Sound Waves Professor K. W. Chow Department of Mechanical Engineering Sound as a wave? You hear sound and music everyday. But you might have overlooked that sound is a kind of waves. How is sound produced, propagated and detected? The physics of waves gives answers to these questions. Sound waves Sound is a mechanical wave that can propagate through a gas (air), liquid (water) or solid. Restoring force – Elasticity of the medium. The analogy with slinky will be illustrative. Instead of air particles, the medium for wave propagation is the coil of the slinky. (Extracted from http://clackhi.nclack.k12.or.us/physics/projects/experiments/1999/Deb%20&%20Liz/slin_com.gif) Sound waves To generate a wave, a disturbance is required. A disturbance is typically generated within the slinky by pushing back and/or forth the first coil of the slinky i.e. the first coil becomes disturbed. It then pushes or pulls the second coil, displacing the second coil from its equilibrium position. The second coil goes on to “disturb” the third coil and so on. (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/waves/u10l1b.html#rest) Sound waves When a coil is displaced, it will return to its equilibrium position afterwards, because of the restoring force/elastic force within the slinky. In other words, the disturbance (wave profile) travels through the slinky but not individual coils. As the disturbance moves through the slinky, the energy introduced into the first coil is also transported along the slinky from the first coil to the last coil. Particles connected by springs (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/mmedia/waves/lw.html) Sound waves A sound wave is similar to a slinky wave in nature. The medium now consists of the air particles (or water/solid). It requires a disturbance to generate the sound. The source could be our vocal cords, a guitar or violin or the vibrating diaphragm of a radio speaker. These sources “push” the air particles to generate the disturbance. The disturbance propagates as a sound wave. When it reaches our ear, we hear the sound. Animation courtesy of Dr. Dan Russell, Kettering University Sound waves A tuning fork vibrates and disturbs the surrounding air particles. When it moves to one side, it pushes on the surrounding air particles on that side. These air particles collide with those in front of them, creating a pressure increase. This is called compression. When the fork moves to the other side, it pulls in the surrounding particles, creating a pressure drop. The drop in pressure pulls in more surrounding air particles. This is called rarefaction. (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l1a.html ) Rarefaction and Compression (Extracted from http://www.le.ac.uk/se/centres/sci/selfstudy/snd2.htm) (Extracted from http://academic.umf.maine.edu/~magri/phy110/c19/unit3so.html) Speed of Sound Sound travels faster in water than in air, as the elastic restoring force in water is larger. Sound moves even faster in a solid. In general, sound propagates faster in denser materials. The speed of sound in air is still high (relative to a running human)! (~340 meters per second). However, light moves much, much faster than sound (~300,000,000 meters per second). Hence, you “see” before you “hear” a thunder. Can we “hear” our Sun? Our common experience tells us that explosion creates sound. Explosions arise from a localized release of a large amount of energy. The air particles are forced to vibrate violently and generate sound. There are many explosions happening in the Sun, but they cannot be heard on Earth, as there are too few air particles between the Earth and the Sun to transmit sound. Sound cannot travel in outer space either. Astronauts cannot hear each other in space. (Extracted from http://www.smh.com.au/ffxImage/urlpicture_id_1070127350191_2003/12/01/400sun,0.jpg) Experiment Cover a bell with a glass tube/container. Extract the air inside the glass tube gradually. You shall notice that the sound diminishes. (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l1a.html) Frequency and Amplitude of Sound One important feature of a sound wave is the pitch. Different vibrating objects generate sound of different pitches. The vibrating object can be the vocal cords of girls, boys, violin or guitar. Although the air particles vibrate back and forth in all sound waves, the frequency will be different. Frequency Frequency is the number of complete back-and-forth oscillations of an air particle per second (the unit is Hertz). For instance, for a 100Hz sound, as the sound wave propagates, the air particle vibrates for 100 times in 1 second, i.e. 1 Hertz = 1 vibration/second Frequency If we record the pressure at a particular time as time go, it will be a sinusoidal curve as shown: (Extracted from http://www.glenbrook .k12.il.us/GBSSCI/P HYS/CLASS/sound/ u11l2a.html) The period is the time taken for an air particle to complete 1 vibration. Hence, a higher frequency sound means a smaller period. Graphically, the sinusoidal curve appears to be more “compressed”. Loudness While frequency characterizes the pitch of a sound, the loudness is related to the amplitude (or more precisely, the intensity = the square of the amplitude) of the sound wave. The unit of sound intensity is the ‘BEL’ or one-tenth of it, the ‘Decibel’. Loudness (cont’d) This is a logarithmic scale, meaning that each 10 dB increase will imply a 10-fold change in energy intensity. Thus a 50 dB sound is ten times louder than a 40 dB sound. The faintest sound a human can hear is roughly given a level of 0.1 dB. Loudness (cont’d) A normal conversation has a level of 60 dB, while the siren of a police car is roughly 80 dB. A very powerful rock concert might be at a level of 120 dB, while close to a jet engine at takeoff will be roughly 140 dB. Sound intensity levels How do our ears work? Human bodies, sometimes, are perceived as very complicated machines (probably the most complicated one on Earth). This is true in the sense that every organ has its critical roles in performing a task, like gearbox and bearings in a car. To hear a sound, our ears have to do three basic things: – 1. Direct the sound waves into the hearing part of the ear; – 2. Sense the fluctuations in air pressure; – 3. Convert these fluctuations into an electrical signal which can be understood by our brain. Doppler Effect The Doppler Effect is a phenomenon observed where a source of waves is moving with respect to an observer. This phenomenon is relevant to all types of waves but we shall focus on sound wave here. Doppler Effect When a source of waves moves, say a moving ambulance with its speaker turned on, there will be an apparent upward shift in frequency for the observer when the ambulance is approaching the observer. A higher pitch is heard. However, when the ambulance is receding, an apparent downward shift in frequency will occur. You can experience Doppler Effect in real life, say by standing at the platform with a approaching/leaving train. (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l3b.html) Explanation for Doppler Effect Assume that the source of sound always emits the same number of waves for a fixed time period. If the source is stationary, the same frequency is heard in all locations. However, if the source is moving towards the observer, the distance between the source of sound and the observer is reduced. Hence ‘the number of waves’ received by the observer will increase for any fixed time period, as the distance the waves need to travel to the observer is smaller, i.e. the ‘apparent frequency’ will increase. The converse is true when the source is moving away from the observer. Animation courtesy of Dr. Dan Russell, Kettering University Explanation for Doppler Effect (cont’d) A simple animation Animation courtesy of Dr. Dan Russell, Kettering University Doppler Effect - Remark It is important to note that Doppler Effect is not a result of an actual change in the frequency of the source. The source always emits at the same frequency. The observer only perceives a different frequency due to the relative motion between the source and the observer. The Doppler Effect Supersonic Jets Modern aircrafts fly at very high speeds. Combat jets can fly at a speed faster than the speed of sound. Interesting phenomena occur in these regimes. When the aircraft is traveling exactly at the speed of sound, the observer will detect nothing until the aircraft arrives. Animation courtesy of Dr. Dan Russell, Kettering University Supersonic Jets When the aircraft is flying above the speed of sound (supersonic), the aircraft actually leads the advancing wave front. The aircraft will pass by a stationary observer before the observer actually hears the sound the aircraft creates! There will be a time delay and then you hear “boom”. Animation courtesy of Dr. Dan Russell, Kettering University Zone of Silence A zone of silence, where no sound can be heard, will appear. (Extracted from http://www.adl.gatech.edu/classes/dci/hispd/dci09.html) Supersonic Flights M=3.5 M=6 Free-flight models of the X-15 being fired into a wind Tunnel vividly detail the shock-wave patterns for airflow. Credit: NASA History Division http://history.nasa.gov/SP-60/ch-5.html Standing Waves Generally, standing waves are formed when two identical wave trains propagate in opposite directions. Energy is ‘trapped’ locally. (Extracted from http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l4c.html) Standing wave Typically there are sequences of nodes (locations with zero displacement) and antinodes (maximum displacement) in a pattern of standing waves. Animation courtesy of Dr. Dan Russell, Kettering University (Extracted from http://en.wikipedia.org/wiki/Image:Standing_wave_2.gif) Nodes and antinodes Nodes – points where there are no motion at all times. Antinodes – points which can attain maximum displacement. (Extracted from http://www.glenbrook.k12.il.us/gbssci/Phys/Class/waves/u10l4b.html) Nodes and Antinodes Harmonics A variety of actual standing wave patterns can be produced, with each pattern characterized by distinctly different number of nodes. These standing wave patterns can only be produced within the medium at certain frequencies known as harmonic frequency or simple harmonics. First Harmonic Standing Wave Pattern Second Harmonic Standing Wave Pattern Third Harmonic Standing Wave Pattern How does a guitar work? Nearly all objects will vibrate when disturbed (say, hit, struck, plucked, or strummed). Try to hold a ruler on end of table and pull handing edge down, then release the ruler. The ruler will vibrate. The vibration disturbs the air particles nearby and