The sonic boom problem - Katerina Kaouri

5,024,883 views ใƒป 2015-02-10

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Ido Dekkers ืขืจื™ื›ื”: Tal Dekkers
00:06
Humans have been fascinated with speed for ages.
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ื”ืื ื•ืฉื•ืช ื”ื™ืชื” ืžื•ืงืกืžืช ืžืžื”ื™ืจื•ืช ื‘ืžืฉืš ืขื™ื“ื ื™ื.
00:10
The history of human progress is one of ever-increasing velocity,
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ื”ื”ืกื˜ื•ืจื™ื” ืฉืœ ื”ื”ืชืงื“ืžื•ืช ื”ืื ื•ืฉื™ืช ื”ื™ื ืื—ืช ืฉืœ ืžื”ื™ืจื•ืช ืžืชื’ื‘ืจืช,
00:14
and one of the most important achievements in this historical race
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ื•ืื—ื“ ืžื”ื”ืฉื’ื™ื ื”ื›ื™ ื—ืฉื•ื‘ื™ื ื‘ืžืจื•ืฅ ื”ื”ืกื˜ื•ืจื™ ื”ื–ื”
00:18
was the breaking of the sound barrier.
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ื”ื™ื” ืฉื‘ื™ืจืช ืžื—ืกื•ื ื”ืงื•ืœ.
00:21
Not long after the first successful airplane flights,
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ืœื ื”ืจื‘ื” ืื—ืจื™ ื”ื˜ื™ืกื•ืช ื”ืžื•ืฆืœื—ื•ืช ื”ืจืืฉื•ื ื•ืช,
00:24
pilots were eager to push their planes to go faster and faster.
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ื˜ื™ื™ืกื™ื ื”ื™ื• ืœื”ื•ื˜ื™ื ืœื“ื—ื•ืฃ ืืช ื”ืžื˜ื•ืกื™ื ืฉืœื”ื ืœื˜ื•ืก ืžื”ืจ ื™ื•ืชืจ ื•ื™ื•ืชืจ.
00:29
But as they did so, increased turbulence
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ืื‘ืœ ื›ืฉื”ื ืขืฉื• ื–ืืช, ืžืขืจื‘ื•ืœื•ืช ืžืชื’ื‘ืจื•ืช
00:32
and large forces on the plane prevented them from accelerating further.
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ื•ื›ื•ื—ื•ืช ื’ื“ื•ืœื™ื ืขืœ ื”ืžื˜ื•ืก ืžื ืขื• ืžื”ื ืœื”ืื™ืฅ ื™ื•ืชืจ.
00:37
Some tried to circumvent the problem through risky dives,
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ื›ืžื” ื ื™ืกื• ืœืขืงื•ืฃ ืืช ื”ื‘ืขื™ื” ื“ืจืš ืฆืœื™ืœื•ืช ืžืกื•ื›ื ื•ืช,
00:41
often with tragic results.
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ืฉื”ืจื‘ื” ืคืขืžื™ื ื”ืกืชื™ื™ืžื• ื‘ื˜ืจื’ื“ื™ื•ืช.
00:44
Finally, in 1947, design improvements,
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ืœื‘ืกื•ืฃ, ื‘ 1947, ืฉื™ืคื•ืจื™ ืขื™ืฆื•ื‘,
00:47
such as a movable horizontal stabilizer, the all-moving tail,
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ื›ืžื• ืžื™ื™ืฆื‘ื™ื ืื•ืคืงื™ื™ื ื ืขื™ื, ื”ื–ื ื‘ ื”ื ืข ื›ื•ืœื•,
00:52
allowed an American military pilot named Chuck Yeager
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ืืคืฉืจื• ืœื˜ื™ื™ืก ื”ืฆื‘ื ื”ืืžืจื™ืงืื™ ืฆ'ืืง ื™ื™ื’ืจ
00:55
to fly the Bell X-1 aircraft at 1127 km/h,
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ืœื”ื˜ื™ืก ืืช ืžื˜ื•ืก ื”ื‘ืœ X-1 ื‘ืžื”ื™ืจื•ืช ืฉืœ 1127 ืงืž"ืฉ,
01:03
becoming the first person to break the sound barrier
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ื•ืœื”ืคื•ืš ืœืื“ื ื”ืจืืฉื•ืŸ ืœืฉื‘ื•ืจ ืืช ืžื—ืกื•ื ื”ืงื•ืœ
01:06
and travel faster than the speed of sound.
