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Lab VII: Homeschoolers are making waves! Objectives: • Demonstration of wave interference using computer speakers and pure tone from computer or mobile device; students will measure amplitudes (dB) at varying locations • Explore general patterns of waves with a jump rope and a slinky • Use cake pan of water and drop of food coloring to illustrate how waves are passage of energy but not matter, per se. Introduction: • A medium is necessary for the movement of some types of waves. Sound waves are vibrations that move from particle to particle. • Energy is travelling in waves, while the particles of the medium show little or no net movement. • A wave travels at a speed according to the equation: v = ƒ × λ , where v stands for velocity, ƒ stands for frequency in Hz or s-‐1, and λ stands for wavelength. • A waves have crests and troughs. Sound waves consist of the compression and rarefaction of particles in longitudinal waves. • Wavelength is the distance between two successive crests of a wave (or one full cycle of a wave or pattern). • Waves may interact with one another or a reflection of itself. The interaction of waves is called interference. Waves that are in phase (crests meet crests and troughs meet troughs) create greater peaks (amplitude), and the interference is constructive. If opposite peaks meet and decrease amplitude, the interference is destructive. Terms: Frequency, wavelength, crests, troughs, compression, rarefaction, longitudinal waves, transverse waves, constructive interference, destructive interference, amplitude, decibel (dB), nodes, antinodes, open end, closed end Supplies: Jump Ropes (enough for everyone or at least 1 per 2 students) Slinky (1 per 2 students is good, but may be shared if supply is limited) Cake pan (9×13) Water Liquid food coloring Computer speakers (2 from the same jack) Large room Software and Technology Supplies: Smart Device App to measure noise levels in decibels (for students’ smart devices if applicable) Smart Device App to emit a steady tone of defined frequency without decay
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Recommended Free Apps for Smart Devices: DecibelMeter v. 1.6, or Decibel 10th for iPhone,-‐ Measures amplitude of sounds in dB; students may download in advance to use in Part A Tuner T1 or C Tuner Lite (Both are free, but the free trial for C Tuner expires quickly.) Teacher Preparation: • The lab begins with a demonstration of wave interference. The instructor will want to test it out before class. In a large room, place two computer speakers a short distance (≈1m) apart on a table. Plug the speakers into a tablet, iPad, computer, or electronic musical instrument that can hold a steady tone without decay (a drop in volume). The speakers should be plugged in to a single jack, and both must make the tone from the same source so that the sounds from the speakers are in phase. Also, be sure the sound is at a safe volume. While the tone is played, students may use a noise-‐measuring app or their ears (their God-‐given qualitative instruments) to walk around the room and see whether the amplitude decreases steadily moving away from the speakers. However, the use of smart devices helps students to be objective. Teacher tip: Students should be able to find quiet spots (not as loud, though perhaps not silent) that are actually a step closer to the speakers than some loud spots. They might even notice a difference in volume between ears. The quiet spots represent spots of deconstructive interference, where the crest of a wave from one speaker combines with the trough of the other speaker, resulting in low to no amplitude. It is also possible to get constructive interference (two peaks combine) in a loud spot. The presence of walls, large objects, or persons in the room can also reflect the sound waves and alter the interference patterns. After this exercise, students should move to the next sections to better understand the shapes of waves. Advanced Options: (i) When a student finds a spot of maximum amplitude, move one speaker backwards or forwards by about ½ meter. Does the amplitude change? Repeat for a place of minimum amplitude. (ii) Use a meter stick to measure distances from each speaker to the site of a maximum or minimum close to the speaker (where the waves may differ by ½ λ). Can you determine the wavelength of the tone? Does it match the predicted frequency using v = ƒ × λ, where vsound = 343 m/s. • There are many questions in the lab write-‐up. Instructors may select a subset of questions as an assignment.
