Sound-based Sensing. Some of these notes have been adapted from Carstens J.R. Electrical Sensors and Transducers

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1 Sound-based Sensing Some of these notes have been adapted from Carstens J.R. Electrical Sensors and Transducers Introduction Topics C Physics of sound and sound measurement Velocity of sound in different media C Position measurement through sonar or similar techniques C Speed sensing using the Doppler effect C Impedance matching for improved power transfer Sound is the result of vibration in a medium, most commonly a gas or as liquid. Sound is generally defined as vibration in the range 20 Hz to 20,000 Hz, the standard range of human hearing. Sound measurement can be used for measuring audible sounds such as noise levels (Sound pressure measurement) but can also be used for measuring other quantities such as distance and velocity. When used for these latter measurements we frequently use either infra-sound (below 20 Hz) or ultrasound (above 20,000 Hz. When measuring distance and velocity ultrasonic sensors have a number of advantages. They are inaudible and thus do not create a nuisance when in use and the higher frequencies can give improved accuracy. Ultrasonic transducers are easily available and cheap. Frequencies can vary from 8 Khz to 200 Khz. Acoustic sensors can be used in a wide variety of circumstances. They are non-contact sensors. They do not require that the system being measured is conductive or magnetic. They do require that there is an unobstructed view of the system to be measured (line of sight) Many of the physical properties of sound are similar to those of light except that velocities are lower and sound requires a medium that vibrates to transmit energy. This does not imply that light and sound are manifestations of the same phenomena, merely that several of their equations and properties have a very similar form. Sound, like light, generally propagates in a straight line, the frequency and wavelength are related through the velocity and sound can be focused in a manner analogous to antennas or reflectors for RF/light frequency signals. We will briefly review physical properties of sound. Velocity of Sound The velocity of sound in different media depends on a variety of factors such as density, temperature, humidity and media properties. Equations for solids, liquids and gases are shown in the appendix. Sound velocity is a key parameter in many sensors.

2 Gases - Air: Generally speaking the velocity of sound in air is quoted as 344 m/s. This figure can be used unless more information about operating conditions is given. The velocity varies somewhat with temperature and less so with frequency and humidity as the tables below show. Table entries are velocity of sound in air at 20EC, for still air (velocity in m/s): 1 Relative Humidity (%) Frequency (Hz) , , As can be seen from the above table the velocity of sound does not vary much with frequency and humidity. The biggest variation in this table is about 0.35%. This should be taken into account for high accuracy instrumentation and large variations in operating conditions but can otherwise be ignored. Although not shown above, atmospheric pressure does not have a significant effect on the velocity of sound either. Sound velocity also varies with temperature (dry air) 2-40EC -20EC 0EC 20EC 40EC 60EC The variations here are somewhat larger. Working between 0EC and 20EC can cause a 3.6% change in the velocity of sound. Other Gases Velocity of sound and rate of change with temperature for some other gases is shown below 3. Gas Velocity (m/s) dv/dt m/sec per EC Hydrogen This table derived from CRC Handbook of Chemistry and Physics, 75 th Ed. P This table copied from CRC Handbook of Chemistry and Physics, 75 th Ed. (Frequency not given) p This table copied from CRC Handbook of Chemistry and Physics, 75 th Ed. p14-34

3 Nitrogen Oxygen Carbon Dioxide Water Vapor (134 EC) Liquids Velocity of sound (at 25 EC) and rate of change with temperature of various liquids is shown below 4. Liquid Velocity (m/s) dv/dt m/sec per EC Water (distilled) Water (sea) Benzene Glycerol Chloroform Castor Oil Kerosene Solids Velocity of sound in solids is a little more complex as the velocity depends on the wave type. The velocity of sound in selected solids is shown below 5. V long = plane longitudinal wave in bulk material V shear = plane transverse (shear) wave V ext = longitudinal wave (extensional wave) in thin rods Material V long V shear V ext Aluminum (rolled) This table copied from CRC Handbook of Chemistry and Physics, 75 th Ed. p This table copied from CRC Handbook of Chemistry and Physics, 75 th Ed. p14-34