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ื•ืœื ื•ืข ืžื”ืจ ืžืžื”ื™ืจื•ืช ื”ืงื•ืœ.
01:09
The Bell X-1 was the first of many supersonic aircraft to follow,
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ื”ื‘ืœ X-1 ื”ื™ื” ื”ืจืืฉื•ืŸ ื‘ื™ืŸ ื”ืจื‘ื” ืžื˜ื•ืกื™ื ืขืœ ืงื•ืœื™ื™ื ืื—ืจื™ื•,
01:13
with later designs reaching speeds over Mach 3.
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ืขื ืขื™ืฆื•ื‘ื™ื ืžืื•ื—ืจื™ื ื™ื•ืชืจ ืฉืžื’ื™ืขื™ื ืœืžื”ื™ืจื•ืช ืฉืœ ื™ื•ืชืจ ืžืžืืš ืฉืœื•ืฉ.
01:17
Aircraft traveling at supersonic speed create a shock wave
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ืžื˜ื•ืกื™ื ื”ื ืขื™ื ื‘ืžื”ื™ืจื•ืช ืขืœ ืงื•ืœื™ื•ืช ื™ื•ืฆืจื™ื ื’ืœ ื”ืœื
01:21
with a thunder-like noise known as a sonic boom,
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ืขื ืจืขืฉ ื“ืžื•ื™ ืจืขื ืฉื™ื“ื•ืข ื›ื‘ื•ื ืขืœ ืงื•ืœื™,
01:25
which can cause distress to people and animals below
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ืฉื™ื›ื•ืœ ืœื’ืจื•ื ืœื—ืฅ ืœืื ืฉื™ื ื•ื—ื™ื•ืช ืžืชื—ืช
01:29
or even damage buildings.
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ืื• ืืคื™ืœื• ืœื”ื–ื™ืง ืœื‘ื ื™ื™ื ื™ื.
01:31
For this reason,
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ืžื”ืกื™ื‘ื” ื”ื–ื•,
ืžื“ืขื ื™ื ืžืกื‘ื™ื‘ ืœืขื•ืœื ื—ืงืจื• ื‘ื•ืžื™ื ืขืœ ืงื•ืœื™ื™ื,
01:32
scientists around the world have been looking at sonic booms,
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01:35
trying to predict their path in the atmosphere,
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ื‘ื ื™ืกื™ื•ืŸ ืœื—ื–ื•ืช ืืช ื”ื ืชื™ื‘ ืฉืœื”ื ื‘ืื˜ืžื•ืกืคื™ืจื”,
01:37
where they will land, and how loud they will be.
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ื”ื™ื›ืŸ ื”ื ื™ืคื’ืขื•, ื•ื›ืžื” ื—ื–ืงื™ื ื”ื ื™ื”ื™ื•.
01:42
To better understand how scientists study sonic booms,
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ื›ื“ื™ ืœื”ื‘ื™ืŸ ื˜ื•ื‘ ื™ื•ืชืจ ืื™ืš ืžื“ืขื ื™ื ื—ื•ืงืจื™ื ื‘ื•ืžื™ื ืขืœ ืงื•ืœื™ื™ื,
01:45
let's start with some basics of sound.
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ื‘ื•ืื• ื ืชื—ื™ืœ ืขื ื”ืขืงืจื•ื ื•ืช ื”ื‘ืกื™ืกื™ื™ื ืฉืœ ืฆืœื™ืœ.
01:48
Imagine throwing a small stone in a still pond.
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ื“ืžื™ื™ื ื• ื–ืจื™ืงืช ืื‘ืŸ ืงื˜ื ื” ืœื‘ืจื™ื›ื” ืฉืงื˜ื”.
