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THAKUR INSTITUTE OF AVIATION TECHNOLOGY TRAINING NOTES FORWORD UNCONTROLLED COPY ITISIMPORTANTTONOTE THAT THE INFORMATION IN THIS BOOK IS OF STUDY/ TRAINING PURPOSES ONLY AND NO REVISION SERVICE WILL BE PROVIDED TO THE HOLDER. WHEN CARRYING OUT APROCEDURE/ WORK ONAIRCRAFT/ AI...

THAKUR INSTITUTE OF AVIATION TECHNOLOGY TRAINING NOTES FORWORD UNCONTROLLED COPY ITISIMPORTANTTONOTE THAT THE INFORMATION IN THIS BOOK IS OF STUDY/ TRAINING PURPOSES ONLY AND NO REVISION SERVICE WILL BE PROVIDED TO THE HOLDER. WHEN CARRYING OUT APROCEDURE/ WORK ONAIRCRAFT/ AIRCRAFT EQUIPMENT YOU MUSTALWAYS REFER TOTHE RELEVANT AIRCRAFT MAINTENANCE MANUAL OREQUIPMENT MANUFACTURER'S HANDBOOK. FOR HEALTH ANDSAFETY IN THE WORKPLACE YOU SHOULD FOLLOW THE REGULATIONS/ GUIDELINES AS SPECIFIED BYTHE EQUIPMENT MANUFACTURER, YOUR COMPANY, NATIONAL SAFETY AUTHORITIES AND NATIONAL GOVERNMENTS. JULY 2024 Copyright Notice © Copyright. All worldwide rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form by any other means whatsoever: i.e. photocopy, electronic, mechanical recording or otherwise without the prior written permission of Thakur Institute of Aviation Technology. TIAT 2.5 5- 1 THAKUR INSTITUTE OF AVIATION TECHNOLOGY Knowledge Levels – Category A, B1, B2, B3 and C Aircraft Maintenance Licence Basic knowledge for categories A, B1, B2 and B3 are indicated by the allocation of knowledge levels indicators (1, 2 or 3) against each application subject. Category C applicants must meet either the category B1 or the category B2 basic knowledge levels. The knowledge level indicators are defined as follows : LEVEL 1  A familiarization with the principal elements of the subject. Objectives : The applicant should be familiar with the basic elements of the subject.  The applicant should be able to give a simple description of the whole subject, using common words and examples.  The applicant should be able to use typical terms. LEVEL 2  A general knowledge of the theoretical and practical aspects of the subject.  An ability to apply that knowledge. Objectives : The applicant should be able to understand the theoretical fundamentals of the subject.  The applicant should be able to give a general description of the subject using, as appropriate, typical examples.  The applicant should be able to use mathematical formulae in conjunction with physical laws describing the subject.  The applicant should be able to read and understand sketches, drawings and schematics describing the subject.  The applicant should be able to apply his knowledge in a practical manner using detailed procedures. LEVEL 3  A detailed knowledge of the theoretical and practical aspects of the subject.  A capacity to combine and apply the separate elements of knowledge in a logical and comprehensive manner. Objectives : The applicant should know the theory of the subject and interrelationships with other subjects.  The applicant should be able to give a detailed description of the subject using theoretical fundamentals and specific examples.  The applicant should understand and be able to use mathematical formulae related to the subject.  The applicant should be able to read, understand and prepare sketches, simple drawings and schematics describing the subject.  The applicant should be able to apply his knowledge in a practical manner using manufacturer’s instructions.  The applicant should be able to interpret results from various sources and measurements and apply corrective action where appropriate. TIAT 2.5 5- 2 THAKUR INSTITUTE OF AVIATION TECHNOLOGY Module 2.5: Wave Motion and Sound Certification Statement These Study Notes comply with the syllabus of EASA Regulation (EC) No.2042/2003 Annex (Part-66) Appendix I, as amended by Regulation (EC) No.1149/2011, and the associated Knowledge Levels as specified below: EASA 66 Level Objective Reference B1 B2 Wave Motion and Sound : 2 2 Wave motion: mechanical waves, sinusoidal wave motion, interference phenomena, standing waves; Sound: speed of sound, production of sound, intensity, pitch and quality, Doppler effect. TIAT 2.5 5- 3  THAKUR INSTITUTE OF AVIATION TECHNOLOGY 2.5 WAVE MOTION AND SOUND manner as the cork. This oscillatory motion is transverse motion because the oscillations are at right angles to the direction of WAVES travel of the waves, which are represented diagrammatically by lines known as wave fronts. Figure shows the nature of the The idea of a wave is useful for dealing with a wide range of transverse motion and its relationship to the direction of motion of phenomena and is a one of the basic concepts of physics. A wave the wave. carries energy, but there is no transport of matter. Knowledge of wave behavior is also important for engineers. Wave may be Key point classified as mechanical or electromagnetic. Mechanical waves are