# Sound - Physics for Aviation

Sound has been defined as a series of disturbances in matter that the human ear can detect. This definition can also be applied to disturbances which are beyond the range of human hearing. There are three elements which are necessary for the transmission and reception of sound. These are the source, a medium for carrying the sound, and the detector. Anything which moves back and forth, or vibrates, and disturbs the medium around it may be considered a sound source.

An example of the production and transmission of sound is the ring of a bell. When the bell is struck and begins to vibrate, the particles of the medium, or the surrounding air, in contact with the bell also vibrate. The vibrational disturbance is transmitted from one particle of the medium to the next, and the vibrations travel in a “wave” through the medium until they reach the ear. The eardrum, acting as detector, is set in motion by the vibrating particles of air, and the brain interprets the eardrum’s vibrations as the characteristic sound associated with a bell.

## Wave Motion

Since sound is a wave motion in matter, it can best be understood by first considering water waves, like a series of circular waves travel away from the disturbance of an object thrown into a pool.

 Figure 1. Relationship between sound and waves in water

In Figure 1 such waves are seen from a top perspective, with the waves traveling out from the center. In the cross-section perspective in Figure 1, notice that the water waves are a succession of crests and troughs. The wavelength is the distance from the crest of one wave to the crest of the next. Water waves are known as transverse waves because the motion of the water molecules is up and down, or at right angles to the direction in which the waves are traveling. This can be seen by observing a cork on the water, bobbing up and down as the waves pass by.

Sound travels through matter in the form of longitudinal wave motions. These waves are called longitudinal waves because the particles of the medium vibrate back and forth longitudinally in the direction of propagation. [Figure 2] When the tine of a tuning fork moves in an outward direction, the air immediately in front of the tine is compressed so that its momentary pressure is raised above that at other points in the surrounding medium. Because air is elastic, this disturbance is transmitted progressively in an outward direction from the tine in the form of a compression wave.

 Figure 2. Sound propagation by a tuning fork

When the tine returns and moves in an inward direction, the air in front of the tine is rarefied so that its momentary pressure is reduced below that at other points in the surrounding medium. This disturbance is transmitted in the form of a rarefaction, or expansion, wave and follows the compression wave through the medium. The progress of any wave involves two distinct motions: (1) The wave itself moves forward with constant speed, and (2) simultaneously, the particles of the medium that convey the wave vibrate harmonically. Examples of harmonic motion are the motion of a clock pendulum, the balance wheel in a watch, and the piston in a reciprocating engine.

## Speed of Sound

In any uniform medium, under given physical conditions, the sound travels at a definite speed. In some substances, the velocity of sound is higher than in others. Even in the same medium under different conditions of temperature, pressure, and so forth, the velocity of sound varies. Density and elasticity of a medium are the two basic physical properties which govern the velocity of sound.

In general, a difference in density between two substances is sufficient to indicate which one will be the faster transmission medium for sound. For example, sound travels faster through water than it does through air at the same temperature. However, there are some surprising exceptions to this rule of thumb. An outstanding example among these exceptions involves comparison of the speed of sound in lead and aluminum at the same temperature. Sound travels at 16,700 fps in aluminum at 20 °C, and only 4,030 fps in lead at 20 °C, despite the fact that lead is much denser than aluminum. The reason for such exceptions is found in the fact, mentioned above, that sound velocity depends on elasticity as well as density.

Using density as a rough indication of the speed of sound in a given substance, it can be stated as a general rule that sound travels fastest in solid materials, slower in liquids, and slowest in gases. The velocity of sound in air at 0 °C (32 °F) is 1,087 fps and increases by 2 fps for each Centigrade degree of temperature rise, or 1.1 fps for each degree Fahrenheit.

## Mach Number

In the study of aircraft that fly at supersonic speeds, it is customary to discuss aircraft speed in relation to the velocity of sound, which is approximately 760 miles per hour (mph) at 59 °F. The term “Mach number” has been given to the ratio of the speed of an aircraft to the speed of sound, in honor of Ernst Mach, an Austrian scientist. If the speed of sound at sea level is 760 mph, an aircraft flying at a Mach number of 1.2 at sea level would be traveling at a speed of 760 mph × 1.2 = 912 mph.

## Frequency of Sound

The term “pitch” is used to describe the frequency of a sound. The outstanding recognizable difference between the tones produced by two different keys on a piano is a difference in pitch. The pitch of a tone is proportional to the number of compressions and rarefactions received per second, which in turn, is determined by the vibration frequency of the sounding source. A good example of frequency is the noise generated by a turbofan engine on a commercial airliner. The high tip speeds of the fan in the front of the engine create a high frequency sound, and the hot exhaust creates a low frequency sound.

## Loudness

When a bell rings, the sound waves spread out in all directions and the sound is heard in all directions. When a bell is struck lightly, the vibrations are of small amplitude and the sound is weak. A stronger blow produces vibrations of greater amplitude in the bell, and the sound is louder. It is evident that the amplitude of the air vibrations is greater when the amplitude of the vibrations of the source is increased. Hence, the loudness of the sound depends on the amplitude of the vibrations of the sound waves. As the distance from the source increases, the energy in each wave spreads out, and the sound becomes weaker.

As the sound wave advances, variations in pressure occur at all points in the transmitting medium. The greater the pressure variations, the more intense the sound wave is. The intensity is proportional to the square of the pressure variation regardless of the frequency. Thus, by measuring pressure changes, the intensities of sounds having different frequencies can be compared directly.

## Measurement of Sound Intensity

Sound intensity is measured in decibels, with a decibel being the ratio of one sound to another. One decibel (dB) is the smallest change in sound intensity the human ear can detect. A faint whisper would have an intensity of 20 dB, and a pneumatic drill would be 80 dB. The engine on a modern jetliner, at takeoff thrust, would have a sound intensity of 90 dB when heard by someone standing 150 ft. away. A 110 dB noise, by comparison, would sound twice as loud as the jetliner’s engine. Figure 3 shows the sound intensity from a variety of different sources.

 Figure 3. Sound intensity from different sources

## Doppler Effect

When sound is coming from a moving object, the object’s forward motion adds to the frequency as sensed from the front and takes away from the frequency as sensed from the rear. This change in frequency is known as the Doppler Effect, and it explains why the sound from an airplane seems different as it approaches compared to how it sounds as it flies overhead. As it approaches, it becomes both louder and higher pitched. As it flies away, the loudness and pitch both decrease noticeably. If an airplane is flying at or higher than the speed of sound, the sound energy cannot travel out ahead of the airplane, because the airplane catches up to it the instant it tries to leave. The sound energy being created by the airplane piles up, and attaches itself to the structure of the airplane. As the airplane approaches, a person standing on the ground will not be able to hear it until it gets past their position, because the sound energy is actually trailing behind the airplane. When the sound of the airplane is heard, it will be in the form of what is called a sonic boom.

## Resonance

All types of matter, regardless of whether it is a solid, liquid, or gas, have a natural frequency at which the atoms within that matter vibrate. If two pieces of matter have the same natural frequency, and one of them starts to vibrate, it can transfer its wave energy to the other one and cause it to vibrate. This transfer of energy is known as resonance. Some piston engine powered airplanes have an rpm range that they are placarded to avoid, because spinning the prop at that rpm can cause vibration problems. The difficulty lies in the natural frequency of the metal in the prop, and the frequency of vibration that will be set up with a particular tip speed for the prop. At that particular rpm, stresses can be set up that could lead to the propeller coming apart.

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