01:51
What do you see?
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ืžื” ืชืจืื•?
01:53
The stone causes waves to travel in the water
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ื”ืื‘ืŸ ื’ื•ืจืžืช ืœื’ืœื™ื ืœื ื•ืข ื‘ืžื™ื
01:55
at the same speed in every direction.
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ื‘ืื•ืชื” ืžื”ื™ืจื•ืช ื‘ื›ืœ ื›ื™ื•ื•ืŸ.
01:58
These circles that keep growing in radius are called wave fronts.
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ื”ืขื™ื’ื•ืœื™ื ื”ืืœื” ืฉืžืžืฉื™ื›ื™ื ืœื’ื“ื•ืœ ื‘ืจื“ื™ื•ืก ื ืงืจืื™ื ื—ื–ื™ืช ื”ื’ืœ.
02:02
Similarly, even though we cannot see it,
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ื‘ื“ื•ืžื”, ืœืžืจื•ืช ืฉืื ื—ื ื• ืœื ืจื•ืื™ื ืื•ืชื,
02:05
a stationary sound source, like a home stereo,
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ืžืงื•ืจ ืงื•ืœ ื ื™ื™ื—, ื›ืžื• ืžืขืจื›ืช ืกื˜ืจืื• ื‘ื™ืชื™ืช,
02:09
creates sound waves traveling outward.
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ื™ื•ืฆืจ ื’ืœื™ ืงื•ืœ ืฉื ืขื™ื ื”ื—ื•ืฆื”.
02:12
The speed of the waves depends on factors
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ื”ืžื”ื™ืจื•ืช ืฉืœ ื”ื’ืœื™ื ื”ืืœื” ืชืœื•ื™ื” ื‘ื’ื•ืจืžื™ื
02:14
like the altitude and temperature of the air they move through.
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ื›ืžื• ื”ื’ื•ื‘ื” ื•ื”ื˜ืžืคืจื˜ื•ืจื” ืฉืœ ื”ืื•ื™ืจ ื“ืจื›ื• ื”ื ื ืขื™ื.
02:18
At sea level, sound travels at about 1225 km/h.
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ื‘ื’ื•ื‘ื” ืคื ื™ ื”ื™ื, ืงื•ืœ ื ืข ื‘ืขืจืš ื‘ 1225 ืงืž"ืฉ.
02:24
But instead of circles on a two-dimensional surface,
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ืื‘ืœ ื‘ืžืงื•ื ืขื™ื’ื•ืœื™ื ืขืœ ืžืฉื˜ื— ื“ื• ืžื™ืžื“ื™,
02:27
the wave fronts are now concentric spheres,
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ื—ื–ื™ืชื•ืช ื”ื’ืœื™ื ื”ืŸ ืขื›ืฉื™ื• ื›ื“ื•ืจื™ื ืงื•ื ืฆื ื˜ืจื™ื™ื,
02:30
with the sound traveling along rays perpendicular to these waves.
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ืขื ื”ืงื•ืœ ืฉื ืข ืœืื•ืจืš ืงืจื ื™ื™ื ืฉื ื™ืฆื‘ื•ืช ืœื’ืœื™ื ื”ืืœื”.
02:35
Now imagine a moving sound source, such as a train whistle.
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ืขื›ืฉื™ื• ื“ืžื™ื™ื ื• ืžืงื•ืจ ืงื•ืœ ื ืข, ื›ืžื• ืฉืจื™ืงืช ืจื›ื‘ืช.
02:40
As the source keeps moving in a certain direction,
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ื›ืฉื”ืžืงื•ืจ ืžืžืฉื™ืš ืœื”ืชืงื“ื ื‘ื›ื™ื•ื•ืŸ ืžืกื•ื™ื,
02:43
the successive waves in front of it will become bunched closer together.
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ื”ื’ืœื™ื ื”ื‘ืื™ื ืœืคื ื™ื• ื™ืชืฆื˜ื•ืคืคื• ืœืคื ื™ื•.