produced by a disturbance (i.e. a vibrating body) in a Transverse waves oscillate at right angles to the direction of travel mechanical medium and are transmitted by the particles of the of the wave motion. medium oscillating to and fro. Such waves can be felt and include waves on a spring, water waves, and sound waves. Many of the properties of mechanical waves can be shown using water waves in a ripple tank. TRANSVERSE WAVES Fig. 5.1 Transverse waves, where the vibratory motion is at right angles to the direction of movement of the wave and longitudinal waves where particles oscillate (stretch and compress) in the same Direction as the wave travels. If a cork is placed into a still pond and Longitudinal wave then a pebble is dropped into the center of the pond, ripples start to spread out from the source of the disturbance, i.e. where we dropped the pebble, at the same time the cork will bob up and down, these actions are as a result of the energy created by transverse wave motion. The cork does not move in the direction of travel of the Fig. 5.2 wave fronts (ripples) that travel outwards from the center, but it does oscillate about the mid-position of the still water, prior to the disturbance. We know that the waves are Compression and rarefaction progressive (moving) because, e.g. sea waves break on the shore, you However instead of crests and troughs, longitudinal waves can see the wave front traveling towards you! However ignoring have compressions and rarefactions. currents, then in deep water, the effect of hitting the wave front is to cause you to bob up and down, in the same TIAT 2.5 5- 4  THAKUR INSTITUTE OF AVIATION TECHNOLOGY the same but the phase changes continuously. No particle is Definition: permanently at rest. Different particles attain the state of Compression: momentary rest at different instants; all the particles attain the A compression is a region in a longitudinal wave where the particles same maximum velocity when they pass through their mean are closest together. positions. In the case of a longitudinal progressive wave all the parts of the medium undergo similar variation of density one after Rarefaction: the other. At every point there will be a density variation. There is A rarefaction is a region in a longitudinal wave where the particles a flow of energy across every plane in the direction of are furthest apart. propagation. As seen in Fig. 5.3, there are regions where the medium is Stationary waves-There is no onward motion of the disturbance compressed and other regions where the medium is spread out in a as no particle transfers its motion to the next. Each particle has its longitudinal wave. own characteristic vibration. The amplitudes of the different The region where the medium is compressed is known as a particles are different, ranging from zero at the nodes to maximum compression and the region where the medium is spread out is at the antinodes. All the particles in a given segment vibrate in known as a rarefaction. phase but in opposite phase relative to the particles in the adjacent segment. The particles at the nodes are permanently at rest but other particles attain their position of momentary rest simultaneously. All the particles attain their own maximum velocity at the same time when they pass through their mean positions. In the case of a longitudinal stationary wave the variation of density is different at different points being maximum at the nodes and zero at the antinodes. Energy is not transported across any plane. Fig. 5.3 Compressions and rarefactions on a longitudinal wave. PROGRESSIVE WAVES AND STATIONARY WAVES Progressive waves: The disturbance produced in the medium travels onward, it being handed over from one particle to the next. Each particle executes the same type of vibration as the preceding one, though not at the same time. The amplitude of each particle is TIAT 2.5 5- 5  THAKUR INSTITUTE OF AVIATION TECHNOLOGY The period (T) of a wave is the time required for one complete wave to pass a given point. The frequency (f) is the number of waves that pass that point per second (Fig. 5.5). Period Amplitude Fig. 5.4 Graphical representation of a wave showing the period (T) Fig. 5.6 WAVE PROPERTIES The wavelength () (Greek letter lambda) of a periodic wave is Frequency and wave length are related to wave velocity by: the distance between adjacent wave crests or troughs or other v = f  Equal points (Fig. 5.5) Wave velocity = (frequency) (wavelength) Frequency and period are related by: 1 f  T 1 Wavelength Frequency  Period As in the case of periodic motion the unit of frequency is the hertz Amplitude (Hz). Example: The velocity of sound in sea water is 1531 ms-1. Calculate the wavelength in seawater of a sound wave whose frequency is 256Hz. Fig. 5.5 Using: v = f and rearranging gives: Graphical representation of