Wave experiments using low-cost 40 kHz ultrasonic transducers

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Mak Se-yuenRegions where secondary maximaand minima can be detectedTransmitterReceiverFixed ruleTo CROTo SGSliding ruleFigure 5. Qualitative demonstration of diffraction through a single slit.To SGdPair oftransmittersLReceiverTo CRO(a)TransmitterTo SGd/2LReceiverTo CROImage oftransmitterVertical reflector as Lloyd’s mirror(b)Figure 6. (a) Young’s double source. (b) Young’s experiment using one transmitter and a Lloyd’s mirror.a Lloyd’s mirror (a flat vertical surface at least30 cm long, figure 6(b)) or a double slit. The traceamplitude and fringe separations obtained fromthe first two methods are sufficiently distinct forquantitative measurement of the wavelength. Atypical data set is as follows:• Source separation, d = 10.0 ± 0.5cm• Distance between midpoint of sources anddetector, L = 44 ± 0.4 cm• Fringe separation, x = 3.8 ± 0.2 cm• Angular fringe separation,θ ≈ x/L = 0.086 ± 0.006• Wavelength, λ = d sin θ = 0.86 ± 0.06 cmAmplitude modulationAmplitude modulation can be done if the outputtransducer is driven by a signal generator equippedwith such a function. The transmitted range is overa metre when a CRO is used to display a periodicmodulated signal, but limited to only a fewcentimetres if a low-power amplifier–loudspeakeris used to play music.Music transmitted by a waveguideThe range of audio-signal transmission can beincreased to about 1.0 m by feeding the ultrasoundwave into one end of a 1.5 cm bore air-pipe with444 P HYSICS E DUCATION September 2003
Wave experiments using low-cost 40 kHz ultrasonic transducersAmplifier/speakerAudio equipmentAMSGTransmitterAir pipeReceiverGe diodeFigure 7. Transmission of an audio signal using a waveguide.PlanereflectorSignalgeneratorTransmitterReceiverChannel 1 Channel 2Straight ruleFigure 8. Determination of wavelength by a stationary wave method.the receiver placed a few mm from the other end(figure 7). In this way, a standing wave is set upinside the pipe and a local pressure antinode iscreated at the diaphragm of the pick-up transducer.By slightly adjusting the position of the receiver,the speaker can respond to a rectified audio signaleven when the pipe is bent. The method oftransmitting audio information by an air-pipe isactually used in some monophonic earphones andpublic address systems.Wavelength and speed measurementA standing wave in free space. A standing wavecan be set up by directing a beam of ultrasoundtowards a vertical plane reflector (figure 8).If the receiver is moved slowly and smoothlytowards or away from the reflector, the amplitudeof the CRO trace will vary periodically andrepeatedly every time the receiver traverses adistance of half a wavelength (λ/2 = node-tonodeseparation ≈ 4.3 mm). The same result canbe obtained by moving the reflector while keepingthe receiver stationary.Phase shift of a progressive wave. Theexperiment is best carried out using a dualtraceCRO with the transmitter (T) connectedto channel 1 and the receiver (R) to channel 2(figure 9). The T signal should be the triggersource if the CRO can display only the R trace.In any case, the xy mode can also be used insteadof the trigger sweep mode and Lissajous’ figureswould be observed.When R is moved towards or away fromT a distance of one wavelength λ, a change inphase of 2π is observed in the R trace. Soby counting the number (n) of complete wavesof trace 2 passing trace 1 and the distance (d)moved by R, the wavelength of the wave can bedetermined. A typical result would be n = 10 andd = 8.6 ± 0.5 cm, givingλ = L n= 0.86 ± 0.05 cm.September 2003 P HYSICS E DUCATION 445
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Wave experiments using low-cost 40 kHz ultrasonic transducers

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