Brendan Conkle

Advanced Experimental Physics

Block 1- 2018

Advisor: Derin Sherman

Cornell College

Visualizing Ultrasonic Wave Interference Using Schlieren Imaging

Intro/ Background Ideas

For my Capstone Project I wanted to create a demonstration that I could use years from

now in order to teach someone an abstract physical concept. The goal for the demo that I ended

up settling on was to create a way to physically see sound waves propagating through the air. Not

only that, but I also wanted to be able to demonstrate interference patterns between to wave

producing sources. Sound is a wave similar to ocean waves. And just like ocean waves, some

soundwaves are much longer than others. Humans can hear in the frequency range of 20-20,000

Hertz on average. In other words humans can hear 20-20,000 waves a second from a source of

sound, with 20,000Hz being a high pitch ringing sound. Anything past this 20,000Hz threshold is

considered ultrasonic.

While the average person can not see let alone hear any “waves of sound” produced

above 20,000Hz, we can use an imaging technique called Schlieren Imaging along with a

stroboscopic effect to be able to see these waves produced in plain air. (NatSciDemos, 2018) The

stroboscopic effect refers to a strobe light flashing at a certain frequency in order to make it seem

like an oscillating object isn’t moving at all. For example, if you flash a light at a tire every one

rotation, all you will be able to see is the tire at that one point. Therefore it will seem as if the tire

isn’t moving. I will be doing the same in my system, but with much faster moving ultrasound

waves. In addition, Schlieren Imaging is a really cool technique used to view the flow of various

medium. It has numerous applications in aerodynamics, epidemiology, and especially

thermodynamics. You can witness Schlieren Imaging by shining a light onto a parabolic mirror

and having the light bounce back into a camera. Add a filter in its path and any disturbances in

the air will be picked up by the camera and appear as a darker or lighter spot. Figure 7 below is a

good example and shows heat coming off of someone’s hand.

Figure 7:

https://www.google.com/url?sa=i&rct=j&q=&esrc=s&source=images&cd=&cad=rja&uact=8&ved=2ahUKEwig2-

rO4rvdAhXk6YMKHSP-Cg8QjRx6BAgBEAU&url=https%3A%2F%2Fdissolve.com%2Fvideo%2FHeat-hand-

schlieren-video-Schlieren-photography-rights-managed-stock-video-footage%2F002-D30-4-

290&psig=AOvVaw3eRaF1Y22aBGq3aVjGzEV7&ust=1537057462799938

Motivation

When originally coming up with the idea for this experiment, my intent was always to

focus on the demonstrative aspect of experiment for educational purposes. For new learners, I

feel that some of the hardest subjects to learn are those that you can not physically observe using

many of your senses. With the sense of sight being key to understanding a concept for many

people, I wanted to create something that can visually demonstrate a physical phenomenon that

is normally only observed one way. The more senses you can use to demonstrate an abstract

concept like sound, the better.

While Schlieren flow visualization is not a new method, it is a extremely versatile one

that not many have explored. In my case, I had never seen, in any of the video demonstrations I

found online, anyone have two ultrasonic sources interfere with each other and then shown

through Schlieren Imaging. This is also very important to me as a future reference as I plan to

take my knowledge to teaching. Because of its versatility, I, as well as others, can use Schlieren

Imaging to demo a variety of physical phenomena that normally go unnoticed. So, this technique

will be a valuable asset for my future endeavors, and I’m excited to further explore its well

known applications as well as its less explored applications. Just from this project I feel like I

have proven to myself the accessibility of Schlieren Imaging for classroom use and I’m confident

that there are other applications for this wonderful visual trick that I would like to explore.

