Wave experiments using low-cost 40 kHz ultrasonic transducers

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Mak Se-yuenreflections from the signal generator and the CRO,both bits of apparatus should be kept at least 50 cmaway from the path of propagation. A shuntresistor, of the order of 10 k, connected acrossthe receiver will filter out unwanted 50 Hz noisefrom the mains.Figure 1. A simple set-up using a pair of bare 40 kHztransducers.are placed on the bench facing one another. Inthis way, the bench acts as a Lloyd’s mirror [3],generating a pressure antinode all the way alongthe line of transmission on the bench surface. Theoutput signal of the receiver at resonance, 1 maway from the transmitter, gives a CRO displayof V pp ≈ 80 mV.Set-up precautionsWith the exception of focusing experiments usingspherical lenses and mirrors, all experiments willbe carried out with the transmitter fixed to thebench with Blu-Tack and the receiver attachedto a small weight (figure 1) sufficiently heavy toprevent turning and sliding caused by the twistingof connecting cables. To prevent unwantedExperimentsFinding the resonance frequency of thetransducerConnect the circuit as shown in figure 2. Thetransmitter is driven by a signal generator withan output voltage set at 6.0 V rms and frequencyin the range 10 kHz to 100 kHz. The receiver isheld facing the transmitter about 50 cm away. It isconnected to a CRO at some convenient settings,say, e.g., 0.5 V cm −1 and 10 µscm −1 .To find the resonance frequency, the finefrequency control dial of the signal generatoris adjusted until a maximum voltage trace isdisplayed on the CRO screen. In the absence ofmechanical defects in the transducers, resonancenormally happens at 40 kHz with a tolerance nobigger than that specified. The period can beread directly from the on-screen trace, which issinusoidal irrespective of the triggering waveform.Timebase10 µs cm –1V 1GainY 1shiftSignalgenerator1 Vcm –1Channel 1TransmitterReceiver andshunt resistorFigure 2. Determination of the resonance frequency of the transducer. (The transmitter and the receiver arerepresented by different symbols but they are identical in structure.)442 P HYSICS E DUCATION September 2003
Wave experiments using low-cost 40 kHz ultrasonic transducersPlane reflectorTransmitter (fixed)Movable receiverTransmitterirReceiverTo SGTo CROConcavemirror30 cmTo SGTo CRO(a)(b)Figure 3. (a) Reflection by a flat surface. (b) Reflection by a concave mirror.Reflection by plane/concave mirrorTo show the law of reflection (figure 3(a)), apartially collimated ‘beam’ can be obtained byattaching a small paper cone to the opening of eachtransducer. Any flat vertical surface can be usedas the reflector. Maximum reception is observedwhen i ≈ r.Like the 2.8 cm microwave, ultrasound canbe focused by a giant concave mirror. Whenin use, both transducers should be placed on themirror axis and facing the mirror. The receiver ismoved along the axis until a maximum is detected(figure 3(b)). Lloyd’s reflection from the benchsurface has little effect in this experiment becausethe converging signal comes mainly from themirror.(a)Refraction by a ‘lens’A ‘skinless’ condom-balloon 1 about 20 cm indiameter filled with liquid petroleum gas 2 (LPG)can be used as a converging lens. The arrangementand procedure are similar to that in the mirror setup.Figure 4 shows the CRO trace with and withoutthe lens.Diffraction through a single slitFigure 5 shows an arrangement to show qualitativelythe diffraction of ultrasound througha5cmslit. The source is placed about 50 cm behindthe slit and the detector 25 cm in front. Thecentral maximum can be found near the axis of1 A condom-balloon is used instead of a rubber balloonbecause the ultrasound generated by a SG–transmittercombination available in most schools is not powerful enoughto penetrate the skin of an inflated rubber balloon.2 LPG is used instead of CO 2 because the latter leaks rapidly ina condom. Moreover, LPG is acoustically denser and producesa better converging effect than CO 2 .(b)Figure 4. (a) Refraction and focusing by a LPG lens.(b) Same arrangement without the lens.symmetry with secondary maxima and minima intwo ‘shaded’ regions. Attaching the receiver to astraight rule, which can slide against a fixed ruleon the bench, will minimize disturbances by hand.Young’s interference experimentsYoung’s experiment can be carried out using adouble source (figure 6(a)), a single source withSeptember 2003 P HYSICS E DUCATION 443
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Wave experiments using low-cost 40 kHz ultrasonic transducers

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