Name: sonic booms and supersonic motion
Uploaded: 2023-04-30T11:12:06.000Z
Duration: 1 min 16 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.6

PS.6.c

Shock Waves

例えば、飛行機などの音源が、速度 vs で静止した観測者に向かって移動するとします。空気中の音速がvの場合、マッハ数は2つの速度の比率として定義されます。
vsがvより大きい場合、マッハ数は1よりも大きくなり、その速度は超音速と呼ばれます。次に、ドップラーの公式によれば、音の観測周波数は負であり、これは事実上不可能です。
それどころか、音源が音を通過するまで、観察者は音を知覚しません。
音波は、3次元の円錐の線に沿って建設的に干渉します。円錐内では、それらは破壊的に干渉します。したがって、円錐のエッジは、音がなく、破壊的な干渉がない領域の鋭い分割器です。結果として生じるパターンは衝撃波と呼ばれます。
幾何学的な概念を適用すると、円錐角度の正弦はマッハ数の逆数に等しくなります。
衝撃波が突然やってくることをソニックブームといいます。高圧のため、移動する飛行機によって生成されるソニックブームは窓を粉々にし、私たちの神経をガタガタさせる可能性があります。

衝撃波

観測された音波の周波数のドップラー公式を導出する際、媒体内の音の速度は媒体を通過する音源の速度よりも速いと想定されます。 この条件が破られると、衝撃波が発生します。

発生源の速度が音速に近づくと、発生源から発せられる連続する波面間の建設的な干渉が発生します。 当初、科学者たちは、この建設的な干渉により非常に高い圧力が発生し、たとえば飛行機は音速を突破できず、最終的には破壊されるだろうと考えていました。 しかし、飛行機は現在、超音速とも呼ばれる音速を超える速度で飛行できるようになりました。 それらは、背後に見慣れた円錐形の波の構造を作成します。

衝撃波の現象は 3 次元であり、円錐の端に沿った圧力の急激な差からその名前が付けられました。 この円錐は音源に沿って移動し、マッハ数 (音源の速度を音速で割ったもの) が大きいほど狭くなります。 観測者は衝撃波を衝撃波が通過した後にのみ体験することができます。 その際、ソニックブームとして知られる突然の圧力変化が発生します。

衝撃波は、船首航跡と呼ばれる一般的な波現象の特殊なケースです。 衝撃波と同じ原理が、表面水波などの他の波にも当てはまります。 アヒルや汽船が水面上を高速で移動すると、船首の航跡が水面上に残ります。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/17-8-shock-waves"> から編集されたものです。 Openstax, University Physics Volume 1, Section 17.8: Shock Waves.</a>

音波の観測周波数のドップラー式を導出する一方で、媒体内の音速は...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Sound

KEY TERMS AND CONCEPTS

主要用語と概念

sonic booms and supersonic motion

Sonic booms and supersonic motion happen when a sound source moves as fast as, or faster than, sound in the medium. In the Doppler formula for sound, it is usually assumed that sound travels faster than the source. When that assumption fails, a shock wave can form.

As the source gets close to the speed of sound, successive wavefronts build up by constructive interference right behind it. Scientists once thought this pressure buildup would keep an airplane from breaking the sound barrier and might even destroy it. Airplanes can now travel at supersonic speeds, which are speeds greater than the speed of sound.

A supersonic source creates a cone of waves behind it. This three-dimensional shape is called a shock wave. The name comes from the sharp pressure change along the edges of the cone. The cone moves with the source, and it becomes narrower when the Mach number is higher. The Mach number is the speed of the source divided by the speed of sound.

An observer does not feel the shock wave until the source has passed by. At that moment, the observer experiences a sudden pressure change called a sonic boom. Shock waves are also a special case of a broader wave pattern called a bow wake. The same idea appears in surface water waves, such as the wake left by a fast-moving duck or steamer on the water.

Sonic Booms and Supersonic Motion

sound waves

How Sound Travels Through Matter

Sound travels through matter as pressure changes in a medium. These changes make the particles of the medium move back and forth around their mean position. Sound can also be modeled as particle displacement as the wave passes through air, water, or another material. In most fluids, sound waves are longitudinal waves. That means the particles vibrate in the same direction that the wave moves. Fluids do not support lateral pressure well, so sound in liquids and gases mainly moves this way. <br...

sound as pressure waves

Sound Pressure in Longitudinal Waves

Sound waves are longitudinal waves that create changing pressure in a medium. Their displacement amplitude can be modeled as a function of position and time. As one column of the medium moves, nearby columns also move. The difference between these successive displacements produces a pressure change compared with the surrounding pressure. This pressure change is called gauge pressure. It varies across the medium because the pressure fluctuation depends on how much one point is displaced...