02:47
This greater wave frequency is the cause of the famous Doppler effect,
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ืชื“ื™ืจื•ืช ื”ื’ืœื™ื ื”ื’ื‘ื•ื”ื” ื™ื•ืชืจ ื”ื™ื ื”ื’ื•ืจื ืœืืคืงื˜ ื“ื•ืคืœืจ ื”ืžืคื•ืจืกื,
02:52
where approaching objects sound higher pitched.
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ื‘ื• ืขืฆืžื™ื ืžืชืงืจื‘ื™ื ื ืฉืžืขื™ื ืขื ื’ื•ื‘ื” ืฆืœื™ืœ ื’ื‘ื•ื” ื™ืชืจ.
02:55
But as long as the source is moving slower than the sound waves themselves,
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ืื‘ืœ ื›ืœ ืขื•ื“ ื”ืžืงื•ืจ ื ืข ืœืื˜ ื™ื•ืชืจ ืžื’ืœื™ ื”ืงื•ืœ ืขืฆืžื,
02:59
they will remain nested within each other.
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ื”ื ื™ืฉืืจื• ืžืงื•ื ื ื™ื ืื—ื“ ื‘ืชื•ืš ื”ืฉื ื™.
03:02
It's when an object goes supersonic, moving faster than the sound it makes,
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ื–ื” ื›ืฉื”ืขืฆื ื ืข ื‘ืžื”ื™ืจื•ืช ืขืœ ืงื•ืœื™ืช, ื ืข ืžื”ืจ ืžื”ืงื•ืœ ืฉื”ื•ื ื™ื•ืฆืจ,
03:07
that the picture changes dramatically.
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ืฉื”ืชืžื•ื ื” ืžืฉืชื ื” ื“ืจืžื˜ื™ืช.
03:10
As it overtakes sound waves it has emitted,
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ื›ืฉื”ื•ื ืขื•ืงืฃ ื’ืœื™ ืงื•ืœ ืฉื”ื•ื ืขืฆืžื• ื™ืฆืจ,
03:13
while generating new ones from its current position,
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ื‘ืขื•ื“ื• ืžื™ื™ืฆืจ ื—ื“ืฉื™ื ืžื”ืžื™ืงื•ื ื”ื ื•ื›ื—ื™ ืฉืœื•,
03:15
the waves are forced together, forming a Mach cone.
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ื”ื’ืœื™ื ื ืœื—ืฆื™ื ื™ื—ื“, ื•ื™ื•ืฆืจื™ื ืืช ื—ืจื•ื˜ ื”ืžืืš.
03:19
No sound is heard as it approaches an observer
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ืืฃ ืฆืœื™ืœ ืœื ื ืฉืžืข ื›ืฉื”ื•ื ืžืชืงืจื‘ ืœืฆื•ืคื”
03:22
because the object is traveling faster than the sound it produces.
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ืžืคื ื™ ืฉื”ืื•ื‘ื™ื™ืงื˜ ื ืข ืžื”ืจ ื™ื•ืชืจ ืžื”ืงื•ืœ ืฉื”ื•ื ื™ื•ืฆืจ.
03:27
Only after the object has passed will the observer hear the sonic boom.
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ืจืง ืื—ืจื™ ืฉื”ื•ื ืขื•ื‘ืจ ื”ืฆื•ืคื” ื™ืฉืžืข ืืช ื”ื‘ื•ื ื”ืขืœ ืงื•ืœื™.
03:33
Where the Mach cone meets the ground, it forms a hyperbola,
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ื‘ืžืงื•ื ื‘ื• ื—ืจื•ื˜ ื”ืžืืš ืคื•ื’ืฉ ืืช ื”ืื“ืžื”, ื”ื•ื ื™ื•ืฆืจ ื”ื™ืคืจื‘ื•ืœื”,
03:37
leaving a trail known as the boom carpet as it travels forward.
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ื•ืžืฉืื™ืจ ืฉื•ื‘ืœ ื”ื™ื“ื•ืข ื‘ืฉื˜ื™ื— ื”ื‘ื•ื ื›ืฉื”ื•ื ื ืข ืงื“ื™ืžื”.
03:41
This makes it possible to determine the area affected by a sonic boom.