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Student Activity: A Wave interference Students should be shown the two speakers and told that both speakers will play a tone simultaneously. Students should hypothesize (1) where in the room the sound will be loudest and the quietest and (2) how will the volume (amplitude) change between those locations, i.e. will it be a steady decrease in amplitude as you move away from the speakers, or will there be loud and quiet spots along the way. Test your hypotheses. Measure the volume in decibels (dB) near and far from the speakers using an App on a smart device. Walk diagonally through the room. Try to disprove your hypothesis. B. Investigate traveling waves 1. Jump ropes and slinky show transverse waves • Students will make transverse waves. In a transverse wave, the medium is disturbed perpendicular to the direction of motion. In this case, a bump moves along a jump rope or slinky. i. Send a bump along the jump rope that is not held by anyone (an open end). This bump is the incident pulse (Send the bump sideways to see it better). This is a traveling wave, which moves with a definite speed.
• Is there any net movement of the medium, i.e. the jump rope? No. Despite the illusion of movement, only energy is moved from one point to another. The jump rope does not move in the direction of the wave. ii. Send a bump to a closed end (Partner holds steady and tight, or tie one end to a chair) If you send a wave on your right side, on which side does it return? The returning bump (called a reflected pulse) is inverted on the left side. Question: Is there any net movement of the medium, i.e. the jump rope? iii. Shake one end of the jump rope very quickly side to side in short movements to make a standing wave. Observe the nodes (little to no movement) and the antinodes (greatest movement and appears as a “U” shape on both sides).
• Is there any net movement of the medium, i.e. the jump rope?
!!
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Interesting nugget: In a standing wave, the reflected pulses are interfering with the incident pulses, giving the illusion of still waves. The Tacoma Narrows Bridge, nicknamed Galloping Gertie, collapsed on November 7, 1940 as result of standing vertical waves. The number and locations of antinodes along the length of a bridge are important to its stability. Use a slinky for the next three exercises. If there are not enough slinkies, then continue to use the jump ropes. iv. Place a slinky on a flat surface and gently stretch it apart. Do not hyperextend the slinky! If you and your partner send incident pulses simultaneously on the same side, what happens when they collide? v. If you and your partner each send incident pulses on opposite sides, what happens when the waves collide? vi. Make longitudinal waves with the slinky. Hold one end in each hand and send a straight shake (not a curved bump as before!) down the slinky. The hand motion should be like bouncing a ball. You should see locations of compressed slinky (compression) and stretched slinky (rarefaction). In a longitudinal wave, the medium is disturbed parallel to the direction of motion. C. Making water waves • Fill the bottom of a cake pan with water. Put a single drop of food coloring near the edge of the pan and a second drop in the middle of the pan. • Tap the pan lightly with your finger on the long side or the short side. Observe the wave as it passes along the pan. Question: Is there any net movement of the medium, i.e. the water?
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Lab VII: Making Waves Lab Part A Questions: 1. Why should you try to disprove and not “prove” your idea? 2. Did the amplitude decrease steadily as you moved away from the speakers? Did you notice any patterns? 3. How can there be sites of low amplitude closer to the speakers than some sites of high amplitude? What is happening with the waves? 4. When does wave interference occur? 5. If you listen to an orchestra in a concert hall, do you need to be concerned that you might accidentally choose a spot of deconstructive interference and be unable to hear? 6. The interference experiment was performed with sound waves. Does wave interference also happen with light waves? Advanced research question: 7. How does the shape of a concert hall affect acoustics? What are key features in the design of a concert hall that improve overall acoustics? Part B Questions (Interspersed in the activity): 1. Is there any net movement of the medium, i.e. the jump rope, when a pulse is sent to an open end? 2. Is there any net movement of the medium, i.e. the jump rope, when a pulse is sent to a closed end? 3. Is there any net movement of the medium, i.e. the jump rope, when many pulses are sent in standing waves? 4. What happens to the pulse when it is sent to a closed end? 5. How does a standing wave form? 6. Organ pipes have “stops” that can block open-‐end pipes. What happens to a resonating wave in air when it encounters a stop? 7. When incident pulses were sent from opposite ends, but on the same side, of the slinky, what happened when they collided? 8. When you and your partner each sent incident pulses on opposite sides of the slinky, what happened as the pulses collided? 9. Is the sound from a beating of a drum a transverse wave or a longitudinal wave? 10.What is the difference between a longitudinal wave and a transverse wave? Advanced: Watch an online video of the collapse of The Tacoma Narrows Bridge. Prepare a short report of what was wrong with the bridge design. What did bridge engineers learn from this catastrophe? Part C Question 1. As the water wave moves along the pan, is it mostly a movement of matter, energy, or both? How did the drop of food coloring help you to answer this question?
