating north at 10 5 m/s 2. b. A proton moving south at 3000 m/s. c. An electron being turned in a circular path by a magnetic field. d. A proton moving in simple harmonic motion. 6. A computer speaker is oscillating at a rate of 100 Hz. What wavelength will the sound have in air (the speed of sound in air is 343 m/s)? 7. We hear sound because the sound waves cause bones in our ears and our eardrums to vibrate (or resonate) at the same frequency as the source of the sound. If the sound waves move at 343 m/s and have a wavelength of 2.75 meters, what is the frequency that we hear? 8. Which (if any) of the following statements are true? a. Sound waves and electromagnetic waves both exhibit interference. b. Sound waves and electromagnetic waves can both be reflected. c. Sound waves and electromagnetic waves can both be refracted. d. Sound waves and electromagnetic waves can both be diffracted. e. Sound waves and electromagnetic waves both travel at the same speed. f. Sound waves and electromagnetic waves are both longitudinal waves. g. Objects can travel faster than both sound waves and light waves. 9. A sound wave can travel through gas, liquid and solid. In which material would you expect sound to travel at the greatest speed? Would you expect sound to travel at a faster speed in air at sea level or air at Denver? What about just outside the shuttle? 10. A shuttle astronaut shines a laser toward the Earth. What happens to the speed of light as the light gets closer to the ground? What happens to the index of refraction during this trip? 11. What is the speed of light in diamond if its index of refraction is 2.42?
12. If the speed of light in a material is 2.1 x 10 8 m/s, what is its index of refraction? Waves Unit: Worksheet 5 Topics B5 B6 1. How do humans perceive differences in sound frequency? 2. What is the name given for sound waves with frequencies too low for humans to hear? 3. What is the name given for sound waves with frequencies too high for humans to hear? 4. Why can dogs hear sound that are with too high of a frequency for humans to hear? 5. What is the approximate frequency range of human hearing? 6. One of the symptoms of problems (like friction between the bearings) for machines in a manufacturing production line are vibrations in the machinery. However, these vibrations are ultrasonic and require special equipment to detect. a. What is the longest these waves could be given that they can t be heard? b. Would you expect these sounds to diffract a great deal (making them hard to track to the source) or stay fairly directional? Why? 7. What is the speed of electromagnetic radiation with a frequency of 5 x 10 13 Hz and a wavelength 6 x 10-6 m? Is this surprising? 8. List the categories of EM radiation in order from longest to shortest wavelength. 9. List the categories of EM radiation in order of increasing velocity. 10. List the components of the visible spectrum from longest to shortest wavelength. 11. Why is white light not listed in the visible spectrum? 12. The index of refraction of glass is larger for shorter wavelengths. Thus which color of light should be refracted through the largest angle when passing from air into glass? 13. White light is projected through a diffraction grating. Which color of visible light should be diffracted through the greatest angle? 14. Order the following components of EM radiation in from the highest frequency to the lowest: radio waves, yellow light, X-rays, blue light, microwaves. 15. What parts of the EM spectrum are too long to be seen by humans? 16. Which EM waves should diffract more after passing through an aperture; infrared or ultraviolet?
Waves Unit: Test Review 1. a. Describe the motion and parts of transverse waves. Give an example. b. Describe the motion and parts of longitudinal waves. Give an example. 2. How long does it take a sound waving moving at 340 m/s to travel 85 meters? 3. Sound travels through salt water at a velocity of 1560 m/s. A submarine sends a sound wave forward and the echo returns after 0.45 seconds. How far is the obstacle? 4. Astronauts that landed on the moon left a mirror on the surface (with their lander). A laser is fired at the position of the mirror. How long should it take until the signal returns to Earth? The average Earth-Moon distance is 3.84 x 10 8 m and the speed of light in a vacuum is 3 x 10 8 m/s. 5. How long is a sound wave with a speed of 340 m/s if has a frequency of 20 Hz (at the low end of the audible spectrum)? What type of wave is it? Would it diffract more or less after passing through an aperture than the high end of the spectrum 20,000 Hz? 6. What is the frequency of a light wave with a wavelength the size of an atom: 1 x 10-10 m? 7. A particular earthquake shakes the ground with a frequency of 0.5 Hz and travels at about 8000 m/s. What is the wavelength of this wave? 8. The following diagram shows wave pulses moving in opposite directions towards each other. In the space below show (a) the pulses when the completely overlap and (b) what they would look like if the pulse heading left was inverted when the overlapped. 9. A crest from a wave of amplitude 15 cm hits a buoy at the same time as a trough from a wave of amplitude 20 cm. What is the total displacement of the buoy from its normal position? A. +35 cm B. + 5 cm C. -5 cm D. -35 cm 10. A laser beam is projected through two closely spaced apertures and onto a screen several meters away. The laser has a listed frequency of 5.32 x 10-7 m. a. A bright spot appears at a point exactly equidistant to both apertures. What kind of interference is this? b. How much further is one aperture than the other from the first dark spot adjacent to the spot described in part a? What kind of interference is this? 11. The star shown to the right sends light out in all directions including in the path which hits the reflective surface as shown.
Show the reflected ray and how you would determine its exact path. Show the location where the image of the star would appear. 12. Imagine that the reflective surface shown in problem 11 is the surface of a pond. If some of the starlight moves into the water show the path that it would take? 13. The diagram to the right shows a ray of light passing from material X into material Y. a. Which material has the higher index of refraction? b. In which material does light travel faster? 14. Sound waves traveling through a room pass through a door. A person is standing outside the room but not right in front of the door. a. Which sounds would they be most likely to hear; high frequencies or low frequencies? b. Would making the doorway more narrow make it more or less likely for sound to be heard from the same location? 15. a. What is the source of sound waves? b. A microphone detects sound waves which have a wavelength of 4 meters in air with a speed of 340 m/s. What is the frequency of the oscillator producing the sounds? 16. Which of the following would create electromagnetic waves? a. An electron moving at a constant 500 m/s in a circle? b. A proton oscillating up and down? c. A sodium ion speeding up due to an electric field? d. A neutron slamming into a target and coming to a sudden stop? e. An electron moving in a straight line at 200,000 m/s? 17. Rank the following materials from fastest to slowest as to the speed of sound through them in general: vacuum, solid, liquid, gas. 18. Rank the following materials from fastest to slowest as to the speed of light through them in general: vacuum, solid, liquid, gas. 19. Light travels through a material at 8.4 x 10 7 m/s. What is the index of refraction for that material? 20. EM waves just a little too long for humans to see are called what? 21. Rank the parts of the EM spectrum in order of decreasing frequency. 22. Rank the parts of the visible spectrum in order of increasing wavelength. 23. A 30,000 Hz tone would be classified as which of the following: audible, ultrasonic or infrasonic? 24. Mrs. Toneva is running towards the school just as the tardy bell is ringing. If the bell is set to ring with a 500 Hz tone, which of the following frequencies is she most likely to hear? A. 200 Hz B. 498 Hz C. 500 Hz D. 502
Hz E. 800 Hz 25. The Chipmunks are singing one of their annoying songs. Which of the following adjustments would make their voices seem more normal; moving towards them, having them move towards you, moving away from them, having them move away from you. 26. If a galaxy is moving away from us, the visible light it emits will seem to be redder or bluer?