Sound Longitudinal Waves Pressure vs. Position Graph Speed of Sound Speed of Sound (cont.)
Daynor, Jessica, Managing Editor has reference to this Academic Journal, PHwiki organized this Journal Sound Longitudinal Waves Pressure Graphs Speed of Sound Wavefronts Frequency & Pitch (human range) The Human Ear Sonar & Echolocation Doppler Effect ( in addition to sonic booms) Interference St in addition to ing Waves in a String: Two fixed ends St in addition to ing Waves in a Tube: One open end Two open ends Musical Instruments ( in addition to other complex sounds) Beats Intensity Sound Level (decibels) Longitudinal Waves As you learned in the unit on waves, in a longitudinal wave the particles in a medium travel back & as long as th parallel to the wave itself. Sound waves are longitudinal in addition to they can travel through most any medium, so molecules of air (or water, etc.) move back & as long as th in the direction of the wave creating high pressure zones (compressions) in addition to low pressure zones (rarefactions). The molecules act just like the individual coils in the spring. The faster the molecules move back & as long as th, the greater the frequency of the wave, in addition to the greater distance they move, the greater the waves amplitude. wavelength, Animation rarefaction compression molecule Sound Waves: Molecular View When sound travels through a medium, there are alternating regions of high in addition to low pressure. Compressions are high pressure regions where the molecules are crowded together. Rarefactions are low pressure regions where the molecules are more spread out. An individual molecule moves side to side with each compression. The speed at which a compression propagates through the medium is the wave speed, but this is different than the speed of the molecules themselves. wavelength,
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Pressure vs. Position The pressure at a given point in a medium fluctuates slightly as sound waves pass by. The wavelength is determined by the distance between consecutive compressions or consecutive rarefactions. At each com-pression the pressure is a tad bit higher than its normal pressure. At each rarefaction the pressure is a tad bit lower than normal. Lets call the equilibrium (normal) pressure P0 in addition to the difference in pressure from equilibrium P. P varies in addition to is at a max at a compression or rarefaction. In a fluid like air or water, Pmax is typically very small compared to P0 but our ears are very sensitive to slight deviations in pressure. The bigger P is, the greater the amplitude of the sound wave, in addition to the louder the sound. wavelength, B Pressure vs. Position Graph P x A C A: P = 0; P = P0 B: P > 0; P = Pmax C: P < 0; P = Pmin animation Pressure vs. Time The pressure at a given point does not stay constant. If we only observed one position we would find the pressure there varies sinusoidally with time, ranging from: P0 to P0 + Pmax back to P0 then to P0 - Pmax in addition to back to P0 The time it takes to go through this cycle is the period of the wave. The number of times this cycle happens per second is the frequency of the wave in Hertz. There as long as e, the pressure in the medium is a function of both position in addition to time! The cycle can also be described as: equilibrium compression equilibrium rarefaction equilibrium Pressure vs. Time Graph P T t Rather than looking at a region of space at an instant in time, here were looking at just one point in space over an interval of time. At time zero, when the pressure readings began, the molecules were at their normal pressure. The pressure at this point in space fluctuates sinusoidally as the waves pass by: normal high normal low normal. The time needed as long as one cycle is the period. The higher the frequency, the shorter the period. The amplitude of the graph represents the maximum deviation from normal pressure (as it did on the pressure vs. position graph), in addition to this corresponds to loudness. Comparison of Pressure Graphs Pressure vs. Position: The graph is as long as a snapshot in time in addition to displays pressure variation as long as over an interval of space. The distance between peaks on the graph is the wavelength of the wave. Pressure vs. Time: The graph displays pressure variation over an interval of time as long as only one point in space. The distance between peaks on the graph is the period of the wave. The reciprocal of the period is the frequency. Both Graphs: Sound waves are longitudinal even though these graphs look like transverse waves. Nothing in a sound wave is actually waving in the shape of these graphs! The amplitude of either graph corresponds to the loudness of the sound. The absolute pressure matters not. For loudness, all that matters is how much the pressure deviates from its norm, which doesnt have to be much. In real life the amplitude would diminish as the sound waves spread out. Speed of Sound As with all waves, the speed of sound depends on the medium through which it is traveling. In