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Lab VII: Making Waves Lab Part A Answers: 1. Scientists can only disprove a hypothesis or conclude that the data are consistent with a hypothesis. Although the hypothesis may seem right, there could be, eventually, a better hypothesis or better experiment that better explains a natural phenomenon. People should be skeptical whenever new evidence is said to “prove” something. Scientific guesses may only be disproved. Trying to disprove your own hypothesis also helps keep you objective. 2. Answers may vary. 3. Waves move with crests and troughs. Sound waves move with particle compression and rarefaction. The waves are initially in phase (crests and troughs line up with those of a different wave), but they travel different lengths along a path, bringing them out of phase. A minimum is a place where crests line up with troughs, and the wave is flattened temporarily as a node as the waves pass though each other. 4. Wave interference occurs anytime waves from two sources (or reflected sources) are not in phase. “In phase” means that the crests and troughs of the waves align perfectly. A simple explanation is that the sound waves travel different distances from the speakers to arrive at that spot, so the waves are no longer in phase. 5. In theory, this could happen, but orchestra instruments do not produce “pure tones” in phase. Nevertheless, engineers also use the shape of the hall to reflect sounds from the walls to fill in places where deconstructive interference might occur. 6. Yes. For example, a radio broadcast on your car stereo might suddenly be disrupted when you drive near a large object that reflects radio waves from the broadcasting station. Or operating a household appliance (microwave, hair dryer, baby monitor) might cause static on your television or lower your WiFi signal and speed because they share a common frequency (2.4GHz). Part B Answers. 1. No. Despite the illusion of movement, only energy is moved from one point to another. The jump rope does not move in the direction of the wave. 2. No. After the passage of the pulse, the jump rope falls to rest in the same place. Only energy has been displaced. 3. No. Despite the illusion of movement, only energy is moved from one point to another. The jump rope does not move in the direction of the wave. 4. The pulse is reflected on the opposite side. 5. A standing wave is the combination of many incident and reflected pulses with a closed end. 6. The stop in an organ pipe creates a closed-end. Therefore, the sound wave would be reflected and would not pass through an open end.
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7. The waves combined to form a bigger wave (constructive interference = greater amplitude) as they passed through each other. Neither wave was destroyed. 8. The waves flattened as they passed through each other (destructive interference = lower amplitude), but again, neither wave was destroyed. 9. The sudden hitting of a drum sends a pulse of energy that is continually passed along a line of particles. This is similar to the compression that is sent in a straight shake through the coils of the slinky. 10. In a longitudinal wave, the medium is disturbed parallel to the direction of motion, as in a sound wave or slinky. In a transverse wave, the medium is disturbed perpendicular to the direction of motion, as in a water wave or light wave. Part C Answer: 1. The waves are mostly a movement of energy. The waves pass through the drops of food coloring, but the waves do not significantly increase the diffusion rate of the coloring.