Explanation of Methods

In Figure 2 below You can see my general set up to utilize Schlieren Imaging. It's a

system that depends on high frequency sound waves, a strobing point light source, and large

concave, parabolic mirror. The mirror catches the light from the point light source that is at two

times its focal length (needs to be a point as to avoid any visual interference and darkness) and

focuses that light back to another nearby point at two times its focal length (127.46in). At this

point you can put a sharp filter under the image. Any light that is refracted (changed the angle of

the light) hits the filter or shoots above it, changing the image. Any source that I put inbetween

the mirror and the filter that changes the air by either condensing it, expanding it, heating it up,

or cooling it down will be observed in the image. Ultrasonic speakers do just that by condensing

and expanding the air in front of them producing waves just centimeters apart and noticeably

dense due to the high power these ultrasonic waves are being driven at.

Figure 2

The reason why I need a stroboscopic aspect added to my circuit is because of how fast

these sound waves move. The speed of sound is listed at 343m/s (1,125ft/s) and my mirror is

only 0.3556m (14in) in diameter. Using these two stats we can calculate how long it will take

one wave to travel the length of the mirror. (1s/343m)*0.3556m=1.04ms. So it would take just

over one millisecond for a wave of ultrasound to travel across my mirror. Slomo on current

IPhone cameras can be shot at 240 frames per second. That’s 4.17ms in between each frame. We

wouldn't catch a soundwave at that frame rate. However 10,000fps cameras can be used to

capture the movement of sound as you can see in this video that inspired my project (link

here***). At 10,000fps you will get 0.1ms in between each frame. Using my mirror that only

grants you at most ten frames of sound wave movement. So, in order to not spend hundreds of

dollars renting a 10,000fps camera, I decided to implement the stroboscopic effect for my

project.

One of the fundamental equations related to frequency is f = c / λ with f- frequency, c-

speed of wave (speed of sound = 343 m/s), and λ- wavelength (the peak to peak distance between

two waves). So, running the ultrasonic transducer at 28,000Hz we can also calculate roughly

how many waves we should see on our mirror using our frequency equation. f=c/λ →

28,000Hz=343m/s/λ → λ=1.23cm

With a wavelength of 1.23cm we should be expecting around 28 full waves to show up on our

mirror.

Figure 1 below is a color coded map coordinating to what my final image should look

like for my demo. The two wave sources in the image are separated by four of their wavelengths

as they both have the same frequency.

Figure 1: http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/?C=M;O=A

Figure 3

Figure 4: http://www.ian.org/Schlieren/HowTo.html

Density changes throughout the air cause a slight refraction or “bending” of light passing

through it. Raising the temperature in an area expands the gases that make up the air and reduces

the densities of the gases. The refraction of light passing through a patch of hotter or cooler air is

usually not noticeable by the human eye. However, light is also refracted when it passes from a

dense medium to a less dense medium or vice versa. You may be able to notice this effect while

trying to grab a rock in the water at a river. The index of refraction of water higher than the index

of air so that your hand may actually overshoot the rock’s actual position by a little bit. The

index of refraction is commonly denoted by the letter “n” from Snell’s Law and is affected by

both the density of the medium it represents, as well as the temperature. (“Refractive Index

Theory”) The equation for Snell’s Law is

Figure 11:https://www.utsc.utoronto.ca/webapps/chemistryonline/production/refractive.php

The refractive index of air is typically given as 1 while water is typically given as 1.33. What

Snell’s equation tells you is that as the ratio between nb and na grows the refracted angle θb will

shrink in regard to the normal line intersecting the two mediums. You can see this in the diagram

below.

Figure 12:https://www.utsc.utoronto.ca/webapps/chemistryonline/production/refractive.php

The highest amount of refraction will occur when the angle of incidence, θa, is at its maximum.

θa is at its maximum when the incident light ray is the closest to being parallel with the border

between the two mediums. So, if you stand over the the rock in the river before trying to grab it

instead of reaching for it from the shore, you will see the rock closer to where it physically is.

In my experiment I am trying to make any refracted light rays stand out from the rest.

When the light rays are refracted through the different density areas of my ultrasound wave they

will either hit the filter or pass over it creating dark or light bands respectively. If I’m using two

colored filters then the dark and light bands will be replaced by two different colored bands.