a wave showing the wavelength () TIAT 2.5 5- 6 THAKUR INSTITUTE OF AVIATION TECHNOLOGY  v Sound has been defined as a series of disturb acnes in  1531 f  matter that the human ear can detect. This definition can 256 = 5.98 m also be applied to disturbances which are beyond the range of The amplitude (A) of a wave is the maximum displacement of the human hearing. particles of the medium through which the wave passes on either side of their equilibrium positions. In a transverse wave, the There are three elements which are necessary for the amplitude is half the distance between the top of a crest and the transmission and reception of sound. These are the source, a bottom of a trough. medium for carrying the sound, and the detector. Anything The intensity (I) of a wave is the rate at which it transports energy which moves back and forth (vibrates) and disturbs the medium per unit area perpendicular to its direction of motion. The intensity around it may be considered a sound source. of a mechanical wave is proportional to f², the square of its frequency, and to A², the square of its amplitude. It is measured in An example of the production and transmission of sound is the Watts per meter square (Wm-2). ring of a bell. When the bell is struck and begins to vibrate, the particles of the medium (the surrounding air) in contact with the Standing waves bell also vibrate. The vibrational disturbance is transmitted from If one end of a narrow stretched spring or rope is fixed and the one particle of the medium to the next, and the vibrations travel other is moved continuously from side to side, a progressive in a "wave" through the medium until they reach the ear. transverse wave is generated. The eardrum, acting as detector, is set in motion by the At the fixed end it is reflected, travels back to the vibrating end vibrating particles of air, and the brain interprets the eardrum's and repeated reflection occurs. Two progressive trains of waves vibrations as the characteristic sound associated with a bell. travel along the spring/rope in opposite directions. If the shaking Speed of sound in different medium speed. Sound wave travels frequency is slowly increased, at certain frequencies one or more fastest in solid compare to water and air. Temperature increases vibrating loops of large amplitude are formed in the spring. speed of sound increases and vice - versa. A Stationary or standing wave is said to have been produced since the waveform does not seem to be travelling along the spring/rope  Intensity of Sound in either direction. There are points on a standing wave where the displacement is The intensity of sound is the energy per unit area per second. In a always zero these are called nodes (N). The points on a standing wave where the maximum displacement sound wave of simple har monic motion, the energy is half kinetic occurs are called antinodes (A). and half potential; half is due to the speed of the particles, and half is due to the compression and rarefaction of the medium. SOUND These two energies are 90 degrees out of phase at any instant. That is, when the speed of particle motion is at a maximum, the pressure is normal, and when the pressure is at a maximum or a minimum, the speed of the particles IS zero. TIAT 2.5 5- 7 THAKUR INSTITUTE OF AVIATION TECHNOLOGY The intensity of a sound wave in a given medium is proportional each displaced upward 1 unit at its crest and has the shape of a to the following quantities; sine wave. As the sine pulses move towards each other, there will 1. Square of the frequency of vibration. eventually be a moment in time when they are completely 2. Square of the amplitude. overlapped. At that moment, the resulting shape of the medium 3. Density of the medium. 4. Velocity of propagation. would be an upward displaced sine pulse with amplitude of 2 units. The diagrams below depict the before and during  Measurement of Sound Intensity interference snapshots of the medium for two such pulses. The individual sine pulses are drawn in red and blue and the resulting The loudness (intensity) of sound is not measured by the same displacement of the medium is drawn in green. type of scale used to measure length. The human ear has a nonlinear response pattern, and units of sound measurement are used that vary logarithmically with the amplitude of the sound variations. These units are the "bel" and "decibel," which refer to the difference be tween sounds of unequal intensity or sound Fig. 5.7 levels. The decibel, which is one-tenth of a bel, is the minimum change of sound level perceptible to the human ear. Hence, the decibel merely de scribes the ratio of two sound levels. For  Constructive Interference example, S decibels may represent almost any volume of sound, depending on the intensity of the reference level or the sound level This type of interference