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perception of sound waves

How Ear Sensitivity Shapes Sound

The human ear does not respond the same way to every sound frequency. Sounds with the same pressure can seem louder or softer when their frequencies change. Ear health also affects this perception, and hearing can decline with age. Regular exposure to loud noises may also damage the ears over time. Pitch depends on both frequency and pressure amplitude, which is the size of the sound wave’s pressure change. Two sounds with the same frequency and pressure amplitude have the same pitch. If the...

speed of sound in solids and liquids

Why Sound Moves Faster in Dense Materials

Sound moves faster in solids and liquids because their particles are close together and can pass along disturbances quickly. Most solids and liquids are incompressible, which means their densities stay nearly constant throughout. When an external force acts on them, the molecules try to return to their original positions. That restoring motion happens because the particles interact with one another. These interactions let sound waves carry information through the material. As a result, sound...

speed of sound in gases

What Changes Sound Speed in Gases?

Sound speed in gases depends on gas properties, pressure, volume, and temperature. Gas molecules move freely, so gases are highly compressible. Because of that compressibility, sound waves travel more slowly through gases than through many other media. The speed of sound in an ideal gas can be found using thermodynamics. Thermodynamics links pressure, volume, and temperature, which helps describe how sound moves through a gas. Newton's laws of motion and the continuity equation from fluid...

deriving the speed of sound in a liquid

Sound Speed in Fluids: Bulk Modulus

Sound speed in fluids depends on a fluid’s bulk modulus and density. These two properties describe how stiff the fluid is and how much inertia it has. For mechanical waves in a fluid, that relationship follows the same pattern used for Young’s modulus and density in solids. The speed of sound in a liquid can be derived by treating the wave as a longitudinal wave moving through the medium. The derivation uses the gauge pressure expression and the impulse-momentum theorem. This same result...

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sound intensity

Measuring How Loud Sound Is

Sound intensity helps describe how loud a sound source is. It depends on how energetically the source vibrates, because those vibrations make the molecules in the medium vibrate as well. Intensity is the energy emitted per unit time per unit area. The area must be perpendicular to the direction the sound wave travels. Using time and area makes the measure reflect the source’s own loudness, even when the source vibrates over a longer time or spreads energy over a larger area. A sound source...

sound intensity level

Measuring Sound with Decibels

Sound intensity level helps measure how loud sound is. The human ear sends sound waves to the brain, and the brain turns those waves into hearing. The loudness of the surrounding environment affects whether a person can tell different sound sources apart. The ear can detect a very wide range of sound intensity. Because of that range, scientists use a logarithmic scale to describe intensity level. Intensity level is a ratio of two intensities, so it has no unit. The standard reference is the...

intensity and pressure of sound waves

Sound Intensity from Displacement and Pressure

Sound intensity can be linked to displacement and pressure in a wave. The key idea is to use the wave expressions and the definition of intensity. To do that, the power carried by the particles is written as force times velocity, and the force per unit area is treated as pressure. The particle velocity can be found from the displacement of the medium. A sinusoidal term averages to zero over time because it is positive and negative for equal parts of each cycle. Its square does not average to...

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sound waves: interference

Sound Wave Interference in Speakers

Sound wave interference can change the loudness of sound when two waves meet. Sound waves may be modeled as longitudinal waves, where molecules move around an equilibrium position, or as pressure waves. When two identical waves from the same source overlap, their crests or troughs can add together. This is called constructive interference, and it increases amplitude. If identical waves start in phase but travel different path lengths, they can become out of phase. Then a crest can meet a...

interference: path lengths

Interference from Different Path Lengths

Interference from different path lengths explains how two sound sources can create changing patterns in space. The sources may or may not start in phase, but they emit waves at the same frequency. When they are in phase, they are called coherent sources, and that is easy to arrange by feeding both speakers from the same source, such as a tuning fork. These synchronized sources start with the same frequency and the same phase. As the waves move outward, they travel different distances to reach...

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sound waves: resonance

Sound Waves in Tubes and Strings

Sound waves can form resonance patterns in strings and tubes when the boundary conditions match the wave frequency. On a string under tension, symmetrical boundary conditions create a node at each end. A node is a fixed point where the string does not move. Some frequencies then produce standing waves, while other frequencies interfere destructively. Resonance also appears in a hollow tube. In a tube closed at one end and open at the other, a vibrating tuning fork near the open end sends an...

beats

Sound Interference and Beats

Sound interference creates beats when two or more close frequencies combine. In music, this shows up as a changing loudness that rises and falls. The pattern comes from superposition, the adding together of waves. Constructive interference makes the sound stronger, while destructive interference makes it weaker. Music usually contains many changing frequencies from instruments and voices. A single sound at one frequency for a long time can feel dull or even irritating. It can sound like the...

