Module 10—Introduction to Wave Propagation, Transmission Lines, and Antennas
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2-1 to 2-10
, 2-11 to 2-20
2-21 to 2-30
, 2-31 to 2-40
2-40 to 2-47
, 3-1 to 3-10
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When you use the above equation, be careful to express velocity and wavelength in the proper units of length. For example, in the English system, if the velocity (expressed in feet per second) is divided by the frequency (expressed in cycles per second, or Hz), the wavelength is given in feet per cycle. If the metric system is used and the velocity (expressed in meters per second) is divided by the frequency (expressed in cycles per second), the wavelength is given in meters per cycle. Be sure to express both the wavelength and the frequency in the same units. (Feet per cycle and meters per cycle are normally abbreviated as feet or meters because one wavelength indicates one cycle.) Because this equation holds true for both transverse and longitudinal waves, it is used in the study of both electromagnetic waves and sound waves.
Consider the following example. Two cycles of a wave pass a fixed point every second, and the velocity of the wave train is 4 feet per second. What is the wavelength? The formula for determining wavelength is as follows:
NOTE: In problems of this kind, be sure NOT to confuse wave velocity with frequency. FREQUENCY is the number of cycles per unit of time (Hz). WAVE VELOCITY is the speed with which a wave train passes a fixed point.
Here is another problem. If a wave has a velocity of 1,100 feet per second and a wavelength of 30 feet, what is the frequency of the wave?
By transposing the general equation:
To find the velocity, rewrite the equation as:
v = λf
Let’s work one more problem, this time using the metric system.
Suppose the wavelength is 0.4 meters and the frequency is 12 kHz. What is the velocity? Use the formula:
Other important characteristics of wave motion are reflection, refraction, diffraction, and the Doppler effect. Big words, but the concept of each is easy to see. For ease of understanding, we will explain the first two characteristics using light waves, and the last two characteristics using sound waves. You should keep in mind that all waves react in a similar manner.
Within mediums, such as air, solids, or gases, a wave travels in a straight line. When the wave leaves the boundary of one medium and enters the boundary of a different medium, the wave changes direction. For our purposes in this module, a boundary is an imaginary line that separates one medium from another.
When a wave passes through one medium and encounters a medium having different characteristics, three things can occur to the wave: (1) Some of the energy can be reflected back into the initial medium; (2) some of the energy can be transmitted into the second medium where it may continue at a different velocity; or (3) some of the energy can be absorbed by the medium. In some cases, all three processes (reflection, transmission, and absorption) may occur to some degree.
REFLECTION WAVES are simply waves that are neither transmitted nor absorbed, but are reflected from the surface of the medium they encounter. If a wave is directed against a reflecting surface, such as a mirror, it will reflect or "bounce" from the mirror. Refer to figure 1-9. A wave directed toward the surface of the mirror is called the INCIDENT wave. When the wave bounces off of the mirror, it becomes known as the REFLECTED wave. An imaginary line perpendicular to the mirror at the point at which the incident wave strikes the mirror’s surface is called the NORMAL, or perpendicular. The angle between the incident wave and the normal is called the ANGLE OF INCIDENCE. The angle between the reflected wave and the normal is called the ANGLE OF REFLECTION.
Figure 1-9.—Reflection of a wave.
If the reflecting surface is smooth and polished, the angle between the incident ray and the normal will be the same as the angle between the reflected ray and the normal. This conforms to the law of reflection which states: The angle of incidence is equal to the angle of reflection.
The amount of incident wave energy reflected from a given surface depends on the nature of the surface and the angle at which the wave strikes the surface. As the angle of incidence increases, the amount of wave energy reflected increases. The reflected energy is the greatest when the wave is nearly parallel to the reflecting surface. When the incident wave is perpendicular to the surface, more of the energy is transmitted into the substance and less is reflected. At any incident angle, a mirror reflects almost all of the wave energy, while a dull, black surface reflects very little.
Q11. What is the law of reflection?
Q12. When a wave is reflected from a surface, energy is transferred. When is the transfer of energy greatest?
Q13. When is the transfer of energy minimum?
When a wave passes from one medium into another medium that has a different velocity of propagation, a change in the direction of the wave will occur. This changing of direction as the wave enters the second medium is called REFRACTION. As in the discussion of reflection, the wave striking the boundary (surface) is called the INCIDENT WAVE, and the imaginary line perpendicular to the boundary is called the NORMAL. The angle between the incident wave and the normal is called the ANGLE OF INCIDENCE. As the wave passes through the boundary, it is bent either toward or away from the normal. The angle between the normal and the path of the wave through the second medium is the ANGLE OF REFRACTION.