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ื–ื” ืขื•ืฉื” ืืช ื–ื” ืœืืคืฉืจื™ ืœืงื‘ื•ืข ืืช ื”ืื–ื•ืจ ืฉืžื•ืฉืคืข ืขืœ ื™ื“ื™ ื”ื‘ื•ื ื”ืขืœ ืงื•ืœื™.
03:46
What about figuring out how strong a sonic boom will be?
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ืžื” ืขื ืœื”ื‘ื™ืŸ ื›ืžื” ื—ื–ืง ื”ื‘ื•ื ื”ืขืœ ืงื•ืœื™ ื™ื”ื™ื”?
03:49
This involves solving the famous Navier-Stokes equations
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ื–ื” ื›ื•ืœืœ ืืช ืคืชื™ืจืช ืžืฉื•ื•ืื•ืช ื ื‘ื™ื™ืจ ืกื˜ื•ืงืก ื”ืžืคื•ืจืกืžื•ืช
03:52
to find the variation of pressure in the air
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ื›ื“ื™ ืœืžืฆื•ื ืืช ื”ืฉืชื ื•ืช ื”ืœื—ืฅ ื‘ืื•ื™ืจ
03:56
due to the supersonic aircraft flying through it.
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ื‘ืฉืœ ื”ืžื˜ื•ืก ื”ืขืœ ืงื•ืœื™ ืฉื ืข ื“ืจื›ื•.
03:59
This results in the pressure signature known as the N-wave.
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ื”ืชื•ืฆืื” ื”ื™ื ื—ืชื™ืžืช ืœื—ืฅ ืฉื™ื“ื•ืขื” ื›ื’ืœ N.
04:03
What does this shape mean?
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ืžื” ื”ืžืฉืžืขื•ืช ืฉืœ ื”ืฆื•ืจื” ื”ื–ื•?
04:05
Well, the sonic boom occurs when there is a sudden change in pressure,
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ื•ื‘ื›ืŸ, ื”ื‘ื•ื ื”ืขืœ ืงื•ืœื™ ืžืชืจื—ืฉ ื›ืฉื™ืฉ ืฉื™ื ื•ื™ ืคืชืื•ืžื™ ื‘ืœื—ืฅ,
04:09
and the N-wave involves two booms:
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ื•ื’ืœื™ ื” N ื›ื•ืœืœื™ื ืฉื ื™ ื‘ื•ืžื™ื:
04:11
one for the initial pressure rise at the aircraft's nose,
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ืื—ื“ ืœืขืœื™ื™ืช ื”ืœื—ืฅ ื”ืจืืฉื•ื ื™ืช ื‘ืืฃ ืฉืœ ื”ืžื˜ื•ืก,
04:15
and another for when the tail passes,
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ื•ื ื•ืกืคืช ื›ืฉื”ื–ื ื‘ ืขื•ื‘ืจ,
04:18
and the pressure suddenly returns to normal.
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ื•ื”ืœื—ืฅ ืคืชืื•ื ื—ื•ื–ืจ ืœื ื•ืจืžืœื™.
04:21
This causes a double boom,
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ื–ื” ื’ื•ืจื ืœื‘ื•ื ื›ืคื•ืœ,
04:23
but it is usually heard as a single boom by human ears.
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ืื‘ืœ ื–ื” ื‘ื“ืจืš ื›ืœืœ ื ืฉืžืข ื›ื‘ื•ื ื™ื—ื™ื“ ืœืื•ื–ื ื™ ื”ืื ืฉื™ื.