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Lab VIII: Dual Particle-Wave Nature of Light Objectives: • Use a prism to show dispersion of white light and qualitatively determine which wavelengths of light bend more • Use LEDs in a string of Christmas lights to investigate photon energy • Use the equations E=hc and c = λƒ, using wavelengths measured in a spectroscope • Measure the focal length of a convex lens to illustrate bending of light Introduction: The refraction of light as through water, glass lenses, or a prism helps to demonstrate how light has wave-‐like properties. Refraction is a change in the direction of wave movement. Refraction of light occurs anytime a ray of light enters a different, transparent medium. The “medium” means the substance (air, water, glass) or even lack of substance (vacuum) in which the wave is propagating. The speeds of sound and light depend on the medium. For example, the speed of light in a vacuum (c) is 2.99 × 108 m s-‐1, but 2.25 × 108 m s-‐1 in water and 1.93 × 108 m s-‐1 in quartz. The speed of light slows in non-‐vacuum media because the wavelengths become shorter. The extent of refraction (light bending) also depends on the wavelength. Lenses can be made that bend light, and prisms can be used to disperse white light into a visible light spectrum. Refraction and dispersion of light do not prove that light is a wave, but they do depend on the wave-‐properties of light. However, light behaves not simply as a wave but seems to also have particle-‐like properties. In 1922, Albert Einstein received the 1921 Nobel Prize for his explanation of the photoelectric effect, published in 1905. (Incidentally, Einstein did not receive the Nobel Prize for his theory of Special Relativity or his famous equation, E=mc2.) The photoelectric effect happens when light rays of sufficient energy are absorbed by some types of metal, and excited electrons (called photoelectrons) are released, generating an electric current. To explain this, Einstein proposed that light waves move in discrete, particle-‐like packets of energy called photons. We can measure the energy of photons in electron volts (eV). An electron volt is the small amount of energy (1.6 × 10-‐19 Joule) gained by an electron when it accelerates through a potential difference of 1 volt. In this experiment, students will be able to calculate the energy of photons from light-‐emitting diodes (LEDs). Teacher Preparation: • Students may do these stations in any order. However, a student should use the same convex lens for Stations B and C to see if the focal length is the same between
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the two methods. Convex lenses with relatively small focal lengths (10-‐30cm) should be used. Lenses from the telescope-‐building lab should be fine. • Measuring focal lengths (Stations B and C) requires that no bright lights be near the white surface where the refracted image will appear. • For Station B, arrange a framed picture and a white posterboard vertically (or white wall) facing each other 1-‐2 meters apart. Shine a bright lamp on the framed picture, but keep the posterboard somewhat shadowed. • The cone for the prism experiment needs to be made only once. You may prefer to make it before class and allow all the students to share the setup. • The focal length experiment is best performed in a dimly-‐lit room. Terms: Refraction, Dispersion, Photoelectric Effect, photoelectrons, electric current, electron Volt (eV), photons, index of refraction, directly proportional, inversely proportional, photon Supplies: • Spectroscope (EISCO Premium Quantitative Spectroscope. $5-‐10 on Amazon) • String of multicolor LED Christmas tree lights • Convex lenses or magnifying lens, 1 per student or student pair • Desk lamp • Framed picture • Prism • Small flashlight (white light, preferably LED, single bulb) • Small cardboard tube (e.g. toilet paper tube) • Scissors and Tape • White, flat, vertical surface (wall, paper against a box, etc.) • Optional: Diagram of full visible and invisible light spectrum • Optional: String of ordinary (not LED) multicolor Christmas lights Equations and constants: (1) E = hƒ (2) c = λƒ c = speed of light in vacuum = 3 × 108 m/s = 3 × 1010 cm/s = 3 × 1017 nm/s Equations (1) and (2) substitute to form: (3) E = hc/λ Constants: 1 eV = 1.6 × 10-‐19 Joule; h = Planck constant = 6.63 × 10-‐34 J·s (4) E(in eV) = 1240 eV·nm (Eqtn #3 with hc constants combined to 1240 eV·nm)
λ(nm) (5) Thin lens equation
1 1 1 ⎯ = ⎯ + ⎯ where f is focal length, do is distance from object f do di and di is distance to focused image
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Student Activities: A. Dispersion of light using a prism
• Cut a cardboard tube along one side. Fashion the tube into a cone with a small opening at one end. Tape the cone to hold shape. • Shine a flashlight through the cone and point it at a certain spot on a white, vertical surface. If possible, mark on the surface where the light hits it (origin). • Stand a prism on its triangular end in the path of the white light. Rotate the prism until a visible light spectrum appears. • Which color in the spectrum has bent the least, i.e. is closest to the origin? Which light has refracted the most?