is sometimes called constructive on which the ratio is based. interference. Constructive interference is a type of interference that occurs at any location along the medium where the two INTERFERENCE interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, Wave interference is the phenomenon that occurs when two the medium has an upward displacement that is greater than the waves meet while traveling along the same medium. The displacement of the two interfering pulses. Constructive interference of waves causes the medium to take on a shape those interference is observed at any location where the two interfering results from the net effect of the two individual waves upon the waves are displaced upward. But it is also observed when both particles of the medium. To begin our exploration of wave interfering waves are displaced downward. This is shown in the interference, consider two pulses of the same amplitude traveling diagram below for two downward displaced pulses. in different directions along the same medium. Let's suppose that TIAT 2.5 5- 8 THAKUR INSTITUTE OF AVIATION TECHNOLOGY 7. NOISE-CANCELLING HEADPHONES In theory, the idea of noise-canceling headphones is quite simple once one understands the basics of sound waves. The simplest way to understand the mechanism behind noise-canceling headphones is to imagine a transverse sinusoidal sound wave at a Fig. 5.8 single frequency. In this case, a sine pulse with a maximum displacement of -1 unit (negative means a downward displacement) interferes with a sine The principle of superposition tells us that, given an arbitrary pulse with a maximum displacement of -1 unit. These two pulses number of waves, we can sum them up at the same position and are drawn in red and blue. The resulting shape of the medium is a time to obtain a new wave. sine pulse with a maximum displacement of -2 units. this simple idea turns out to be the only tool we need to develop the theory behind noise-cancellation. Since we want to cancel  Destructive Interference incoming sound, our goal is to create our own “noise” that can Destructive interference is a type of interference that occurs at produce destructive interference with the noise coming from the any location along the medium where the two interfering waves environment. This is the same idea as above, except this time we have a displacement in the opposite direction. For instance, when have a specific end-result in mind: a waveform that is as close to a sine pulse with a maximum displacement of +1 unit meets a sine zero amplitude as possible, minimizing the sound intensity we pulse with a maximum displacement of -1 unit, destructive hear. interference occurs. This is depicted in the diagram below Notice that destructive interference occurs when a wave interferes with its exact inverted self. Hence, the design becomes clear. All we need is a way to capture the noise from the outside, invert the signal and output it in time such that we can match the crests of the original wave to the troughs of the inverted wave. For this, we require a microphone that can convert the noise outside into the form of an audio signal and circuitry that will invert the signal and Fig. 5.9 output it through the headphones, illustrated in Fig. 5. 10 TIAT 2.5 5- 9 THAKUR INSTITUTE OF AVIATION TECHNOLOGY Fig. 5.11 Fig. 5.10 BEAT When two sound of different frequency approach your ear, the alternate constructive and destructive interference causes the sound to be alternatively soft and loud- a phenomenon which is called beating or produce beats. The beat frequency is equal to the absolute value of difference in frequency of two waves. Arising from simple interference, the applications of beats are extremely far ranging. Fig. 5.12 REFLECTED WAVE: TIAT 2.5 5- 10 THAKUR INSTITUTE OF AVIATION TECHNOLOGY Let us look in more detail at how to set up standing waves. We set The string vibrates naturally at certain frequencies because it is off a short wave on a slinky which has been firmly fixed at its far fixed at both ends. When the outgoing and reflected waves are end. Assume that the wave consists of one and a half wavelengths. added together subject to this condition, a stationary wave is The wave travels along the slinky until it reaches the far end. set up in the string. If the string is plucked centrally we get the fundamental mode (shape of wave). In this case, the string At this point, the wave can travel no further forwards and is vibrates with maximum displacement at the central position reflected back. This means that the velocity has changed sign. In (called the antinode) and the displacement falls away to zero at addition, the phase of the wave has changed. If the displacement the two ends (called nodes. When a string on an instrument is of the forward wave is upwards at the instant of time when it