4 Material V long V shear V ext Brass Copper (rolled) Steel (mild) Tungsten Carbide Polystyrene Wood - Ash (along the fiber) Wood - Ash (along the rings) Cork Tallow Clearly there is a large variation in the speed of sound in solids but in general sound travels much faster in solids and liquids than it does in air. Frequency and wavelength of sound The frequency and wavelength of sound are also related to the velocity c f? (1) c=velocity of sound (m/s), f=frequency (Hz),?=wavelength (m) The range of human hearing is usually given as 50 Hz to 22 Khz. In fact most people can hear somewhat less than this range. High frequency hearing often cuts off at about Khz and this figure decreases with age. Position (Distance) Sensing It is possible to develop instruments that measure position by sending out a pulse of sound and measuring the time it takes to bounce off a target and return. This is the basic principle used in sonar systems. Sonar systems were developed in World war II and used by submarines to detect distance to various objects under water. Accuracy and target size is generally limited by wavelength. The body to be detected should be larger than one wavelength and the detection resolution is similarly limited. It is possible, with sophisticated electronics, to measure smaller objects but it is not easy. In air one wavelength at 1000 Hz is approximately m and in water approximately 1.5 m. It should be mentioned that there are practical problems in designing instruments of this type.

5 Ideally you want a short, sharp burst of sound which goes instantaneously from zero volume to the measuring volume. In practice it takes a finite time for the sound pulse to build up and to die down. Thus there is uncertainty in the pulse start time. When the sound pulse bounces off the target and returns it does not have an instantaneous arrival time either. It will have been distorted by the target and other factors and so will not look exactly the same as the pulse that was sent out. These factors limit the accuracy of this type of position sensor. Frequently the same device is used as the transmitter and receiver. This reduces cost but also creates a dead-band in the measurement range. The pulse must be emitted and ringing must die down before the sensor is switched from transmit to receive. No signals can be detected during this transmit and switch-over period and thus very close objects cannot be detected.. Ultrasonic sensors tend to emit a spreading beam rather than a narrow beam. This can be focused with baffles to a certain extent but in general these sensors reflect best off perpendicular flat surfaces. Example A sonar system is calibrated for sea water. It indicates that an object is at a distance of 500 m in a fresh water river. What is the real distance of the object. Pulse travel time = (500 m x 2) at 1531 m/s (sea-water) => secs. At m/s (fresh water) the distance is 978.2/2 = m. Example An inventor has proposed using an ultrasonic sensor to measure the speed of a machine shaft 1/8" in diameter moving in and out of a machine. He proposes using 24 Khz ultrasonic sensors. Comment on the validity of the proposal. The wavelength of 24 KHz sound in air is 344/24000 = 14.3 mm. You will have considerable difficulty in designing a sensor to detect a 3 mm diameter shaft with this system. You will also have difficulties in focusing the ultrasonic beam on the end of the shaft. Velocity Measurement (Doppler Shift) If a sound wave strikes a moving object the sound wave is reflected back and the frequency of the sound wave is changed by an amount related to the speed of the object. Thus if a sound wave is reflected off an approaching car the wave is reflected and also compressed by the approaching car and the frequency increases. If the car is moving away the reflected wave is stretched out and the frequency decreases. This frequency change is known as the Doppler Shift The Doppler shift can be used by velocity measuring instruments. Frequency can be measured by electronic circuits with very high accuracy. The equations for calculating the Doppler shift are. For a target object moving towards the instrument

6 v TG v med (1& f TX f RX ) cos(?) (2) where v TG = velocity of target v med = velocity of sound in medium f TX = Transmitted frequency f RX = Received frequency? = Angle of misalignment between sensor and direction of target.? = 0E if the target is moving directly towards the sensor (cos(0e)=1). If the target is moving away from the sensor cos(?)=cos(180e)= -1. The Doppler shift only reflects the component of velocity directly in line with the measuring point. If the target is crossing the line of measurement at an angle, the measurement will be reduced by the cosine of the angle until? passes 90E. Thereafter it becomes an increasing negative angle. i.e. actual speed = speed measured in line with sensor / cos (angle cutting across path). From this equation it can be seen that if the target is traveling perpendicular to the sensor (90E) then no velocity component will be sensed at all. Example An ultrasonic Doppler shift speed sensor is used for checking the speed of a school bus. The frequency transmitted by the instrument is 40 Khz and the received frequency is Khz. What speed is the bus traveling and is it moving toward or away from the sensor? For a bus we assume the medium is air at about 21EC and thus the velocity is 344 m/s. Let us assume that the bus is moving towards the instrument and that?=0e. Then v bus = 344 (1 - (40 x 10 3 / x 10 3 )) = 344 ( ) = m/s = mph Since the answer is negative our assumption was wrong. The bus is traveling at 56 mph away from the instrument. If the bus is traveling at an angle to the line of the sensor then its speed is even higher. How large is the error if the temperature was 0EC when the reading was taken? v bus = ( ) = m/s = 54.1 mph -2 mph error Example A underwater speed sensor is being developed for tracking jet skis. The range of expected speeds is 0-50 mph. The transmitted frequency is 24 Khz. What received frequency range must the sensor cope with.