B. Measuring the focal length of a convex lens using a near object. • Use the same lens for B and C. • View the framed picture and a white posterboard arranged vertically and facing each other 1-‐2 meters apart. Illuminate the framed picture with a small desk lamp, but keep the posterboard somewhat shadowed. • Move the convex lens by its edges so that it is parallel to and in-‐between the frame and the posterboard. • Starting against the poster board, slowly move the lens towards the picture frame and away from the poster board. Watch for an inverted image of the framed picture to appear on the poster board. • Have your partner measure the distance between the lens and the poster board (di) and the distance between the lens and the picture frame (do) . • Use the thin-‐lens equation to determine the focal length (f) of the lens. 1 1 1 ⎯ = ⎯ + ⎯ f do di • Repeat the experiment with your partner’s lens. Explanation to Part B. Lenses are made to bend light from objects to focus at a certain distance from the lens. The focal length of the lens depends on the precise curvature of the convex or concave lens. A convex lens focuses the image on the side opposite the object. The distance from the lens where the object comes into focus depends on how far the object is from the lens. The focal length (f) can be determined from the thin-‐lens equation.
C. Measuring focal length of convex lens using a distant object • Use the same lens for B and C. • Hold a convex lens by the edges (or a magnifying glass by its handle) . • Find a bright object that is a good distance away. (e.g. a house or tree across the street on a sunny day. You may be inside looking through a window.)
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• Hold the convex lens parallel to the object and parallel to a light colored wall or a vertical, white sheet of paper. • Slowly move the lens toward the wall. An inverted image of the object will appear on the wall. • When the image on the wall is focused, the distance from the wall to the lens is the focal length of the lens. Use a ruler to measure the focal length of the lens. _____cm Explanation to Part C. If the object being viewed is far away (do is very big, and di is very small) then the value of 1/do will be so small that we may ignore it. In this case, the equation would become: 1 1 ⎯ = 0 + ⎯ f di Therefore, f = di.
D. Measuring the photon energy
• Use a spectroscope to determine the wavelengths of different colored LEDs on a string of Christmas tree lights. Record the wavelengths in a table. • Use the following equation to calculate the energy of the photons from this light. • E(in eV) = 1240 eV·nm
λ(nm) • Optional: For comparison, view a string of regular, multicolor Christmas
tree lights through the spectroscope. How is the diffracted color different from LED lights?
Lab VIII Write-up Part A Questions: 1. What is different about these colors that causes them to refract differently? 2. What is an index of refraction? 3. Which color in the spectrum was refracted the least, i.e. is closest to the origin? Which light has refracted the most?
LED Color Wavelength (nm) E (eV)RedOrangeYellowGreenBluePurple
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Parts B and C Questions. 1. Do the focal lengths of your lens in Parts B and C match? What assumption made the calculation in Part C easier? 2. Would a lensmaker who was testing someone’s reading glasses be able to neglect the distance from the object in the thin-‐lens equation? 3. Were the images inverted? Why? Part D Questions 1. Describe the light from each LED. Was the light a continuous spectrum, discontinuous, or monochromatic? 2. Optional. How is the diffracted color of regular (non-‐LED) Christmas tree multicolor lights different from LED lights? 3. Which color of light has the most energy? The least? 4. What do the terms directly proportional and inversely proportional mean? Use the equations E = hƒ and c = λƒ to justify your answer. 5. What is the relationship between light frequency and energy? Between light wavelength and energy? Use the equations E = hƒ and E = hc/λ to justify your answer. 6. What is an electron volt? Is it a unit of energy or electric potential? Explain. 7. What is the frequency of a red light that has a wavelength of 690 nm? Assume the speed of light (c) is 3 × 108 m/s, and show your work. John 8:12 “I am the light of the world. Whoever follows me will not walk in darkness, but will have the light of life.”