the wave unit we learned that the speed of a wave traveling on a rope is given by: F = tension in rope µ = mass per unit length of rope In a rope, waves travel faster when the rope is under more tension in addition to slower if the rope is denser. The speed of a sound wave is given by: Rope: Sound: B = bulk modulus of medium = mass per unit volume (density) The bulk modulus, B, of a medium basically tells you how hard it is to compress it, just as the tension in a rope tells you how hard it is stretch it or displace a piece of it. (continued) Speed of Sound (cont.) Rope: Sound: Notice that each equation is in the as long as m The bulk modulus as long as air is tiny compared to that of water, since air is easily compressed in addition to water nearly incompressible. So, even though water is much denser than air, water is so much harder to compress that sound travels over 4 times faster in water. Steel is almost 8 times denser than water, but its over 70 times harder to compress. Consequently, sound waves propagate through steel about 3 times faster than in water, since (70 / 8) 0.5 3. Mach Numbers Depending on temp, sound travels around 750 mph, which would be Mach 1. Twice this speed would be Mach 2, which is about the max speed as long as the F-22 Raptor. Speed Racer drives a car called The Mach 5, which would imply it can go 5 times the speed of sound. Temperature & the Speed of Sound The speed of sound in dry air is given by: v 331.4 + 0.60 T, where T is air temp in°C. Because the speed of sound is inversely proportional to the mediums density, the less dense the medium, the faster sound travels. The hotter a substance is, the faster its molecules/atoms vibrate in addition to the more room they take up. This lowers the substances density, which is significant in a gas. So, in the summer, sound travels slightly faster outside than it does in the winter. To visualize this keep in mind that molecules must bump into each other in order to transmit a longitudinal wave. When molecules move quickly, they need less time to bump into their neighbors. Here are speeds as long as sound: Air, 0 °C: 331 m/s Air, 20 °C: 343 m/s Water, 25 °C: 1493 m/s Iron: 5130 m/s Glass (Pyrex): 5640 m/s Diamond: 12 000 m/s Wavefronts Some waves are one dimensional, like vibrations in a guitar string or sound waves traveling along a metal rod. Some waves are two dimensional, such as surface water waves or seismic waves traveling along the surface of the Earth. Some waves are 3-D, such as sound traveling in all directions from a bell, or light doing the same from a flashlight. To visualize 2-D in addition to 3-D waves, we often draw wavefronts. The red wavefronts below could represent the crest of water waves on a pond moving outward after a rock was dropped in the middle. They could also be used to represent high pressure zonesin sound waves. The wavefronts as long as 3-D sound waves would be spherical, but concentric circles are often used to simplify the picture. If the wavefronts are evenly spaced, then is a constant. crest trough Animation Frequency & Pitch Just as the amplitude of a sound wave relates to its loudness, the frequency of the wave relates to its pitch. The higher the pitch, the higher the frequency. The frequency you hear is just the number of wavefronts that hit your eardrums in a unit of time. Wavelength doesnt necessarily correspond to pitch because, even if wavefronts are very close together, if the wave is slow moving, not many wavefronts will hit you each second. Even in a fast moving wave with a small wavelength, the receiver or source could be moving, which would change the frequency, hence the pitch. Frequency Pitch Amplitude Loudness Listen to a pure tone (up to 1000 Hz) Listen to 2 simultaneous tones (scroll down) The Human Ear Animation Ear Anatomy The exterior part of the ear (the auricle, or pinna) is made of cartilage in addition to helps funnel sound waves into the auditory canal, which has wax fibers to protect the ear from dirt. At the end of the auditory canal lies the eardrum (tympanic membrane), which vibrates with the incoming sound waves in addition to transmits these vibrations along three tiny bones (ossicles) called the hammer, anvil, in addition to stirrup (malleus, incus, in addition to stapes). The little stapes bone is attached to the oval window, a membrane of the cochlea. The cochlea is a coil that converts the vibrations it receives into electrical impulses in addition to sends them to the brain via the auditory nerve. Delicate hairs (stereocilia) in the cochlea are responsible as long as this signal conversion. These hairs are easily damaged by loud noises, a major cause of hearing loss! The semicircular canals help maintain balance, but do not aid hearing. Range of Human Hearing Hear the full range of audible frequencies (scroll down to speaker buttons) The maximum range of frequencies as long as most people is from about 20 to 20 thous in addition to hertz. This means if the number of high pressure fronts (wavefronts) hitting our eardrums each second is from 20 to 20 000, then