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doppler effect - i

Doppler Shift in Sound and Light

The Doppler effect describes how the frequency of a wave changes when the source and the observer move relative to each other. It was named after the Austrian physicist and mathematician Christian Johann Doppler in 1842. He studied both moving sources and moving observers. A simple example is an ambulance passing a person standing on a street corner. As the ambulance approaches, the siren seems louder. As it moves away, the sound gets quieter. The pitch also changes. The high siren sound...

doppler effect - ii

Doppler Radar and Heart Blood Flow

Doppler effect applications appear in weather forecasting and medical imaging. In these uses, a change in frequency helps show motion. The reflected signal can reveal whether an object is moving toward or away from the source. Meteorologists use Doppler radar to study weather events. A transmitter sends radio waves at a set frequency toward the sky from a weather station. The waves bounce off clouds and precipitation and return to the station. If the reflected radio frequency decreases, the...

shock waves

Sonic booms and supersonic motion happen when a sound source moves as fast as, or faster than, sound in the medium. In the Doppler formula for sound, it is usually assumed that sound travels faster than the source. When that assumption fails, a shock wave can form. As the source gets close to the speed of sound, successive wavefronts build up by constructive interference right behind it. Scientists once thought this pressure buildup would keep an airplane from breaking the sound barrier and...

echo

Echo Sound and Distance Detection

Echo is a reflected sound that returns after the original sound has been heard. The human ear cannot tell two sounds apart if they arrive within about 0.1 seconds of each other. When the reflected sound takes longer than that to return, the ear hears two separate sounds instead of one. This effect is easy to notice when the sound source is close to a surface that sends the sound back. If the sound and its reflection are separated by enough time, the result is an echo. A minimum distance of...

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key terms and concepts

Explore how supersonic motion creates shock waves, cone-shaped wave patterns, and sonic booms, plus why faster sources make narrower cones.

Sonic Booms and Supersonic Motion | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

PH.5

PH.5.b

Alabama Course of Study Science

9-12

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

9-12.P.3.7.b

Next Generation Science Standards

High School

HS-PS4-1

Florida Department of Education

SC.912.P.10

SC.912.P.10.21

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

P-PS4-2

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-1.

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. ...

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be ...

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a ...

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The ...

/files/media/science-education/science-education-thumbs/14722.jpg

problem-solving-tuning-of-a-guitar-string

Problem-Solving: Tuning of a Guitar String

In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or ...

/files/media/science-education/science-education-thumbs/14744.jpg

Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

The student will investigate and understand that waves are important in the movement of energy. Key ideas include energy may be transferred in the form of longitudinal and transverse waves;

PS.6.a

Sound Waves

Sound waves can be thought of as fluctuations in the pressure of a medium through which they propagate. Since the pressure also makes the medium&#39;s ...

Sound as Pressure Waves

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As ...

Perception of Sound Waves

The human ear is not equally sensitive to all frequencies in the audible range. It may perceive sound waves with the same pressure but different ...

Speed of Sound in Solids and Liquids

Most solids and liquids are incompressible&#8212;their densities remain constant throughout. In the presence of an external force, the molecules tend to ...

Speed of Sound in Gases

The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. ...

Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid&#39;s elastic modulus and inertia. The two relevant ...

The student will investigate and understand that waves are important in the movement of energy. Key ideas include mechanical waves need a medium to transfer energy;

PS.6.b

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second ...

Sound Waves: Interference

Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure ...

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two ...

Sound Waves: Resonance

Resonance is produced depending on the boundary conditions imposed on a wave. Resonance can be produced in a string under tension with symmetrical ...

Beats

The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples ...

While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the ...

Echo

The human ear cannot distinguish between two sources of sound if they happen to reach within a specific time interval, typically 0.1 seconds apart. More ...

The student will investigate and understand that waves are important in the movement of energy. Key ideas include waves can interact; and

Ultrasonography

Ultrasonography is an imaging technique that uses high-frequency sound waves to visualize the body&#39;s internal structures. It is a non-invasive and ...

assessing-blood-pressure-using-a-doppler-ultrasound

Assessing Blood pressure using a doppler ultrasound

To obtain accurate blood pressure measurements in clinical settings, especially when traditional methods are insufficient, healthcare professionals ...

The student will investigate and understand that waves are important in the movement of energy. Key ideas include energy associated with waves has many applications.

PS.6.d

Sonic Booms and Supersonic Motion

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