Phys of Sound Concepts Answers

Understanding Vocabulary Section 20.1 1. transverse waves 2. trough 3. fundamental 4. waves 5. longitudinal waves 6. harmonics Section 20.2 7. circular wave 8. reflection 9. diffraction 10. absorption Section 20.3 11. constructive interference 12. destructive interference Reviewing Concepts Section 20.1 1. Answers are: a. wave motion; vibration of air transformed to electromagnetic wave and transmitted. b. wave motion; energy released in the earthquake is transmitted over ground to the floor of the house. c. wave motion; electromagnetic signal is transformed by the speaker to sound wave. d. wave motion; X rays are a form of electromagnetic waves e. wave motion; visible light is a form of electromagnetic waves 2. Transverse waves vibrate perpendicular to the direction in which the wave travels. Examples include light, X rays, water waves. Longitudinal waves vibrate parallel to the direction in which the wave travels. Examples include sound and the P-wave of an earthquake. 3. Answers are: a. v = fλ b. λ = v ÷ f c. f = v ÷ λ 4. speed = wavelength ÷ period 5. very short wavelength - electromagnetic waves very long wavelength - water waves 6. D shows amplitude; C shows wavelength 7. A standing wave occurs when an object vibrates at multiples of the resonant frequency. Standing waves occur as a result of reflected energy at a boundary between two media. 8. three nodes and two antinodes 10. Answers are: A reflection B absorption C diffraction D refraction 11. The amplitude of the wave decreases as it is absorbed. 12. The interaction between the wave and an opening which is small compared to the wavelength causes the wave to pass through a small opening and spread out as a circular wave front behind the opening. 13. Answers are: a. refraction b. diffraction c. reflection d. absorption e. absorption Section 20.3 14. The superposition principle states that the total vibration at any point is the sum of the vibrations of the individual waves. So, the resulting amplitude will be the sums of the amplitudes of the two individual waves. 15. Yes, if the amplitudes of the two waves are identical and they interfere destructively, the resulting wave will have no amplitude. 16. Answers are: a. The amplitude of the resulting wave is the sum of the amplitudes of the interfering waves. b. The amplitude of the resulting wave is the difference between the amplitudes of the interfering waves. Solving Problems Section 20.1 1. v = fλ = (10 Hz)(2 m) = 20 m/sec 2. λ = v ÷ f = (400 m/sec) ÷ (200 Hz) = 2 m 3. f = v ÷λ = (5 m/sec) ÷ (1 m) = 5 Hz T = 1/f = 1/5 Hz = 0.2 Hz 4. velocity = frequency × wavelength = 10 Hz × 0.08 m = 0.8 m/sec 5. Answers are: a. period = 1/frequency = 1/(30 Hz) = 0.033 sec b. 60 Hz c. 75 Hz d. 3 nodes e. 2 antinodes 6. Third harmonic = sixth harmonic divided by 2 = 48 Hz ÷ 2 = 24 Hz 7. The fourth harmonic has 5 nodes and 4 antinodes. 8. The second harmonic = 2 times fundamental = 2 × 440 Hz = 880 Hz Section 20.2 9. The answer is: Section 20.3 10. A 11. C Applying Your Knowledge Section 20.1 1. Answers are: a. transverse b. 0.000278 Hz c. speed = wavelength ÷ period wavelength = period × speed = (3,600 sec)(200 m/sec) wavelength = 720,000 meters = 720 kilometers 2. When a baseball hits a bat, standing waves occur along the bat. If a ball hits at the sweet spot, both the fundamental and 2nd harmonic waves occur. The sweet spot is between the locations of the nodes of these vibrations, about 17 centimeters from the barrel end of the bat. If the ball hits at another position, the bat vibrates with a relatively large amplitude that hurts your hands. If the ball hits the sweet spot, the vibrations have lower amplitudes and there is no stinging sensation after you hit the ball. Section 20.2 3. Answers are: a. The electromagnetic wave of visible light coming from the eye chart is being refracted. b. Light waves c. Eyes that are near- or farsighted do not refract light in a way that brings image into focus on the retina. Eyeglasses correct this problem by refracting light so that when it enters the eye images are in focus on the retina. 4. The sound must travel from the source to the wall, 34 meters, and back again, a total of 68 meters. time delay = (distance ÷ speed) = (68 m) ÷ (340 m/sec) = 0.2 sec Section 20.3 5. If two waves are superimposed in such a way that their crests are in phase, the amplitude of their resultant wave crest will be the sum of the amplitude of the two waves. A wave twice the height of the normal ocean waves could form if the conditions were right. 