Figure 5*

Figure 6*

In order to make pulsing square waves in my circuit I used the 555 chip (I used the TLC

555). I found an excellent site that lets me not only visually see a light blinking at the frequency I

set the circuit to, but it also gives me the calculated frequency, cycle time, and duty cycle of the

circuit (link here**). The duty cycle is the time the output square wave is high compared to total

time for one cycle (cycle time/period). The duty cycle is represented as a percentage of the total

cycle time, and the equations for it can be found in Figures 5 & 6. (“555 Oscillator Tutorial”) For

my circuit I will need the 555 to output a 50% duty cycle. This helps ensure that I get crisp

visuals of the pulses on the camera by keeping the on time condensed. Also, it helps space out

the pulses from my speakers so I can accurately spot them and differentiate between peaks and

troughs. Having a 50% duty cycle will also help with power consumption as the speakers will be

low half of the time. For the standard rigging of the 555 in astable operation (Figure 5), the duty

cycle can only theoretically be between 50-100%. As you can see from the Time On equation in

Figure 5 above, at 50% duty cycle a key resistor (R1) in our system would have to be completely

missing in order to keep Time On equal to Time Off. Without this resistor we will be damaging

the 555 chip. (“Keeping Duty Cycle”) However, the circuit in Figure 5 can be easily changed to

produce our 50% duty cycle with variable frequency.

By adding two signal diodes to the standard 555 rigging, one for the flow through R1

only on charge up and one for R2 on discharge, we can get a 50% duty cycle as long as R1 and

R2 are the same. As you can see in the equations in Figure 6, duty cycle is ½ if R1 and R2 are

the same. But we want to be able to freely adjust the frequency of the 555 in order to easily

adjust for whatever speaker’s resonant frequency we are using. But we would have to either take

out resistors for every change or adjust two identical potentiometers the same amount. Not

exactly, what I decided to use for part of my resistance for R1 and R2 was a dual pot commonly

found in stereos. This pot will adjust the resistance on two sides with the turn of a single knob,

and therefore is perfect for my 555 setup.

The reason why the waves of a 50% duty cycle will mostly benefit my speaker is because

I will have a shorter pulse for the square wave that drives my LED. This is a safety net to help

ensure that there is less blurriness that may result from pulses that last as long as our speaker’s

pulse. The less the light is on, the less chance that there will be error that makes it look like the

waves are shifting or moving in some way due to a slight difference in frequency between sound

and flash. Also, less light will be scattering, so this will make the image clearer. My flash will

start at the rising side of the square wave produced from the 555. I will keep it on for a set time

shorter than the on time of the 555. Having a short on time for the LED will also prevent it from

burning out due to high power consumption over long periods of time. This means that we can

have the voltage across and current through the LED at close to max values.

Figure 8

In order to get a shorter pulse for my LED I will be using inverted Schmitt triggers and a

D-Type Flip-Flop gate as seen in Figure 8. The output from the 555 will lead to the first inverter

and also to the D-Type Flip-Flop gate. The inverter will take the signal from 5V to 0V or 0V to

5V. After a low pass filter consisting of a 5k resistor and 1nF capacitor the signal will have a

phase delay compared to the original 555 signal still going into the D-Type Flip-Flop gate.

Inverting the signal two more times will give us a delayed, inverted signal that goes into the

other input of the D-Type Flip-Flop gate. Going through the D-Type Flip-Flop gate only the

small section that overlaps between the two signals (the delay) will pass as a on pulse to the

output. We send the signal through three inverted Schmitt triggers in order to clear up our square

wave signal both before and after it gets to the low pass filter. The Schmitt trigger triggers

differently than a normal switch. It is a two level trigger with hysteresis that prevents accidental

triggering (going from high to low or low to high) from spikes that aren't the rising or falling side

of your square wave. (“What is a Schmitt Trigger | How it Works”, 2018) Essentially this means

that we have one higher voltage that the signal from our 555 has to hit in order for it to be

considered the rising side of its square wave at which point the signal is inverted. Conversely, the

inverted Schmitt trigger also has a lower voltage that the signal from the 555 has to hit in order

for it to be considered the falling side of its square wave and, again, the signal is inverted.