plucked, vibrations, that is, waves travel back and forth through reaches the far end, then its displacement is downwards on the medium being reflected at each fixed end. Certain sized waves reflection. This makes sense. At the fixed end, the displacement can survive on the medium. These certain sized waves will not of the incoming and outgoing waves sum to zero. This must be so cancel each other out as they reflect back upon themselves. These because there can be no displacement of the string at the fixed certain sized waves are called the harmonics of the vibration. point. The reflected wave is out of phase by it. It passes back They are standing waves. That is, they produce patterns which do 'through' the forward wave (think how ripples can pass through not move. each other on the surface of a pond). Where the two waves overlap, the displacement of the slinky is the sum of the two On a medium such as a violin string several harmonically related waves. But, eventually, we see the reflected wave emerge standing wave patterns are possible. The first four of them are complete and pass back along the slinky. illustrated above. It is important to understand that for anyone given medium fixed at each end only certain sized waves can The frequency, velocity and wavelength of the wave all remain stand. We say, therefore, that the medium is tuned. the same in reflection. If no energy is lost at the far end, the amplitude of the reflected wave equals that of the incoming The first pattern has the longest wavelength and is called the first one. The phase difference of n is crucial to the setting up of harmonic. It is also called the fundamental. standing waves. The second pattern, or second harmonic, has half the wavelength and When waves pass through each other, the displacement at any twice the frequency of the first harmonic. This second harmonic is point is the sum of the individual displacements of the two waves also called the first overtone. This can get confusing with the second passing in opposite directions. member of the harmonic group being called the first member of the overtone group. TIAT 2.5 5- 11 THAKUR INSTITUTE OF AVIATION TECHNOLOGY The third harmonic, or pattern, has one third the wavelength and Aircraft speed1650 three times the frequency when compared to the first harmonic. Mach no = This third harmonic is called the second overtone. Speed of sound750 The other harmonics follow the obvious pattern regarding = 2.2 Mach wavelengths, frequencies, and overtone naming conventions 11. THE DOPPLER EFFECT described in the above paragraph. The Doppler Effect (or Doppler shift) is the change Depending upon how the string is plucked or bowed, different in frequency of a wave (or other periodic event) for harmonics can be emphasized. In the above animation all an observer moving relative to its source. It is named after harmonics have the same maximum amplitude. the Austrian physicist Christian Doppler, who proposed it in 1842 This is for purposes of illustration. Actually, the higher harmonics in Prague. It is commonly heard when a vehicle sounding almost always have maximum amplitudes much less than the a siren or horn approaches, passes, and recedes from an observer. fundamental or first harmonic. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, It is the fundamental frequency that determines the note that we and lower during the recession. hear. It is the upper harmonic structure that determines the timber of the instrument. When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the 10. SUPERSONIC SPEED AND MACH NUMBER observer than the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. In the study of aircraft that fly at supersonic speeds, it is Hence, the time between the arrivals of successive wave crests at customary to discuss aircraft speed in relation to the velocity the observer is reduced, causing an increase in the frequency. of sound (approximately750 miles per hour). The term "Mach While they are travelling, the distance between successive wave number" has been given to the ratio of the speed of an fronts is reduced, so the waves "bunch together". Conversely, if aircraft to the speed of sound, in honor of Ernst Mach, an the source of waves is moving away from the observer, each wave Austrian scientist. is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is Thus, if the speed of sound at sea level is 750miles per hour, increased, reducing the frequency. The distance between an aircraft flying at a speed of 1650 m.p.h TIAT 2.5 5- 12 THAKUR INSTITUTE OF AVIATION TECHNOLOGY successive wave fronts is then increased, so the waves "spread out". For waves that propagate in a medium, such as sound waves, the velocities of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler Effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered. Fig. 5.13 TIAT 2.5 5- 13