A light wave passing through a block of glass is shown in figure 1-10. The wave moves from point A to B at a constant speed. This is the incident wave. As the wave penetrates the glass boundary at point B, the velocity of the wave is slowed down. This causes the wave to bend toward the normal. The wave then takes the path from point B to C through the glass and becomes BOTH the refracted wave from the top surface and the incident wave to the lower surface. As the wave passes from the glass to the air (the second boundary), it is again refracted, this time away from the normal and takes the path from point C to D. As the wave passes through the last boundary, its velocity increases to the original velocity. As figure 1-10 shows, refracted waves can bend toward or away from the normal. This bending depends on the velocity of the wave through each medium. The broken line between points B and E is the path that the wave would travel if the two mediums (air and glass) had the same density.
Figure 1-10.—Refraction of a wave.
To summarize what figure 1-10 shows:
1. If the wave passes from a less dense medium to a more dense medium, it is bent toward the normal, and the angle of refraction (r) is less than the angle of incidence (i).
2. If the wave passes from a more dense to a less dense medium, it is bent away from the normal, and the angle of refraction (r1) is greater than the angle of incidence (i1).
You can more easily understand refraction by looking at figure 1-11. There is a plowed field in the middle of a parade ground. Think of the incident wave as a company of recruits marching four abreast at an angle across the parade ground to the plowed field, then crossing the plowed field and coming out on the other side onto the parade ground again. As the recruits march diagonally across the parade ground and begin to cross the boundary onto the plowed field, the front line is slowed down. Because the recruits arrive at the boundary at different times, they will begin to slow down at different times (number 1 slows down first and number 4 slows down last in each line). The net effect is a bending action. When the recruits leave the plowed field and reenter the parade ground, the reverse action takes place.
Figure 1-11.—Analogy of refraction.
Q14. A refracted wave occurs when a wave passes from one medium into another medium. What determines the angle of refraction?
DIFFRACTION is the bending of the wave path when the waves meet an obstruction. The amount of diffraction depends on the wavelength of the wave. Higher frequency waves are rarely diffracted in the normal world that surrounds us. Since light waves are high frequency waves, you will rarely see light diffracted. You can, however, observe diffraction in sound waves by listening to music. Suppose you are outdoors listening to a band. If you step behind a solid obstruction, such as a brick wall, you will hear mostly low notes. This is because the higher notes, having short wave lengths, undergo little or no diffraction and pass by or over the wall without wrapping around the wall and reaching your ears. The low notes, having longer wavelengths, wrap around the wall and reach your ears. This leads to the general statement that lower frequency waves tend to diffract more than higher frequency waves. Broadcast band (AM band) radio waves (lower frequency waves) often travel over a mountain to the opposite side from their source because of diffraction, while higher frequency TV and FM signals from the same source tend to be stopped by the mountain.
The last, but equally important, characteristic of a wave that we will discuss is the Doppler effect. The DOPPLER EFFECT is the apparent change in frequency or pitch when a sound source moves either toward or away from the listener, or when the listener moves either toward or away from the sound source. This principle, discovered by the Austrian physicist Christian Doppler, applies to all wave motion.
The apparent change in frequency between the source of a wave and the receiver of the wave is because of relative motion between the source and the receiver. To understand the Doppler effect, first assume that the frequency of a sound from a source is held constant. The wavelength of the sound will also remain constant. If both the source and the receiver of the sound remain stationary, the receiver will
hear the same frequency sound produced by the source. This is because the receiver is receiving the same number of waves per second that the source is producing. Now, if either the source or the receiver or both move toward the other, the receiver will perceive a higher frequency sound. This is because the receiver will receive a greater number of sound waves per second and interpret the greater number of waves as a higher frequency sound. Conversely, if the source and the receiver are moving apart, the receiver will receive a smaller number of sound waves per second and will perceive a lower frequency sound. In both cases, the frequency of the sound produced by the source will have remained constant.
For example, the frequency of the whistle on a fast-moving train sounds increasingly higher in pitch as the train is approaching than when the train is departing. Although the whistle is generating sound waves of a constant frequency, and though they travel through the air at the same velocity in all directions, the distance between the approaching train and the listener is decreasing. As a result, each wave has less distance to travel to reach the observer than the wave preceding it. Thus, the waves arrive with decreasing intervals of time between them.