In the diagram, between the first and second Schmitt trigger there is a low pass filter.

Looking up the equations for a low pass filter you can calculate the delay that will correspond to

our LED’s pulse ON time as well as the “corner frequency” in which all frequencies below will

be unaltered and all those above will be “filtered”. (“Low Pass Filter”)

R= 5kΩ C= 1nF

Corner frequency f=1/(2*π*R*C) → f=1/(2*π*5kΩ*1nF)= 31830Hz

Need to keep the frequency between 20,000-30,000Hz which is fine for our speakers resonance.

With 28,000Hz Frequency

Phase shift ϕ=-arctan(2*π*f*R*C) → ϕ=-arctan(2*π*28,000Hz*5kΩ*1nF)= -41.34°

Period= 1/f → 1/28,000Hz= 3.57*10-5

s

The Period is equal to 180° of the phase

-41.34°/180°= -0.2296 Fraction of the Period that the wave is out of phase

-0.2296*3.57*10-5

s= -8.20*10-6

s lagging

The inverted wave is lagging the non inverted (555) wave by 8.20μs.

For the D-Type Flip-Flop we have a little more leeway in terms of logic than your

traditional AND gate. So, I was able to devise a logic diagram (the square waves in the lower left

of figure 8) that would function in the Flip-Flop and give me the short pulses I needed. For the

D-Type Flip-Flop the signal going in input D is drawn from for our output signal Q. Our clock

signal triggers data collection from D everytime clock rises. In our case D is driven by our

delayed inverted signal from our Schmitt triggers and clock is driven by our 555 output.

Therefore, because of the inverted delay, everytime clock is on its rising edge D will be high and

Q will be high. Q would output high forever like this unless we had something that overruled the

actions of clock. 𝐶𝐿𝑅 is the answer to our questions and overrules the actions of clock. 𝐶𝐿𝑅 sets

the output to 0V when it itself is at 0V. So, if we also set 𝐶𝐿𝑅 to be our signal from our Schmitt

triggers then the output Q will be set back to 0V a very short time after it was activated. We will

then get our desired short pulses to strobe our LED. (cgcclive, 2014)

In Figure 9 below you can see the circuitry leading up to the LED finally. The LM317

acts as a limit to the current. It ensures that no random pulses will get through that burn up our

LED. (Sherman) Considering we are running on high power this component is very useful. You

can find LM317 calculators online to get the value of the resistors you should use based off of

your LED’s capabilities. The IRLZ44A is a MOSFET switch that changes on pulse from the D-

Type Flip-Flop signal from above. This switch will provide clean on and off signals for the LED.

(Sherman)

Figure 9*

Figure 10*

This is the circuit for my amp in the form of an H-Bridge. The pins that make a

difference here are pins 7, 10, 15, and 16. Pin 7 is going to be driving the switching of the circuit

and is supplied by the output of the 555. Pins 10 and 15 are your two direct connections for your

ultrasonic transducer as the circuit will produce an A/C signal making one or the other high on

switch from pin 7 (phase). Pin 16 is for your decoupled power supply and is what is going to

drive the increased power of your circuit. In my limited testing I was only able to see ultrasound

lines at 12V and 25V, so higher voltages for higher power are definitely needed. However you

have to be careful with your speaker as the chip will only output up to 2A so make sure you

know your speakers impedance. (Allegro) The speaker switches outputs by only allowing current

to flow one way across the literal “H bridge” at a time using MOSFETS at each “leg” of the “H”.

So, the middle of the “H” is the ultrasonic transducer and current will either flow from the top

left of the “H” to the bottom right, or flow from the top right of the “H” to the bottom left. In my

experience I found that as long as you stay within the suggested resistor and capacitor values

detailed on the datasheet for the RC combo out of pin 3 then it should have minimal impact on

your waveform.

