soundwaves

SOUND WAVES

Introduction
This model explores the behavior of subsonic and supersonic sound waves in the air and human perception of them. Please read the "Background Information" section first if you are unfamiliar with these concepts and how they occur in nature. Specifically, my model shows you how different kinds of sound waves under different conditions are created and dispersed in the air by an aircraft of varying speeds. It analyzes the differences between the order of creation of subsonic and supersonic sound waves, and the order of reception of these sound waves by human observers on the ground. It also shows the characteristics and intensity of the Sonic Booms heard by our auditory system in the case of a supersonic object passing over.

Background Information on the Behavior of Sound Waves
First of all, subsonic means the speed being lower than the speed of sound, and supersonic means just the opposite. Mach number is just the proportion of the flying object to the speed of sound in the current medium. When an object moves at a speed slower than the speed of sound in the medium, it creates circular shaped sound waves inside one another. However, if the object's speed is faster than the speed of sound in the medium, it creates circular shaped sound waves ahead of one another, thus forming a conical shape of sound waves in the air.

There is an interesting point to this phenomenon. Let's assume there is a plane flying at a subsonic speed over you. You will hear the first sound wave that the plane produces first, the second one secondly, and so on. However, when the plane is flying at a supersonic speed, the speed of sound becomes relatively slow that the first sound wave you hear is not the first one that is created by the plane. In fact, it is one of the sound waves which is created after the first couple of sound waves. In short, there is a "falling behind" issue in supersonic wave creation. Therefore, when a supersonic plane passes over you, you encounter the phenomenon called a "Sonic Boom", which is carried over to you by the "Shockwave". Shockwaves are created because of the sound waves (the circles in this model) produced by the plane being separated by a small distance. Therefore, they add up when received by the auditory system, resulting in a short intense thunder-like sound, which is the "Sonic Boom". In general, when an object moves at a speed faster than the speed of sound in the medium, it creates a region of intense sound. This is the sonic boom created by objects moving at supersonic speed. If a supersonic airplane flies over you, you will hear a sonic boom which will sound like a short thunder-like noise. This short thunder-like noise causes the human auditory system to perceive the direction that the plane is coming from incorrectly. When hearing subsonic sounds, the auditory system is very successful at perceiving the direction of the sounds being created mainly because the sound waves are heard in order. However, supersonic sound waves are mostly heard in different orders so this confuses our auditory system's perception of the direction of sound source.

Note: Speed of Sound changes with varying temperature. Below is the formula used in my model to determine Speed of Sound:

Speed of Sound (in mph) = 740 + 1.34 * Temperature (in Celcius)

Design Rationale
The implementation of this model has the airplane, human observers and sound waves as turtles. Each turtle's shape was drawn manually in the Shapes Editor. Each red circle-shaped turtle is considered as a sound particle. A sound wave is a circle of 100 turtles each of them moving outward in every time step. As the plane moves, it creates these sound waves at a constant frequency which is adjusted by a formula so that subsonic wave creation occurs below the speed of sound, and supersonic wave creation occurs above it. When a sound particle reaches the end of the screen, it dies in the next time step. Human observers are always placed at the bottom half of the screen. When a sound wave intersects a human observer, the human's color changes to green. The first sound wave intersecting a human observer becomes a thicker blue circle. If that human observer is selected during the intersection, it gathers information on the intensity of the sound in a predetermined imaginary radius. The intensity is measured based on the amount of sound particles within the imaginary radius, and drawn in the Intensity plot with respect to time. In the case of a supersonic wave intersecting a human observer, the human observer hears the "Sonic Boom", which is drawn as a sharp peak in the Intensity plot. In musical terms, this sharp peak has the characteristics of a sharp attack and quick decay for the supersonic waves. However, in the subsonic case, this peak decays gradually.

