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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.

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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.

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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.

Figure 2. The operating principle of the transmitter

Figure 3. The operating principle of the receiver

In the next pages, we will show You some sample experiments.

Modulated

sound

Sound

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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 ∙ √𝑑2 + 𝑥2 − 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

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And the destructive interference ∆s=2∙ 𝑘 ∙𝜆

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Type here results of your measurements!

type x [mm] d [mm] ∆s 𝜆

constructive 1. x1: ∆s1 1 constructive 2. x2: ∆s2 2 constructive 3. x3: ∆s3 3

destructive 1. x4: ∆s4 4 destructive 2. x5: ∆s5 5

destructive 3. x6: ∆s6 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

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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.

0 mV

50 mV

100 mV

150 mV

200 mV

250 mV

0 mm 20 mm 40 mm 60 mm 80 mm 100 mm

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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

Figure 8. Detector signal as a function of x

Type here results of your

measurements!

x:……………….. h:…………..

x:……………….. h:…………..

x:……………….. h:…………..

𝜆 =𝑑 ∙ 𝑥

ℎ

λ:……..

The slit design for laser cutting can be downloaded from the following link http://www.trefort.elte.hu/fizika/ultrasounds_all.zip

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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

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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 𝑟𝑛 = √𝑛 ∙ 𝜆 ∙ 𝑓 +𝑛2∙𝜆2

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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.

Figure 10. Calculate the place of constructive interference [4]

The length of the road traveled by the ring of the 𝑟𝑛 radius: 𝑓 + 𝑛 ⋅𝜆

2

Constructive interference: 𝑟𝑛2 + 𝑓2 = (𝑓 + 𝑛 ⋅

𝜆

2)

2

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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

Rn [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

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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]

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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

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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.phywe-

es.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/x-

ultrasound/Ultrasound%20AM%20Transmitter.php

[6] 40 kHz Ultrasound AM Receiver: https://reviseomatic.org/help/x-

ultrasound/Ultrasound%20Simple%20Receiver.php