04:26
In practice, computer models using these principles
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ืœืžืขืฉื”, ืžื•ื“ืœื™ื ืžืžื•ื—ืฉื‘ื™ื ืฉืžืฉืชืžืฉื™ื ื‘ืขื™ืงืจื•ืŸ ื”ื–ื”
04:29
can often predict the location and intensity of sonic booms
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ื™ื›ื•ืœื™ื ื”ืจื‘ื” ืคืขืžื™ื ืœื—ื–ื•ืช ืืช ื”ืžื™ืงื•ื ื•ื”ืขื•ืฆืžื” ืฉืœ ื‘ื•ืžื™ื ืขืœ ืงื•ืœื™ื™ื
04:34
for given atmospheric conditions and flight trajectories,
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ืขื‘ื•ืจ ืžืฆื‘ื™ื ืื˜ืžื•ืกืคืจื™ื™ื ื•ืœื ืชื•ื ื™ื ืขื ื›ื™ื•ื•ื ื™ ื˜ื™ืกื”,
04:37
and there is ongoing research to mitigate their effects.
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ื•ื™ืฉ ืžื—ืงืจ ืžืชืžืฉืš ืœืžืชืŸ ืืช ื”ืฉืคืขื•ืช ื”ืืœื•.
04:40
In the meantime, supersonic flight over land remains prohibited.
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ื‘ื™ื ืชื™ื™ื, ื˜ื™ืกื” ืขืœ ืงื•ืœื™ืช ืžืขืœ ื”ืื“ืžื” ื ืฉืืจืช ืืกื•ืจื”.
04:45
So, are sonic booms a recent creation?
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ืื–, ื”ืื ื‘ื•ืžื™ื ืขืœ ืงื•ืœื™ื™ื ื”ื ื™ืฆื™ืจื” ืขื“ื›ื ื™ืช?
04:48
Not exactly.
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ืœื ื‘ื“ื™ื•ืง.
04:50
While we try to find ways to silence them,
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ื‘ืขื•ื“ ืื ื—ื ื• ืžื ืกื™ื ืœืžืฆื•ื ื“ืจื›ื™ื ืœื”ืฉืชื™ืง ืื•ืชื,
04:52
a few other animals have been using sonic booms to their advantage.
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ื—ื™ื•ืช ืื—ืจื•ืช ื”ืฉืชืžืฉื• ื‘ื‘ื•ืžื™ื ืขืœ ืงื•ืœื™ื™ื ืœืชื•ืขืœืชืŸ.
04:56
The gigantic Diplodocus may have been capable of cracking its tail
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ื”ื“ื™ืคืœื•ื“ื•ืงื•ืก ื”ืขืฆื•ื ื”ื™ื” ืื•ืœื™ ืžืกื•ื’ืœ ืœื”ืฆืœื™ืฃ ื‘ื–ื ื‘ื•
05:00
faster than sound, at over 1200 km/h, possibly to deter predators.
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ืžื”ืจ ืžืžื”ื™ืจื•ืช ื”ืงื•ืœ, ืžืขืœ 1200 ืงืž"ืฉ, ื›ื ืจืื” ื›ื“ื™ ืœื”ืจืชื™ืข ื˜ื•ืจืคื™ื.
05:07
Some types of shrimp can also create a similar shock wave underwater,
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ื›ืžื” ืžื™ื ื™ื ืฉืœ ืฉืจื™ืžืคืก ื™ื›ื•ืœื™ื ืœื™ืฆื•ืจ ื’ืœ ื”ืœื ื“ื•ืžื” ื‘ืžื™ื,
05:12
stunning or even killing pray at a distance
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ื•ืœื”ืžื ืื• ืืคื™ืœื• ืœื”ืจื•ื’ ื˜ืจืฃ ืžืžืจื—ืง
05:16
with just a snap of their oversized claw.
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ืขื ื”ืงืฉื” ื‘ืฆื‘ืชื ื”ืขื ืงื™ืช.
05:19
So while we humans have made great progress
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ืื– ื‘ืขื•ื“ ืื ื—ื ื• ื”ืื ืฉื™ื ื”ืชืงื“ืžื ื• ื”ืจื‘ื”
05:22
in our relentless pursuit of speed,
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ื‘ืžืจื“ืฃ ื—ืกืจ ื”ืžื ื•ื— ืฉืœื ื• ืื—ืจื™ ื”ืžื”ื™ืจื•ืช,
05:24
it turns out that nature was there first.
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ืžืกืชื‘ืจ ืฉื”ื˜ื‘ืข ื”ื™ื” ืฉื ืงื•ื“ื.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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