6. Answers may vary. Brief sample answers: a. Airport noise: Noise pollution from airports is considered to be an environmental problem. There are certain special interest groups who work specifically to reduce noise pollution from airports. Ways that airport noise can be reduced include modifying airplane engines to reduce sound produced and making sure that the area around an airport includes open space so that the loud noise has farther to travel before affecting people. Also, airports are designed so that the people inside do not hear the noise being made by the plane on the runway. The main solution for reducing sound in this situation is by absorbing the sound. b. Highway noise: Sound barriers are often constructed at the edges of highways to absorb the traffic noise. Usually they occur when the highway occurs in residential areas. Also, whenever new highway projects are proposed, noise studies are performed to see how the project will affect noise levels in local areas. The following link to this government site provides interesting information about highway traffic noise: http:// www.fhwa.dot.gov/environment/htnoise.htm. The main solution for reducing sound in this situation is by absorbing sound. c. Teenage hearing protection: Here a student could design a survey to give to students in the school. The objective of the survey would be to learn (1) whether or not teenagers protect their hearing when exposed to loud noises (such as at rock concerts, or in rural areas when farm machinery is in use), and (2) how regularly they use hearing protection. d. Noise/health: The primary cause of hearing loss is due to noise. Hearing damage is permanent. Noise pollution during the night can cause sleep loss when can adversely affect health. Chronic loud noise is thought to increase stress levels in people. Long term stress due to loud noise or any other source can ultimately have deleterious health effects. Understanding Vocabulary Section 21.1 1. decibels 2. acoustics 3. pitch 4. supersonic 5. Doppler effect 6. shock wave Section 21.2 7. reverberation 8. Fourier’s theorem Section 21.3 9. cochlea 10. scales 11. beat 12. consonance 13. dissonance 14. sonogram Reviewing Concepts Section 21.1 1. You would not hear the explosion because in the vacuum of space does not have a continuous medium for carrying the longitudinal wave. Sound needs air molecules and bits of matter to carry the sound waves. 2. The sound of people’s voices is a complex sound, created by the superposition of many frequencies and harmonics. The nerves in the ear respond separately to each different frequency with the brain interpreting the signals. Meaning in different sounds or voices is derived from the patterns of frequency and loudness and softness. 3. The decibel scale measures the loudness (or amplitude) of sound and is measured on a scale of 1 to 100. Note: the scale is logarithmic, which advanced students may recognize. 4. Moving toward you, the pitch will increase. 5. The airplane needs to travel faster than the speed of sound. This speed is referred to as supersonic. 6. Stereo sound is two recordings, one played from the right speaker and one from the left speaker. The “live” sound is created by the slight differences in phase between sound reaching your left and right ears. This is how you would experience the sound if it were played live. Section 21.2 7. Sound is caused by the vibration of the molecules of a substance, most commonly air, at frequencies within the range of hearing. As sound travels through a mass of molecules, it causes molecules to oscillate between being tightly packed and more spread out. However, the molecules do not travel with the sound but vibrate in place. 8. Longitudinal 9. If the pressure of a gas is increased in one area, the gas particles tend to spread out and lower the pressure in surrounding areas. The gas atoms have mass, and therefore inertia. The combination of inertia and restoring force from pressure causes gas molecules to exhibit harmonic motion in the form of sound waves. 10. d; frequency and wavelength are inversely proportional. The sound with the highest frequency will have the shortest wavelength. 11. When temperature of a material increases, the speed of sound through that material increases. This is because the molecules in the material move faster at higher temperatures and sound depends on the movement of molecules. Also, the speed of sound is calculated by multiplying frequency and wavelength. Therefore, because the frequency of the sound stays the same, at higher temperatures, wavelength must increase. 12. In your classroom, because the acoustics indoors allow sound to be reflected, creating reverberation which adds to the direct sound. Outdoors, sound has few barriers and the sound waves continue to spread out. Section 21.3 13. A wave form graph relates how pressure changes over time for a complex sound. This graph shows the harmonic motion of sound. A spectrum graph is a picture of all the different frequencies that make up a complex sound. From this graph, you can identify the loudest frequencies (based on amplitude) and the quietest frequencies. 14. Musicians wear earplugs to avoid damage to their ears from the constant loud noise of the band or orchestra with which they are performing. Listening to loud sounds for an extended period of time may cause the tiny, sound conducting hairs of the middle ear to weaken or break off, causing a loss of hearing. 15. The eardrum 16. Pitch is how high or low we hear frequency. They are directly proportional, but pitch depends upon the human ear and brain. 17. The sound from an instrument is not a pure frequency, but consists of a characteristic pattern of harmonics. As the instrument reproduces a certain fundamental frequency, it is accompanied by the unique pattern of harmonics characteristic of the instrument. 