Now for setting up the complete Schlieren system. I first found the double focal length

point by shining my phone light at the mirror so its image lands back on my phone. I moved the

phone until I could see a clear image of the LED in the reflection and marked that point on the

bench. From there I setup my point light source above that mark. Turning my system on I can

angle my LED where I can get the reflection of its light to land slightly to its side. I next set up

my camera to have the mirror directly in the center of its frame and completely capturing the

reflected bright light of the LED. However the camera needs to be set back at least an inch

relative to how close the LED is to the mirror. In front of the camera you are going to want to set

up your filter. You can do this one of two ways. First, you can find 2x the focal length using the

same strategy that I employed with my phone, a.k.a finding the most clear image of the LED on

the filter and then blocking half the light with the filter. Another way is bringing the filter in

from the left or right and watching through the camera. (“Schlieren Knife Edge Placement”) If

the filter is too far forward you will see the shadow of the filter come in from the correct side. If

the filter is too far behind then you will see the shadow come in from the opposite side your

moving it in on. If you got it just right then the whole image should dim as you block the light

with the filter. I suggest the second method if you use a razor blade and the first method if your

using a two-color filter.

Results

Unfortunately, I wasn’t able to reach my goal of showing interference patterns between

two ultrasound sources, but I was really close. I was able to display ultrasound waves using my

setup. And, I accomplished my goal of getting both photo and video evidence that my methods

worked and show ultrasound. Although, the visibility of the waves in the photo version is much

greater. I wasn’t sure if I was going to get anything resembling ultrasound before I ran out of

time, but I was able to get results but at the cost of my ultrasound interference goal. Although, I

was able to experiment with both the knife edge filter as well as the two colored filters. The two

color filter payed off because in that video was where I first spotted the contrast that indicated

that I had ultrasound waves. Before Derin took down my setup on the last day he noticed that I

was shorting through my oscilloscope which was causing my 3ohm resistor and the H-Bridge to

get hot. After disconnecting the oscilloscope he tested my setup at 25V and got a clear image of

the ultrasound waves just from the projection of the mirror’s image on the wall. He took a picture

of this projection and that is my best result.

This image is my original

This is a version of the image where I tried to enhance it so it would be easier to see the

ultrasound waves

This is my enhanced image with a couple of arrows to show where the first few waves are.

By my count there are about 24 waves visible across the mirror. Based off the fact that

the ultrasonic transducer is already a couple of inches into the image of the mirror I would say

our experimental result is pretty close to the theoretical number of waves I calculated which was

28 waves. For all the videos with actual ultrasound waves I am running the H-Bridge at 12V and

the frequency of the 555 is 28.09kΩ. For the picture the only difference is that the H-Bridge is

being powered by 25V. Even though I didn’t get two speakers set up I am proud of getting a

result and validating my methods right before the end of the block.

Here is my Youtube playlist featuring all the videos I took trying to find results in my project.

(make sure to turn up the quality all the way, enlarge the window, and mute the sound for the

best experience)

https://www.youtube.com/playlist?list=PLsj3fukrOMzg51FyCf0eCef2oaX5hqAG9

Possibilities for Future Experimentation

There are many different ways to create the circuit for Schlieren Flow Visualization.

And, there are also thousands of ways to produce the multivibrator that drives the circuit. While I

used a fancy dual pot for my 555 in order to keep my two resistances the same, someone

replicating this experiment could easily make a more dependable 50% duty cycle using another

method. The fact that the 555 is a widely used chip that has been on the market for a while now

means that there are many different guides available for many different uses. Keeping the duty

cycle at precisely 50% wasn’t critical for my project. So dual pots that were relatively the same

resistances did the trick. However, for a more accurate duty cycle you can easily enough output a

duty cycle that is not 50% from the 555 chip into a counter and wire up a 50% duty cycle that

way. I believe this would make the duty cycle more accurate.