7 The above equation for movement towards the sensor can be rearranged in terms of received frequency. f RX f TX v med v med &v TG (3) For speed = 0, f RX =f TX. 50 mph = m/s, Velocity of sound in water = 1498 m/s f RX = 24x10 3 (1498 / ( )) = x10 3 Hz If it is traveling away from the sensor we would get a similar equation to equation (4) above, with the velocities adding in the denominator, and the frequency would be Khz. So to handle both situations we need a sensor that can measure frequencies in the range Khz. Impedance Matching Sound is attenuated and reflected as it passes from one medium to another. This affects how much sound is emitted from (say) an ultrasonic transducer to the air. The amount that passes through is determined by the acoustic impedances of the interfacing materials. The acoustic impedance can be calculated from the formula Z a?c Y? (4) where Z a = acoustic impedance (kg/m 2 -s),?=mass density (kg/m 3 ), c=velocity of sound (m/s), Y = Young s modulus. The following table shows acoustic impedances for various media 6 Material Sound velocity (m/s) Mass density ( kg/m 3 ) Impedance (kg/m 2 -s) Air Aluminum x 10 6 Brass x 10 6 Copper x 10 6 Hydrogen x 10 6 Iron x 10 6 Clay, ceramic x Carstens, J.R. Electrical Sensors and Transducers Prentice Hall 1993 p113

8 Water x 10 6 Wood x 10 6 Ideally the two media should have the same acoustic impedance. If there is a large difference between the acoustic impedances of the two media then significant power is lost. An impedancematching transformer can be used to improve the sound transfer characteristics. The transformer is simply a third material inserted between the two mismatched materials that has good matching characteristics with both materials. The impedance of the transformer material is given by Z xfmr Z 1 Z 2 (5) So if we had a brass sensor and we wanted to use it under water we calculate that we need a transformer Z = %(29.93 x 10 6 )x(1.46 x 10 6 ) = 6.61 x Looking through the table above we may be able to use a ceramic coating on the transducer to improve power transfer. Applications Sound-based instruments which emit and then measure a signal are usually ultrasonic in preference to audible. This obviously creates less interference for humans. Audible range instruments are used for measuring noise levels, musical instruments (eg. Guitar tuners), sound levels of music systems and so on. In industry ultrasonic sensors are used for measuring flow. A signal is bounced of material or airbubbles flowing in the pipe and speed of flow is thus calculated. Ultrasonic sound has been used for distance sensing for automatic camera-focusing and also for intruder detectors. Ultrasonic sound instruments are well known for their ability to take pictures of unborn babies. This is a variation on the sonar principle. Sound waves penetrate and reflect differently off flesh, bone, body fluids, etc. By transmitting sound waves and then measuring the direction, timing and magnitude of the responses a picture can be built up of the foetus in the mother s womb. Ultrasound does not damage the body but the images have poor resolution. This is improved as far as possible by sophisticated signal processing.

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10 Appendix - Velocity Equations The velocity of sound traveling through solid material can be calculated from the equation c Y? where c=velocity (m/sec), Y=Young s modulus (n/m 2 ) and?=mass density (Kg/m 3 ) For liquids the equation becomes c B? And for gases c GRT M where c=velocity (m/sec), B=bulk modulus constant (n/m 2 ) and?=mass density (Kg/m 3 ) where c=velocity (m/sec), G=ratio of heat capacity at constant pressure to heat capacity at constant volume, R=universal gas constant (J/mol-K), T=temperature (K), and M=molecular mass (Km/mol)