These apparent changes in frequency, called the Doppler effect, affect the operation of equipment used to detect and measure wave energy. In dealing with electromagnetic wave propagation, the Doppler principle is used in equipment such as radar, target detection, weapons control, navigation, and sonar.
Q15. The apparent change in frequency or pitch because of motion is explained by what effect?
The study of sound is important because of the role sound plays in the depth finding equipment (fathometer) and underwater detection equipment (sonar) used by the Navy.
As you know, sound travels through a medium by wave motion. Although sound waves and the electromagnetic waves used in the propagation of radio and radar differ, both types of waves have many of the same characteristics. Studying the principles of sound-wave motion will help you understand the actions of both sound waves and the more complex radio and radar electromagnetic waves. The major differences among sound waves, heat waves, and light waves are (1) their frequencies; (2) their types; the mediums through which they travel; and the velocities at which they travel.
SOUND—WHAT IS IT?
The word SOUND is used in everyday speech to signify a variety of things. One definition of sound is the sensation of hearing. Another definition refers to a stimulus that is capable of producing the sensation of hearing. A third definition limits sound to what is actually heard by the human ear.
In the study of physics, sound is defined as a range of compression-wave frequencies to which the human ear is sensitive. For the purpose of this chapter, however, we need to broaden the definition of sound to include compression waves that are not always audible to the human ear. To distinguish frequencies in the audible range from those outside that range, the words SONIC, ULTRASONIC, and INFRASONIC are used. Sounds capable of being heard by the human ear are called SONICS. The normal hearing range extends from about 20 to 20,000 hertz. However, to establish a standard sonic range, the Navy has set an arbitrary upper limit for sonics at 10,000 hertz and a lower limit at 15 hertz. Even though the average person can hear sounds above 10,000 hertz, it is standard practice to refer to sounds above that frequency as ultrasonic. Sounds between 15 hertz and 10,000 hertz are called sonic, while sounds below 15 hertz are known as infrasonic (formerly referred to as subsonic) sounds.
Q16. What term describes sounds capable of being heard by the human ear?
Q17. Are all sounds audible to the human ear? Why?
REQUIREMENTS FOR SOUND
Recall that sound waves are compression waves. The existence of compression waves depends on the transfer of energy. To produce vibrations that become sounds, a mechanical device (the source) must first receive an input of energy. Next, the device must be in contact with a medium that will receive the sound energy and carry it to a receiver. If the device is not in contact with a medium, the energy will not be transferred to a receiver, and there will be no sound.
Thus, three basic elements for transmission and reception of sound must be present before a sound can be produced. They are (1) the source (or transmitter), (2) a medium for carrying the sound (air, water, metal, etc.), and (3) the detector (or receiver).
A simple experiment provides convincing evidence that a medium must be present if sound is to be transferred. In figure 1-12, an electric bell is suspended by rubber bands in a bell jar from which the air can be removed. An external switch is connected from a battery to the bell so the bell may be rung intermittently. As the air is pumped out, the sound from the bell becomes weaker and weaker. If a perfect vacuum could be obtained, and if no sound were conducted out of the jar by the rubber bands, the sound from the bell would be completely inaudible. In other words, sound cannot be transmitted through a vacuum. When the air is admitted again, the sound is as loud as it was at the beginning. This experiment shows that when air is in contact with the vibrating bell, it carries energy to the walls of the jar, which in turn are set in vibration. Thus, the energy passes into the air outside of the jar and then on to the ear of the observer. This experiment illustrates that sound cannot exist in empty space (or a vacuum).
Figure 1-12.—No air, no sound.
Any object that moves rapidly back and forth, or vibrates, and thus disturbs the medium around it may be considered a source for sound. Bells, speakers, and stringed instruments are familiar sound sources.
The material through which sound waves travel is called the medium. The density of the medium determines the ease, distance, and speed of sound transmission. The higher the density of the medium, the slower sound travels through it.
The detector acts as the receiver of the sound wave. Because it does not surround the source of the sound wave, the detector absorbs only part of the energy from the wave and sometimes requires an amplifier to boost the weak signal.
As an illustration of what happens if one of these three elements is not present, let’s refer to our experiment in which a bell was placed in a jar containing a vacuum. You could see the bell being struck, but you could hear no sound because there was no medium to transmit sound from the bell to you. Now let’s look at another example in which the third element, the detector, is missing. You see a source (such as an explosion) apparently producing a sound, and you know the medium (air) is present, but you are too far away to hear the noise. Thus, as far as you are concerned, there is no detector and, therefore, no sound. We must assume, then, that sound can exist only when a source transmits sound through a medium, which passes it to a detector. Therefore, in the absence of any one of the basic elements (source, medium, detector) there can be NO sound.