the sound may be detectable. If you listen to loud music often, youll probably find that your range (b in addition to width) will be diminished. Some animals, like dogs in addition to some fish, can hear frequencies that are higher than what humans can hear (ultrasound). Bats in addition to dolphins use ultrasound to locate prey (echolocation). Doctors make use of ultrasound as long as imaging fetuses in addition to breaking up kidney stones. Elephants in addition to some whales can communicate over vast distances with sound waves too low in pitch as long as us to hear (infrasound). Echoes & Reverberation Animation An echo is simply a reflected sound wave. Echoes are more noticeable if you are out in the open except as long as a distant, large object. If went out to the dessert in addition to yelled, you might hear a distant canyon yell back at you. The time between your yell in addition to hearing your echo depends on the speed of sound in addition to on the distance to the to the canyon. In fact, if you know the speed of sound, you can easily calculate the distance just by timing the delay of your echo. Reverberation is the repeated reflection of sound at close quarters. If you were to yell while inside a narrow tunnel, your reflected sound waves would bounce back to your ears so quickly that your brain wouldnt be able to distinguish between the original yell in addition to its reflection. It would sound like a single yell of slightly longer duration. Sonar SOund NAvigation in addition to Ranging In addition to locating prey, bats in addition to dolphins use sound waves as long as navigational purposes. Submarines do this too. The principle is to send out sound waves in addition to listen as long as echoes. The longer it takes an echo to return, the farther away the object that reflected those waves. Sonar is used in commercial fishing boats to find schools of fish. Scientists use it to map the ocean floor. Special glasses that make use of sonar can help blind people by producing sounds of different pitches depending on how close an obstacle is. If radio (low frequency light) waves are used instead of sound in an instrument, we call it radar (radio detection in addition to ranging). Doppler Effect Animation (click on The Doppler Effect, then click on the button marked: A tone is not always heard at the same frequency at which it is emitted. When a train sounds its horn as it passes by, the pitch of the horn changes from high to low. Any time there is relative motion between the source of a sound in addition to the receiver of it, there is a difference between the actual frequency in addition to the observed frequency. This is called the Doppler effect. Click to hear effect: The Doppler effect applied to electomagnetic waves helps meteorologists to predict weather, allows astronomers to estimate distances to remote galaxies, in addition to aids police officers catch you speeding. The Doppler effect applied to ultrasound is used by doctors to measure the speed of blood in blood vessels, just like a cops radar gun. The faster the blood cell are moving toward the doc, the greater the reflected frequency. Sonic Booms Wavefront Animations Another cool animation Animation with sound (click on The Doppler Effect, then click on the button marked: Movie: F-18 Hornet breaking the sound barrier (click on MPEG movie) When a source of sound is moving at the speed of sound, the wavefronts pile up on top of each other. This makes their combined amplitude very large, resulting in a shock wave in addition to a sonic boom. At supersonic speeds a Mach cone is as long as med. The faster the source compared to sound, the smaller the shock wave angle will be. Doppler Equation f L = frequency as heard by a listener f S = frequency produced by the source v = speed of sound in the medium vL = speed of the listener v S = speed of the source This equation takes into account the speed of the source of the sound, as well as the listeners speed, relative to the air (or whatever the medium happens to be). The only tricky part is the signs. First decide whether the motion will make the observed frequency higher or lower. (If the source is moving toward the listener, this will increase f L, but if the listener is moving away from the source, this will decrease f L.) Then choose the plus or minus as appropriate. A plus sign in the numerator will make f L bigger, but a plus in the denominator will make f L smaller. Examples are on the next slide. Doppler Set-ups still 10 m/s f L = 1000 343 343 - 10 ) ( = 1030 Hz The horn is producing a pure 1000 Hz tone. Lets find the frequency as heard by the listener in various motion scenarios. The speed of sound in air at 20 C is 343 m/s. still 10 m/s f L = 1000 343 + 10 343 ) ( = 1029 Hz Note that these situation are not exactly symmetric. Also, in real life a horn does not produce a single tone. More examples on the next slide. 3 m/s Doppler Set-ups (cont.) 10 m/s f L = 1000 343 - 3 343 - 10 ) ( = 1021 Hz The horn is still producing a pure 1000 Hz tone. This time both the source in addition to the listener are moving with respect to the air. f L = 1000 343 + 3 343 - 10 ) ( = 1039 Hz 10 m/s 3 m/s Note the when theyre moving toward each other, the highest frequency possible as long as the given speeds is heard. Continued 10 m/s 10 m/s 3 m/s Doppler Set-ups (cont.) f L = 1000 343 - 3 343 + 10 ) ( = 963 Hz The horn is still producing a pure 1000 Hz tone. Here are the final two motion scenarios. f L = 1000 343 + 3 343 + 10 ) ( = 980 Hz 3 m/s Note the when theyre moving toward each other, the highest frequency possible as long as the given speeds is heard. Continued