you hear the sound generated. When you pluck a guitar string, it begins to vibrate. (Extacted from http://www.bsharp.org/physics/stuff/guitar.html) Natural Frequency The frequencies most natural and engineering systems oscillate in are usually fixed by their intrinsic properties. In other words, if you disturb the object and allow it to vibrate freely, it will always tend to vibrate at a frequency known as natural frequency. When you pluck a guitar, you will always hear the same pitch. The guitar string is vibrating at its natural frequency when it is disturbed / plucked. Forcing at Natural Frequency - Resonance When a system (a guitar or a structure) is forced externally at a frequency equal to one of the natural frequencies, the amplitude of the resulting vibration will grow indefinitely (a phenomenon called RESONANCE). Basically, the forcing and oscillator are always in phase, and thus energy is fed into the system continuously. Consequently, the amplitude will build up in time. If the forcing and the motion are not in phase, i.e. opposing each other at some time instants, there will be energy dissipation, and hence the growth of the amplitude will be limited or impeded. More on Natural Frequency and Resonance To avoid exciting resonant conditions, an army of soldiers marching on a bridge will avoid moving at exactly the same frequency. When you listen to a guitarist playing the guitar, you can notice that he/she is pressing the guitar string at different positions. Sounds with different pitches will then be generated by the guitar. What the guitarist is doing is actually altering the natural frequency of the guitar string by changing the effective length of the string. Standing wave in a guitar string First of all, the string has two fixed ends and waves will be reflected at these ends. Therefore, the wave in a guitar string is a standing wave. Animation here As you can imagine, increasing or decreasing the length of the string will alter the wave lengths of the standing wave. (Extracted from http://id.mind.net/~zona/mstm/p hysics/waves/standingWaves/st andingWaves1/StandingWaves1 .html) How do guitars work? For a guitar, there are six strings and each has a different linear density (mass per unit length.) The wider strings are denser on a per meter basis. On varying the tension (roughly, how “tight” the string is) and length, sounds of different frequencies are produced. The frequency depends on the properties of the string i.e. the tightness (tension) and the linear density of the strings. That’s why when a guitar string is loosened, the guitarist has to tune it to the right tension to generate the precise pitch. How do guitars work? During a performance, the guitarist can also press the string against one of the frets on the neck of the guitar to change the length of vibration portion of the string, and hence the wavelength of the standing wave. This modification will in turn change the natural frequency at which the string will vibrate. Consequently, the guitar can generate sounds of different pitches during a performance. The same principle can actually be applied to any string instrument, say harp or violin. (Extracted from http://www.phys.unsw.edu.au/jw/strings.html) Wind Instrument Another example is the trombone, a wind instrument. There is a tube attached to any wind instrument. It acts as a container for a vibrating air column. The air inside the tube will vibrate when the musician start to “blows” the air. Tthe only way to change the natural frequency is to change the wavelength of the waves it produced. This is accomplished by pushing or pulling the tube. The same principle applies to other instruments, say flute or clarinet. Ultrasound Ultrasound broadly refers to the class of sound waves where the frequency greater than the upper limit of human hearing (20,000 Hertz). There are many useful applications. Two examples will be briefly discussed. Applications Diagnostic sonography: Ultrasonography is an ultrasound-based diagnostic medical imaging technique used to visualize internal organs, muscles or fetus. They operate in the frequency range of 2 to 19 Megahertz (hundreds of times greater than the limit of human hearing). The choice of frequency is a trade-off between spatial resolution of the image and imaging depth: low frequencies will produce less resolution but image deeper into the body. (Extracted from http://en.wikipedia.org/wiki/Medical_ultrasonography) Applications SONAR: SONAR stands for sound navigation and ranging. It employs sound propagation to navigate, communicate or to detect other vessels. In an active sonar system, there is a sound transmitter and receiver. (Extracted from http://mainland.cctt.org/istf2006/images/496px-Sonar_Principle_EN.svg%5B1%5D.png) SONAR The operation principle is roughly the following: The active sonar sends a sound pulse and listen for reflections from any objects. The time from transmission of a pulse to reception is measured. The system will then calculate the distance between the SONAR and the object by knowing the speed of sound. SONAR may also be used to detect underwater objects. (Extracted from http://marine.usgs.gov/factsheets/michigan/sonar.gif) Applying Sonar to Measure Distance / Depth Measure the time lapse between the emission of waves and the recording of the reflected signals.