18. When two sound frequencies are close, but not the same, the phase of the combination of waves creates an oscillation of the loudness of the sound, or beat. The more closely matched the frequencies are, the higher the beat count. 19. The limits of human hearing are approximately 20,000 Hz, while a dog’s hearing is sensitive to a higher range of frequencies, including 25,000 Hz. Solving Problems Section 21.1 1. Answers are: a. The ordinary conversation sounds twice as loud as the sound in a restaurant. b. The amplitude of the waves is 10 times greater. 2. The star would be moving away from you if the star gave off red light, because the frequency would be lower. Section 21.2 3. wavelength = speed ÷ frequency wavelength = (340 m/sec) ÷ (680 Hz) = 0.5 meters 4. The longest wavelength occurs at the lowest frequency, 20 Hz. wavelength = speed ÷ frequency wavelength = (340 m/sec) ÷ (20 Hz) = 17 meters. Using the same formula and 20,000 hertz, the shortest wavelength is 0.017 meters. 5. The time it takes to travel over and back is the time it takes to travel 340 meters. time = 2 × (distance ÷ speed) = 2 × (170 m ÷ 340 m/sec) = 1 sec 6. wavelength of the fundamental = 4 × length of pipe wavelength of fundamental = 4 × (1 meter) = 4 m frequency = wave speed ÷ wavelength = (340 m/sec) ÷ (4 m) frequency = 85 Hz Section 21.3 7. Octaves are multiples of the original frequency. The frequency of the C one octave higher: 528 Hz The frequency of the C one octave lower: 132 Hz 8. You would hear oscillations of loudness called beats. These beats are unpleasant sounding.You would hear beats at a frequency of 3 beats per second. Applying Your Knowledge Section 21.1 1. Perfect pitch is the ability to identify or produce a note without a reference note. Often musicians will use a tuning fork to help them tune their instrument. A person with perfect pitch would be able to tune without using the tuning forks. The pros of having perfect pitch are that people with it tend to have an easier time learning music and may have likely started learning music at a young age.The cons of perfect pitch are that a person with it hears when notes are wrong. This sensitivity can be very frustrating when other people around the person aren’t as sensitive. This is true more often than not because perfect pitch is a rare condition. Also, a person with perfect pitch hears all sounds (car horns, machine sounds, etc.) as notes and can’t “tune off” this awareness. Again, this sensitivity can lead to a lot of tension and frustration. Section 21.2 2. Curtains absorb sound waves. Absorption decreases the amplitude of a wave. For sound waves, amplitude is related to loudness, so absorption decreases the loudness of sound waves. The loudness of sound in a room can be reduced by hanging heavy curtains. 3. The superposition principle states that complex sound is created by the superposition of many frequencies: wave A + wave B = complex wave D. For example, the human voice is the result of superposition—a voice contains thousands of different frequencies. Fourier’s theorem states that any wave form can be represented as a sum of single frequency waves: complex wave C = wave A + wave B. Section 21.3 4. Active noise reduction (ANR) is used widely in noisy places such as airplane cockpits where the noise is mechanical due to the airplane engine. ANR headphones contain a microphone that picks up outside noise and electronically inverts the sound waves of the noise. A speaker in the headphones then plays the inverted waves, allowing destructive interference to “cancel out” the outside sounds to your ears. Ear plugs and ear muffs work by absorbing the sound and effectively reduce its amplitude or loudness. This type of hearing protection is “passive” and more useful when the noise is coming from many different sources. 5. Exposure to sounds greater than 85-100 dB for extended periods of time can damage the ear. Short burst of sound greater than 140 dB can also damage the ear. The damage to the ear is cumulative and permanent, so it is important to protect your ears from loud noises. You can protect your hearing by avoiding loud noises and high frequency sounds. Different types of hearing protection include: earmuffs, which fit over the outer ear, earplugs which fit directly into the ear canal, and the Active Noise Reduction (ANR) protection. Places that have excessive noise require hearing protection. Examples include outdoors at airports, environments where power tools or heavy machinery are used, and loud concerts. 6. The word “synthesize” means “to put together”, and that is how these electronic instruments work. The sound of each instrument is synthesized by programming a recipe of harmonics and specifying the rise and fall time for each frequency. A good synthesizer may use 64 different frequencies for each note to simulate an instrument sound. 7. Male voices start around 100 Hz and female voices around 200 Hz, extending up to about 3,000 Hz for a baby’s shrill cry. The human voice range is close to the most sensitive range (200-2,000 Hz) within the range of human hearing.