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Answers to Part A 1. The speed of light is the same for all light, but light waves differ in their wavelength and frequency. Shorter wavelength (higher frequency, blue) light refracts more when passing through a prism than longer wavelength light (red). This difference causes the dispersion of white light into a spectrum. 2. The index of refraction is an intrinsic property of a transparent medium that affects the speed of light and affects how much the light refracts when entering the medium. In general, the index of refraction is related to density. 3. Red, which has the longest wavelength in the visible light spectrum, bends the least. Blue or purple has the longest wavelength and bends the most. (Depending on the flashlight, students might not be able to see the purple color.) Answers to Parts B and C 1. The focal length should match in both methods. When focusing an object at a large distance, relative to the distance to the focused image, is large, the term 1/do becomes negligible. 2. No. Reading glasses are intended to focus an image of a book page on the retina of a person’s eye. Both the distance from the book to the lenses and the distance from the lenses to the eyes are small. Therefore, the lensmaker would have to measure both di and do. 3. Yes, the images were inverted because the shape of the convex lens bends different rays of light towards a central point. Answers to Part D 1. The light from colored LEDs is typically monochromatic, showing a single or narrow set of wavelengths of a single color. 2. In general, regular Christmas tree lights are incandescent and poor filters of colored light. Thus, each bulb emits a continuous spectrum of light. 3. Blue or purple light is the highest frequency of visible light and therefore has the highest energy. Red has the lowest energy. 4. Directly proportional variables are ones that increase or decrease in proportion to each other. For example, energy of a light wave (E) is directly proportional to its frequency. A variable that increases while another decreases in proportion is said to be inversely proportional. For example, wavelength and frequency are inversely proportional in the equation c = λƒ . 5. Light frequency and energy are directly proportional in the equation E = hƒ
i.e. high frequency = high energy. Wavelength and energy are inversely proportional in the equation E = hc/λ i.e. longer wavelength = lower energy. 6. An electron volt is the amount of energy required to push an electron to an electric potential of 1 Volt. An electron volt is not a unit electric
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potential as is a volt. Put simply, electron volts are the amount of energy being held by electrons.
7. c = λƒ 3 × 108 m/s = (690 nm ÷ (109 nm/1 m) × ƒ ƒ = 4.35 × 1014 Hz
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Lab IX: The Sound Waves of Music Sound • Use a phone app to measure sound frequency • Relate frequency of sound to musical notes • Investigate how pitch changes with measured quantities of water in bottles and cylindrical glasses • Make connection between water-‐filled glasses and musical instruments Supplies: Glass cylinder (drinking glass or small vase; 5 identical glasses per small group) Graduated cylinders (25-, 50-, or 100-mL) Metric rulers Knife (or any thin hard metal) Glass soda bottles, empty and clean, 12-‐oz, 7-‐9 inches tall, 1 per student Water, tap Beakers, 500-mL, for re-‐using water Recommended Free Apps for Smart Devices: DecibelMeter v. 1.6, or Decibel 10th for iPhone,-‐ Measures amplitude of sounds in dB; students may download in advance to use in Part A Pano Tuner Free 1.2.14, for iPhone and iPad – Measures tones in both Hz and closest musical note Terms Pitch, Frequency, harmonics, Instructor Prep • Students will use mobile devices and frequency-‐measuring Apps to investigate the making of musical tones. The Pano Tuner App is excellent. Background noises can easily ruin the measurements of their tones. Therefore, students should be instructed to (1) not make any unnecessary noise and (2) alternate their sound-‐making with others in the class. If space allows, students could be separated into pairs in separate rooms. Students will also be blowing into glass bottles (soda or beer bottles work). Bottles should be clean when they start, but for good health, bottles should not be shared. Students may work in pairs or small groups. Plastic bottles might work, too, but are typically oddly shaped and flexible, making it harder to obtain meaningful results. The note blown by an empty bottle is likely to be near the G3 note on a standard piano (≈195 Hz). Introduction In the waves lab, we learned the height of a column of air in a cylindrical pipe determines its pitch. A bottle is a more complex shape than a cylinder. Therefore,
