Experiments with wave, using low-cost amplitude modulated ultrasonic techniques Motivation: It is usually difficult to demonstrate the wave nature of light. The wavelength of visible light is pretty small, therefore one needs objects of very small dimensions (optical gratings, etc.) to show the wave nature of light. Moreover, there is also a didactical challenge that usually the pupils are not familiar even with the wave phenomena! With other words, we would like to demonstrate the wave nature of light with phenomena that they do not know. The main idea of this workshop is to demonstrate wave phenomena with waves that have macroscopic wavelengths; therefore macroscopic objects (slits, gratings etc.) can be used. As soon as the pupils understand what these wave phenomana are, they will better understand what they see when we perform wave-experiments with light. The waves used in this workshop are 40 khz ultrasound waves, which have about 8,5 mm wavelength. 1
Low-cost ultrasonic devices Today the ultrasonic devices are in the home, industrial and medicinal applications. These devices use the low-cost (1 EUR) 40 khz piezoelectric ultrasound transducers (Figure 1). Figure 1. Ultrasonic Sensor Distance Measuring Module for Arduino They are used in remote controls, in parking sensors for cars, or in materials control. Despite of it s low-cost it can be well used for studying waves, because ultrasound has macroscopic size wavelength of 8.5 mm at 25 C. In this workshop, we describe how 40 khz piezoelectric ultrasound transducers can be used to study wave phenomena. We give hints for general usage and tips for individual experiments as well. In this workshop we will conduct wave experiments with macroscopic wavelengths, using the amplitude modulation technique for the purpose of detection by the ear. We use 2 frequencies in these experiments. We need ultrasound (40 khz) carrier signal for the optimum wavelengths (about 8.5 mm), and the 440 Hz modulating frequency so we can use our ears as inexpensive sensor (detector). We try to present easily reproducible sample results for all. In my transmitter we will use 40 KHz ultrasound what allows us to use clearly visible slits, and other diffraction elements. The dispersion elements used during the experiments can be made from paper with laser cutting techniques or even from a pair of scissors. This technique allows us to examine the wave phenomenon easily which would be hard to do otherwise with e.g. light, because of the short wavelength. 2
What is the amplitude modulation? Amplitude Modulation (AM) is the modulation technique used in electronic communication. In the amplitude modulation, the amplitude of the carrier wave is proportional to the waveform of the modulation signal. This technique was used in early radio transmitter stations. Modulated sound Figure 2. The operating principle of the transmitter Sound Figure 3. The operating principle of the receiver In the next pages, we will show You some sample experiments. 3
1. Lloyd's mirror experiment With the help of the Lloyd's mirror experiment you can observe the effect of interference between a sound wave travelling through direct path A,C and a sound wave travelling through indirect (reflected) ABC path. The reflected sound wave interferes with the coherent direct sound from the source. Figure 4. Sketch of the Lloyd's mirror experiment The amplitude of the received signal on the detector depends on the x. The path difference between AC and ABC path: s = 2 d 2 + x 2 2 d Because the sound waves on the mirror get the phase (180 ) change when they reflect, the criterion of the constructive interference: s=(2 k + 1) λ 2 And the destructive interference s=2 k λ 2 Type here results of your measurements! type x [mm] d [mm] s λ constructive 1. x 1 : s 1 1 constructive 2. x 2 : s 2 2 constructive 3. x 3 : s 3 3 destructive 1. x 4 : s 4 4 destructive 2. x 5 : s 5 5 destructive 3. x 6 : s 6 6 f=40 khz Average of the :.. Speed of sound: The mirror design for laser cutting can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip 4
250 mv 200 mv 150 mv 100 mv 50 mv 0 mv 0 mm 20 mm 40 mm 60 mm 80 mm 100 mm Figure 5. U(x) diagram of Lloyd s 2. Ultrasound transmitted by a waveguide Figure 6. Sketch of the waveguide experiment It is known that the intensity of the sound waves decreases with the square of the distance! The range of audio-signal transmission can be increased by a waveguide [1]. In this way, a standing wave is set up inside the pipe. My waveguide is made from an electrical insulation tube. The length of this tube is 50 cm, and the diameter is about 1,5 cm. In this experiment we will use the hole in the cardboard mirror, with a diameter of 1.5 cm. 5
3. Young s double slit experiment in ultra sound range The basic version of this experiment is a coherent light source, such as a laser beam, which illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. This experiment can be repeated with ultrasounds. The configuration of this experiment can be seen on the figure 6. To obtain constructive interference for a double slit, the path length s difference must be an integer multiple of the wavelength! Figure 7. Sketch of the Young s double slit experiment Type here results of your measurements! x:.. h:.. x:.. x:.. h:.. h:.. Figure 8. Detector signal as a function of x 6 d x λ = h λ:.. The slit design for laser cutting can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip
4. Michelson-interferometer A semi-permeable mirror (A paper-fired grid with laser-cut technique, or a prototype universal PCB Breadboard d=1 mm holes) divides the ultrasonic wave into two partial packets which travels to right angles to each other (Figure 8.). They are subsequently reflected at different cardboard paper mirrors, one of (M1) which is fixed in position, and the other (M2) which can be displaced in the direction of the beam, before being reunited. Shifting the displaceable reflector changes the path length of the corresponding packet, so that super positioning of the reunited partial packets gives maximum and minimum of the alternating sound intensity according to the difference in the distance travelled. The wavelength of the ultrasound can be measured from these data. [2] It is interesting to note that the detection of the gravitational waves (LIGO experiment) is also based on this principle. However, they work with light. Figure 9. Michelson-interferometer We are measuring the places of the constructive interference. d is an distance between two peek. 2 d = λ f=40 khz Average of the :.. Speed of sound: The mirror design for laser cutting can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip 7
5. Fresnel-zone plates A zone plate is a device used to focus light or other things which are exhibiting wave character [3]. So if an ultrasonic plane wave strikes a Fresnel zone plate, the intensity of the ultrasound is a function of the distance behind the plate. Very few tools can better illustrate the Huygens-Fresnel principle than the Fresnel Zone Plate. On the zone plate, opaque and transparent concentric rings follow each other. To get constructive interference at the focus, the zones should switch from opaque to transparent at radii where r n = n λ f + n2 λ 2 where n is an integer, λ is the wavelength of the ultrasound, the zone plate is meant to focus and f is the distance from the center of the zone plate to the focus. 4 Figure 10. Calculate the place of constructive interference [4] The length of the road traveled by the ring of the r n radius: f + n λ 2 Constructive interference: r n 2 + f 2 = (f + n λ 2 ) 2 8
This way we can calculate the radius of the circles to be cut. In the next table you can see my calculated Fresnel zones when the frequency is 40 khz and the planned focal length is 5 cm. n 1 2 3 4 5 6 7 8 9 10 11 12 R n [mm] 21 30,4 37,9 44,6 50,8 56,6 62,1 67,5 72,7 77,8 82,8 87,8 Figure 11. Detector on focus Measure the focal length of your lens! Measure the gain value in db! The lens design for laser cutting can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip 9
After the experiments If you would like to repeat these experiments, we will help you to build up the transceiver, and design the diffraction elements. If you want to rebuild the transmitter you can use the next circuit diagram (Figure 12.). For more than one instance, it is worth using printed circuit technology, but if you build just a few instances it is worth using the wire wrapping technique. You only need a universal PCB, or a Breadboard and a creative student, who can place the electric components (figure 15). My simple AM (amplitude-modulated) transmitter circuit is based on a cheap NE556 (two NE555) timer IC. Figure 12. Circuit diagram of my ultrasonic transmitter The 40 khz carrier signal for the AM is generated by an IC U2. The U2 side of the NE 556 timer acts as an astable multivibrator. The vibration frequency of 40 khz can be set by P1. A 440 Hz audio signal is generated by the NE 556 circuit (U1). This signal modulates the carrier frequencies (40 khz). The modulated signal is generated by the transistor Q1. An external modulation sources can be also used. This signal can be connected to the audio by jack. The modulated signal is supplied to the piezoelectric transmitter (TR). [5] 10
The receiver circuit (figure 13.) consists of an ultrasound piezoelectric sensor which is resonant at 40 khz and tunes the receiver. [6] Figure 13. The receiver circuit The signal of the sensor is amplified by an inverting amplifier U3 (TL062) with a gain of near 100. The D1 diode demodulates the received AM signals. The demodulated signals can be connected to an active PC speaker system or an earphone. This audio signal can be perceived by the ear. The amplitude of the modulated signal can be measured objectively by a free computerized program called Vu Meter connected to the J1. You can also use the smartphone application LED VU meter sense the intensity of sound by an internal microphone. Figure 14. The Vu Meter program 11
Figure 15. The breadboard of the transmitter The design of PCB, Breadboard can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip References [1] Mak Se-yuen Wave experiments using low-cost 40 khz ultrasonic transducers Department of Curriculum and Instruction, Faculty of Education, The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mak.pdf [2] Ultrasonic Michelson-Interferometer (1.5.22-00) PHYWE catalogue page 81 http://www.phywees.com/index.php/fuseaction/download/lrn_file/phywe-tess-phy-lep-en.pdf [3] https://en.wikipedia.org/wiki/zone_plate [4] Interferencia a hangok világában: Vitkóczi Fanni ELTE TTK Budapest 2016. Szakdolgozat [5] 40 khz Ultrasound Transmitter: https://reviseomatic.org/help/xultrasound/ultrasound%20am%20transmitter.php [6] 40 khz Ultrasound AM Receiver: https://reviseomatic.org/help/xultrasound/ultrasound%20simple%20receiver.php 12