How the model works
Below is the step-by-step explanation on how to use this model along with explanation of each button and plot on the screen:

1) Click on SETUP to setup the screen with the airplane and 5 initial human observers. 2) Click on PLACE RANDOM OBSERVER to add any random human observers on the screen. 3) Click on CHOOSE OBSERVER to choose one of the human observers to explore the Sonic Boom and Initial Hitting Sound Wave phenomenon. 4) Unclick on CHOOSE OBSERVER after choosing a human observer. 5) Set the Speed of Airplane and Temperature by moving the sliders. You can see how the value of the speed of sound changes in the SPEED OF SOUND monitor. Also, you can view the current mach number in the MACH monitor. 6) Click on GO to start running the model. You can change the values of the sliders dynamically while running the model. In addition, you can re-click on CHOOSE OBSERVER to change the selected human observer on the screen anytime as the model is running. 7) View the SPEED RATIOS plot to see how the speed of airplane and the speed of sound changes according to your dynamic changes in the sliders. 8) View the INTENSITY OF THE WAVES HEARD plot to see the Sonic Boom and the intensity of sound waves in the selected human observer's hearing radius with respect to time. Note: Do not try to reset plane position while the plane is flying (the GO button is on). First, stop the plane and then reset its position.

Analysis of the model under different simulations

When the airplane flies below Mach 1 (below the speed of sound in the medium): The sound waves that the airplane generates form a circular shape as a whole. The darker colored sound waves represent the first waves being generated. As you can see, the first created sound wave intersects the human observers first, the secondly created one second, and so on. Therefore, the order of intersection is proportional to the order of creation of the sound waves. Also, the intensity of the sound heard by the chosen observer does not form a sharp peak with a quick decay. Therefore, the Sonic Boom doesn't occur.
When the airplane flies at Mach 4.5: The sound waves that the airplane generates form a conical shape as a whole. This time the order of the sound waves hitting the human observers is not proportional to the order of their creation. You can see that sound particles are closer to each other at the edges of the cone, creating an intense region of sound. Sonic Boom is heard when the human observer encounters this intense region of sound. As you can see from the plot, the Sonic Boom forms a sharp peak with a sharp attack and quick decay.
When the airplane flies at Mach 2.5: Everything is the same as the Mach 4.5 simulation, except for the intensities. This time sound waves are generated closer to each other, and the sound particles at the edges of the cone are close to each other. However, as you look towards the center of the cone, the sound particles are not far enough this time. Therefore, they keep the intensity of the sound high at the center of the cone as well as the edges. Therefore, the plot will draw a peak with a decreasing decay by a slower amount than the decay we have seen in Mach 4.5, instead of a very quick decay.