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the resonance from blowing into a bottle is determined not only by the height of the column of air but the overall bottle shape. Blowing air over the top of the bottle to make sound is an example of Helmholtz Resonance. Helmholtz Resonance happens when there is a change in air pressure in a cavity. Blowing air into the cavity causes changes in the air pressure in the bottle and vibrations through the air inside the bottle. Helmholtz resonance in an ordinary bottle follows a complex relationship with its shape. Students will explore this relationship by plotting data and fitting a computer-‐generated curve to it. Student Activities: • Work in pairs or small groups. A. Water organ using glass cylinders • You will need 5 identical glass cylinders for this experiment. • Measure the empty space of the glass in centimeters. Do NOT include the thickness of the glass at its base. Height of empty space in glass _______ cm Internal diameter of empty space in mouth of glass ______cm Internal diameter of empty space in mouth of glass ______cm • Fill the glass cylinder with a measured amount of water, keeping track of the total. Total full volume ____ mL • Multiply the full volume by 0.75, 0.5, and 0.25. Fill three glasses with the resulting volumes. Leave the fifth glass empty. • Use a knife blade to tap the side of the full glass. Practice getting a resonating tone that follows the initial “clink”. Once you have your method, try to do it the same way throughout the entire experiment. You want to listen for the tone and not the clink. • Listen to the pitch when the glass is full. This is the Fundamental frequency. The sound is proportional to the height of the column of water. • Tap each of the glasses. Rank the glasses according to their pitch (high to low). Is the fundamental frequency high or low in pitch? • Advanced activity: If time allows or at home, and if there is a piano available, try to identify the letter note that is produced by each of the glasses. Do you see a pattern related to the tones produced by empty, ¼, ½, ¾, and full glasses? B. Air resonance in bottles • Work with a partner. Each should have a bottle. Each should complete the next two sections. • Place the mouth of the bottle perpendicular to your lips. Gently blow across the mouth of the bottle to get a low, resonating tone. Practice so that you will be able to blow into the bottle the same way throughout the experiment. • The resonance of air inside an empty bottle is called Helmholtz frequency (ƒH). • Measure the ƒH of the empty bottle using the Pano Tuner App, or its equivalent. Record this value and the musical note in the Pitch column of the table.
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• Add 25-‐mL water to the bottle. Measure the new ƒH. Be sure to hold the bottle still so that the water is level. By adding water, you have effectively made the air space in the bottle smaller. • Repeat the previous step and measure the ƒH with each addition of water. Record of the total water volume and the ƒH with each addition. Repeat until the bottle is completely full, but do not try to get a measurement when the bottle is completely full. • What volume of water is in a completely full bottle? _____ mL • You will plot these data in the lab write-‐up.
Part C. Playing soda bottles in a jug band • Again, blow into the empty bottle and measure the pitch. Record the pitch and letter note. ƒH = ______Hz; Letter Note = ______ • Optional: If the ƒH of the empty bottles is not in tune with a real musical note, add small, measured amounts of water to the bottle to bring the frequency up to the next real note. Record the new ƒH of the “in-‐tune” letter note, and the amount of added water. Water added = ____ mL; ______ ƒH ; Letter Note = ______
Volume added (mL) fH (Hz) Letter Note Air Volume (mL)0255075100125150175200225250275300325
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• You must now find out how to fill one of the bottles to get a pitch exactly one octave higher than the empty (or slightly filled) bottle. • Look at the piano key diagram. Find the note of your (almost) empty bottle. This is the Tonic note of your scale. • Find the key that is one octave higher than your Tonic note (same letter, higher number; e.g. if your empty bottle plays B2, one octave higher would be B3). Record this letter/number and its pitch (Hz) This is your “Target note”. Target Note: _____ ƒH ; Letter Note = ______ • Use the data you collected in the previous table to determine approximately how much water to add to your bottle. Add this amount, and then either add or take away water until you obtain the right pitch by blowing into the bottle. Measure exactly what you add or subtract. • How much water did it take to increase the pitch by one octave? ______mL • There are 12 half steps in an octave (a half step is an increase or decrease by one note). If you add 1/12th of the volume, does the pitch increase by one note? • If you have time, try this again with a different note. Add only enough water to increase the tone by a half step (one musical note). Record the starting pitch and volume and the final pitch and volume. Is it always the same volume? • If you and your partner are musically inclined, you could try to fill 2-‐3 bottles to play a major chord, such as C3, E3, and G3.