Q18. Sound waves transmitted from a source are sometimes weak when they reach the detector. What instrument is needed to boost the weak signal?
TERMS USED IN SOUND WAVES
Sound waves vary in length according to their frequency. A sound having a long wavelength is heard at a low pitch (low frequency); one with a short wavelength is heard at a high pitch (high frequency). A complete wavelength is called a cycle. The distance from one point on a wave to the corresponding point on the next wave is a wavelength. The number of cycles per second (hertz) is the frequency of the sound. The frequency of a sound wave is also the number of vibrations per second produced by the sound source.
Q19. What are the three basic requirements for sound?
CHARACTERISTICS OF SOUND
Sound waves travel at great distances in a very short time, but as the distance increases the waves tend to spread out. As the sound waves spread out, their energy simultaneously spreads through an increasingly larger area. Thus, the wave energy becomes weaker as the distance from the source is increased.
Sounds may be broadly classified into two general groups. One group is NOISE, which includes sounds such as the pounding of a hammer or the slamming of a door. The other group is musical sounds, or TONES. The distinction between noise and tone is based on the regularity of the vibrations, the degree of damping, and the ability of the ear to recognize components having a musical sequence. You can best understand the physical difference between these kinds of sound by comparing the waveshape of a musical note, depicted in view A of figure 1-13, with the waveshape of noise, shown in view B. You can see by the comparison of the two waveshapes, that noise makes a very irregular and haphazard curve and a musical note makes a uniform and regular curve.
Figure 1-13.—Musical sound versus noise.
Sound has three basic characteristics: pitch, intensity, and quality. Each of these three characteristics is associated with one of the properties of the source or the type of waves which it produces. The pitch depends upon the frequency of the waves; the intensity depends upon the amplitude of the waves; and the quality depends upon the form of the waves. With the proper combination of these characteristics, the tone is pleasant to the ear. With the wrong combination, the sound quality turns into noise.
The Pitch of Sound
The term PITCH is used to describe the frequency of a sound. An object that vibrates many times per second produces a sound with a high pitch, as with a police whistle. The slow vibrations of the heavier strings of a violin cause a low-pitched sound. Thus, the frequency of the wave determines pitch. When the frequency is low, sound waves are long; when it is high, the waves are short. A sound can be so high in frequency that the waves reaching the ear cannot be heard. Likewise, some frequencies are so low that the eardrums do not convert them into sound. The range of sound that the human ear can detect varies with each individual.
The Intensity of Sound
The intensity of sound, at a given distance, depends upon the amplitude of the waves. Thus, a tuning fork gives out more energy in the form of sound when struck hard than when struck gently. You should remember that when a tuning fork is struck, the sound is omnidirectional (heard in all directions), because the sound waves spread out in all directions, as shown in figure 1-14. You can see from the figure that as the distance between the waves and the sound source increases, the energy in each wave spreads over a greater area; hence, the intensity of the sound decreases. The speaking tubes sometimes used aboard a ship prevent the sound waves from spreading in all directions by concentrating them in one desired direction (unidirectional), producing greater intensity. Therefore, the sound is heard almost at its original intensity at the opposite end of the speaking tube. The unidirectional megaphone and the directional loudspeaker also prevent sound waves from spreading in all directions.
Introduction to Matter, Energy, and Direct Current,
to Alternating Current and Transformers, Introduction to Circuit Protection,
Control, and Measurement
, Introduction to Electrical Conductors, Wiring Techniques,
and Schematic Reading
, Introduction to Generators and Motors
Introduction to Electronic Emission, Tubes, and Power Supplies,
Introduction to Solid-State Devices and Power Supplies
Introduction to Amplifiers, Introduction to
Wave-Generation and Wave-Shaping Circuits
, Introduction to Wave Propagation, Transmission
Lines, and Antennas
, Microwave Principles,
, Introduction to Number Systems and Logic Circuits, Introduction
to Microelectronics, Principles of Synchros, Servos, and Gyros
Introduction to Test Equipment
, Radar Principles,
The Technician's Handbook,
Master Glossary, Test Methods and Practices,
Introduction to Digital Computers,
Magnetic Recording, Introduction to Fiber Optics