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WHAT IS IT? ----------- This model explores the behavior of subsonic and supersonic sound waves in the air and human perception of them. As a sidenote, subsonic means the speed being lower than the speed of sound, and supersonic means just the opposite. When an object moves at a speed slower than the speed of sound in the medium, it creates circular shaped sound waves inside one another. However, if the object's speed is faster than the speed of sound in the medium, it creates circular shaped sound waves ahead of one another, thus forming a conical shape of sound waves in the air. There is an interesting point to this phenomena. Let's assume there is a plane flying at a subsonic speed over you. You will hear the first sound wave that the plane produces first, the second one secondly, and so on. However, when the plane is flying at a supersonic speed, the speed of sound becomes relatively slow that the first sound wave you hear is not the first one that is created by the plane. In fact, it is one of the sound waves which is created after the first couple of sound waves. In short, there is a "falling behind" issue in supersonic wave creation. Therefore, when a supersonic plane passes over you, you encounter the phenomena called a "Sonic Boom", which is carried over to you by the "Shockwave". Shockwaves are created because of the sound waves(the circles in this model) produced by the plane being separated by a small distance. Therefore, they add up when received by the auditory system, resulting in a short intense thunder-like sound, which is the "Sonic Boom". In general, when an object moves at a speed faster than the speed of sound in the medium, it creates a region of intense sound. This is the sonic boom created by objects moving at supersonic speed. If a supersonic airplane flies over you, you will hear a sonic boom which will sound like a short thunder-like noise. This short thunder-like noise causes the human auditory system to perceive the direction that the plane is coming from incorrectly. When hearing subsonic sounds, the auditory system is very successful at perceiving the direction of the sounds being created mainly because the sound waves are heard in order. However, supersonic sound waves are mostly heard in different orders so this confuses our auditory system's perception of the direction of sound source. This model shows you the shapes of these different sound wave types produced by an airplane, the sound wave which hits a human observer in different cases and the sonic boom encountered by the human observer. IMPORTANT NOTE: Each red particle coming out of the plane represents a sound particle. The circle they form represents the sound waves. For those who are not familiar with these concepts, the speed of sound changes with varying temperature. Below is the formula that is used in my model to calculate the speed of sound: | Speed of Sound (in mph) = 740 + 1.34 * (Temperature) Also, below is the formula for calculating the Mach Number: | Mach Number = Speed of Flying Object / Speed of Sound HOW TO USE IT ------------- 1) Click on SETUP to setup the screen with the airplane and 5 initial human observers. 2) Click on PLACE RANDOM OBSERVER to add any random human observers on the screen. 3) Click on CHOOSE OBSERVER to choose one of the human observers to explore the Sonic Boom and Initial Hitting Sound Wave phenomena. 4) Unclick on CHOOSE OBSERVER after choosing a human observer. 5) Set the Speed of Airplane and Temperature by moving the sliders. You can see how the value of the speed of sound changes in the SPEED OF SOUND monitor. Also, you can view the current mach number in the MACH monitor. 6) Click on GO to start running the model. You can change the values of the sliders dynamically while running the model. In addition, you can re-click on CHOOSE OBSERVER to change the selected human observer on the screen anytime as the model is running. 7) View the SPEED RATIOS plot to see how the speed of airplane and the speed of sound changes according to your dynamic changes in the sliders. 8) View the INTENSITY OF THE WAVES HEARD plot to see the Sonic Boom and the intensity of sound waves in the selected human observer's hearing radius with respect to time. Note: Do not try to reset plane position while the plane is flying (the GO button is on). First, stop the plane and then reset its position. THINGS TO NOTICE ---------------- When the airplane is flying below Mach 1, the sound waves it generates form a circular shape as a whole. However, when the airplane exceeds Mach 1, then the sound waves it generates form a conical shape as a whole. This is explained by the "falling behind" phenomena, mentioned above in the second paragraph. Note that Sonic Boom occurs at the sudden peak point in the INTENSITY OF THE WAVES HEARD plot. Then, the total volume of sound gradually decreases. The first sound wave encountered by any human observer highlights itself as a thicker blue wave. Note how the order of this sound wave changes as you change the airplane speed and the speed of sound. THINGS TO TRY ------------- Try setting the airplane speed just below the speed of sound and see how the circles are being formed inside one another. Then, try setting its speed to maximum (3750mph) value in the slider and see how the first wave hitting the selected human observer is not the first wave created. After that, start running the model as decreasing the plane's speed by a specific amount each time the model runs to see how the first wave hitting the human observer changes each time. Try comparing the intensities of Sonic Booms from the sound waves generated at different speeds by the airplane. EXTENDING THE MODEL ------------------- There may be some other flying objects placed on the screen and interference of the sound waves in the air can be measured on the screen. In addition, the model can have an option to analyze the sound waves traveling in another medium than air, such as water. CREDITS AND REFERENCES ---------------------- This model has been constructed and implemented by Umut Tekin. You may obtain a copy of the model from http://www.angelfire.com/ut2/umuttekin/. For any academic, commercial and/or non-commercial use, please consult Umut Tekin (u-tekin@northwestern.edu) for obtaining a permission to use the model.