Starting pitch (Hz)
Starting note
Initial volume
Target pitch
Target Note
Final Volume Δvolume
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Lab IX Write-Up Part A Questions: 1. Consider the measured dimensions of the glasses. Were the glasses perfect cylinders? If not, do you think this affected the results? To help understand pipe organs, why would we want to use cylinders? 2. What is the fundamental frequency of a vibrating object? 3. What happened to the pitch as you moved from full to less full glasses? 4. How are the tones produced with water-‐filled glasses different from that of pipes in organs? What medium resonates in the organ pipes? What medium resonates in the glasses? 5. How does the size of an organ pipe affect its pitch? Advanced Question: 6. If you have not already, try the advanced activity listed at the end of Part A. Can you produce a musical scale of 8 notes with 8 glasses? How much water did you add for each note in the scale? If you are musically inclined, discover how much water to add for a half step or whole step. Present your findings to your instructor, parents, friends, or at a science fair. Answers to Part A: 1. Organ pipes are made of cylinders. The height of the pipes is related to the frequency of the organ tones. 2. The fundamental frequency is the lowest frequency produced by an oscillating object or instrument. For a cylinder, the fundamental frequency is proportional to the height of the resonating medium in the cylinder. 3. The pitch became higher (greater frequencies) as the column of water became shorter. 4. The air resonating within the organ pipes produces the tones. In this experiment, the glass is resonating, but the pitch is affected by the columns of air and water. 5. A longer organ pipe will have a lower pitch (smaller frequency) while a shorter pipe will have a higher frequency. Part B Questions: 1. Plot the data collected in Part B by following these steps.
A. Complete Table 1. Find the “Air volume” by subtracting the “Volume added” from the volume of a completely full bottle. Repeat for each data point. B. Type the data points for Air volume and ƒH in adjacent columns in a computer spreadsheet, such as Microsoft Excel. C. Generate a X-‐Y Scatter plot of ƒH (y-axis) versus Air volume (x-axis). Remember to add a title and to label the units on the axes. D. Add a trendline for the data. Select “Power” under Trend/Regression type. Under options, click the box to “Display equation on chart”.
2. What is meant by “Air volume”? Why is this a better independent variable than “Volume added”?
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3. Describe the pattern displayed in the graph. 4. In Part C, you determined the amount of water to increase pitch by one octave. Would this same amount of water increase pitch by one octave if you started with a different Tonic note? Explain.
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Answers to Part B: 1.Sample Data Graph
2. Bottles are different sizes and shapes. With two different bottles, the volume of air in each is not necessarily the same when an equal volume of water is added to each. To show the relationship between the volume of a bottle and its air resonance frequency, it is better to plot the data as the volume of air space remaining. To think about it another way, by adding water you have effectively made a smaller bottle. 4. The relationship on the graph is not linear. Rather the pitch increases by a complex relationship likely involves the inverse of the square root of the air volume. Therefore, the pitch does not increase by the same amount when a fixed volume of water is added. A half step in pitch cannot be achieved by adding 1/12th the volume for increasing by one octave.
y"="4549.7x*0.529"R²"="0.99878"
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Figure: Standard 88-key piano tones with frequencies (Hz)
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D#7#$2489.0$C#7#$2217.5$$
A#6#$1864.7$G#6#$1661.2$F#6#$1480.0$
D#6#$1244.5$C#6#$1108.7$
A#5#$932.3$G#5#$830.6$F#5#$740.0$
D#5#$622.3$C#5#$554.4$
A#4#$466.2$G#4#$415.3$F#4#$370.0$
D#4#$$311.1$C#4#$277.2$
A#3#$233.1$G#3#$207.7$F#3#$185.0$
D#3#$155.6$C#3#$138.6$
A#2#$116.5$G#2#$103.8$F#2#$92.5$
D#2#$77.8$C#2#$69.3$
A#1#$58.3$G#1#$51.9$F#1#$46.2$
D#1#$38.9$C#1#$34.6$
A#0#$29.1$
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