One could also possibly work with ultrasonic levitation and use Schlieren Imaging as a

way to show how it works. Even though there are a few videos demonstrating this, a project can

be made where someone can utilize this method more. In past years students here at Cornell have

worked on ultrasonic levitation projects as well. In order to do this, the power out to the circuit

would need to be higher than anything I used. So, exploring other options of high power

amplification outside the chip H-Bridge I was using could be useful. One option is to use a

power MOSFET instead. (Kapp, 2015)

Of course, one day I would love to get this all set back up to finally show interference

patterns, and it would probably be easier as I now know my method works. I could also goof

around and show the sound waves reflecting off of objects. Anyways, there are a lot of options

here for me in the future as well as anyone else who wants to do a project like this.

References

Allegro. (n.d.). 3952 Full-Bridge PWM Motor Driver[PDF]. Worcester:

Allegro MicroSystems, Inc.

*Figure 10 Uses the chip in this PDF

Cgcclive. (2014, January 03). Retrieved September 15, 2018, from

https://www.youtube.com/watch?v=XG2mQDi9tW4

Clip D30_4_290, from Dissolve. (n.d.). Retrieved September 14, 2018, from

https://dissolve.com/video/Heat-hand-schlieren-video-Schlieren-photography-rights-man

aged-stock-video-footage/002-D30-4-290

Figure 7

D. (2018, February 25). What is Schmitt Trigger | How It Works. Retrieved September 12, 2018,

from https://howtomechatronics.com/how-it-works/electrical-engineering/schmitt-trigger/

D., & Kapp, H. (2015, July 29). Audio amplifier from biased square wave [Web log post].

Retrieved September 06, 2018, from https://www.electronicspoint.com/threads/audio-

amplifier-from-biased-square-wave.274864/

555 Oscillator Tutorial - The Astable Multivibrator. (2018, March 04).

Retrieved August 30, 2018, from https://www.electronics-

tutorials.ws/waveforms/555_oscillator.html

JoshTheEngineer. (2017, October 02). Retrieved September 19, 2018, from

https://www.youtube.com/watch?v=kSectSljZlQ

Low Pass Filter - Passive RC Filter Tutorial. (2018, May 15). Retrieved September 13, 2018,

from https://www.electronics-tutorials.ws/filter/filter_2.html

NatSciDemos, & Wolfgang (2018, June 12). Visualizing Ultrasound with Schlieren Optics Part I.

Retrieved August 28, 2018, from https://www.youtube.com/watch?v=MBPh410Gnes

Part One of Three Part Series

Part 2: https://www.youtube.com/watch?v=VrgyKFBPQW4

Part 3: https://www.youtube.com/watch?v=doxDOlwEblg

Refractive Index Theory. (n.d.). Retrieved September 03, 2018, from

https://www.utsc.utoronto.ca/webapps/chemistryonline/production/refractive.php

Figure 11 & 12

Sherman, D. (n.d.). Building a polychrome strobe light. Retrieved August 27, 2018, from

https://people.cornellcollege.edu/dsherman/funky-science/polychrome1.html

*Figure 9 is an edited circuit drawing I found from here.

[Two Interfering Wave Sources Separated by Four Wavelengths]. (n.d.).

Retrieved August 29, 2018, from

http://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/?C=M;O=A

Figure 1

W. (n.d.). Keeping duty cycle constant while changing frequency.

Retrieved August 30, 2018, from https://forum.allaboutcircuits.com/threads/keeping-

duty-cycle-constant-while-changing-frequency.51975/

*Figures 5 & 6 are edited circuit drawings I originally found here.

**https://visual555.tardate.com/

Site for Visual 555 outputs where you can input your own resistor and capacitor values and

watch an LED blink. You can simulate both the astable and monostable set up of the 555.

Alternatively you can just look up “555 calculator” for alternatives.

***https://www.youtube.com/watch?v=px3oVGXr4mo

Youtube link to the original video that inspired my project. “What Does Sound Look Like” by

NPR. They demonstrate a variety of effects using Schlieren with a really nice 10,000fps camera

and do a nice job explaining their setup. It's definitely worth the watch.