Doppler Problem Mr. Magoo & Betty Boop are heading toward each other. Mr. Magoo drives at 21 m/s in addition to toots his horn (just as long as fun; he doesnt actually see her). His horn sounds at 650 Hz. How fast should Betty drive so that she hears the horn at 750 Hz Assume the speed o sound is 343 m/s. 21 m/s vL Interference As we saw in the wave presentation, waves can passes through each other in addition to combine via superposition. Sound is no exception. The pic shows two sets of wavefronts, each from a point source of sound. (The frequencies are the same here, but this is not required as long as interference.) Wherever constructive interference happens, a listener will here a louder sound. Loudness is diminished where destructive interference occurs. A: 2 crests meet; constructive interference B: 2 troughs meet; constructive interference C: Crest meets trough; destructive interference Interference: Distance in Wavelengths Weve got two point sources emitting the same wavelength. If the difference in distances from the listener to the point sources is a multiple of the wavelength, constructive interference will occur. Examples: Point A is 3 from the red center in addition to 4 from the green center, a difference of 1 . For B, the difference is zero. Since 1 in addition to 0 are whole numbers, constructive interference happens at these points. If the difference in distance is an odd multiple of half the wavelength, destructive interference occurs. Example: Point C is 3.5 from the green center in addition to 2 from the red center. The difference is 1.5 , so destructive interference occurs there. Animation
Interference: Sound Demo Listen to a pure tone (up to 1000 Hz) Using the link below you can play the same tone from each of your two computer speakers. If they were visible, the wavefronts would look just as it did on the last slide, except they would be spheres instead of circles. You can experience the interference by leaning side to side from various places in the room. If you do this, you should hear the loudness fluctuate. This is because your head is moving through points of constructive interference (loud spots) in addition to destructive interference (quiet regions, or dead spots). Turning one speaker off will eliminate this effect, since there will be no interference. Interference: Noise Reduction Noise reduction graphic (Scroll down to Noise Cancellation under the Applications of Sound heading.) The concept of interference is used to reduce noise. For example, some pilots where special headphones that analyze engine noise in addition to produce the inverse of those sounds. This waves produced by the headphones interfere destructively with the sound waves coming from the engine. As a result, the noise is reduced, but other sounds can still be heard, since the engine noise has a distinctive wave pattern, in addition to only those waves are being cancelled out. Acoustics Acoustics sometimes refers to the science of sound. It can also refer to how well sounds traveling in enclosed spaces can be heard. The Great Hall in the Krannert Center is an example of excellent acoustics. Chicago Symphony Orchestra has even recorded there. Note how the walls in addition to ceiling are beveled to get sound waves reflect in different directions. This minimizes the odds of there being a dead spot somewhere in the audience. Click in addition to scroll down to zoom in on the Great Hall pic.
Credits F-22 Raptor http://members.home.net/john-higgins/index2.htm Sonar Vision http://www.elender.hu/~tal-mec/html/abc.htm Krannert Center (acoustics) http://www.krannertcenter.com/center/venues/foellinger.php Ukulele: http://www.glass-artist.co.uk/music/instruments/ukepics.html Tuning Forks: http://www.physics.brown.edu/Studies/Demo/waves/demo/3b7010.htm Wave as long as ms: http://www.ec.v in addition to erbilt.edu/computermusic/musc216site/what.is.sound.html http://www.physicsweb.org/article/world/13/04/8 Piano : http://www.mathsyear2000.org/numberl in addition to /88/88.html Credits Mickey Mouse: http://store.yahoo.com/rnrdist/micmousgoofp.html Dumbo: http://www.phil-sears.com/Folder%202/Dumbo%20sericel.JPG Sound Levels: http://library.thinkquest.org/19537/Physics8.htmltqskip1=1&tqtime=0224 Angus Young: http://kevpa.topcities.com/acdcpics2.html Wine Glass: http://www.artglassw.com/ewu.htm Opera Singer: http://www.ljphotography.com/photos/bw-opera-singer.jpg
Daynor, Jessica Managing Editor
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