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Picture is a photograph of the blue glow in a reactor pool.
The blue glow in this research reactor pool is Cerenkov radiation caused by subatomic particles traveling faster than the speed of light in water. (credit: U.S. Nuclear Regulatory Commission)

Summary

  • The Mach number is the velocity of a source divided by the speed of sound, M = v s v .
  • When a sound source moves faster than the speed of sound, a shock wave is produced as the sound waves interfere.
  • A sonic boom is the intense sound that occurs as the shock wave moves along the ground.
  • The angle the shock wave produces can be found as sin θ = v v s = 1 M .
  • A bow wake is produced when an object moves faster than the speed of a mechanical wave in the medium, such as a boat moving through the water.

Key equations

Pressure of a sound wave Δ P = Δ P max sin ( k x ω t + ϕ )
Displacement of the oscillating molecules of a
sound wave
s ( x , t ) = s max cos ( k x ω t + ϕ )
Velocity of a wave v = f λ
Speed of sound in a fluid v = β ρ
Speed of sound in a solid v = Y ρ
Speed of sound in an ideal gas v = γ R T M
Speed of sound in air as a function of temperature v = 331 m s T K 273 K = 331 m s 1 + T C 273 ° C
Decrease in intensity as a spherical wave expands I 2 = I 1 ( r 1 r 2 ) 2
Intensity averaged over a period I = P A
Intensity of sound I = ( Δ p max ) 2 2 ρ v
Sound intensity level β ( d B ) = 10 log 10 ( I I 0 )
Resonant wavelengths of a tube closed at one end λ n = 4 n L , n = 1 , 3 , 5 ,…
Resonant frequencies of a tube closed at one end f n = n v 4 L , n = 1 , 3 , 5 ,…
Resonant wavelengths of a tube open at both ends λ n = 2 n L , n = 1 , 2 , 3 ,…
Resonant frequencies of a tube open at both ends f n = n v 2 L , n = 1 , 2 , 3 ,…
Beat frequency produced by two waves that
differ in frequency
f beat = | f 2 f 1 |
Observed frequency for a stationary observer
and a moving source
f o = f s ( v v v s )
Observed frequency for a moving observer
and a stationary source
f o = f s ( v ± v o v )
Doppler shift for the observed frequency f o = f s ( v ± v o v v s )
Mach number M = v s v
Sine of angle formed by shock wave sin θ = v v s = 1 M

Conceptual questions

What is the difference between a sonic boom and a shock wave?

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Due to efficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number). If the aircraft flies from warm air into colder air, should it increase or decrease its speed? Explain your answer.

The speed of sound decreases as the temperature decreases. The Mach number is equal to M = v s v , so the plane should slow down.

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When you hear a sonic boom, you often cannot see the plane that made it. Why is that?

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Problems

An airplane is flying at Mach 1.50 at an altitude of 7500.00 meters, where the speed of sound is v = 343.00 m/s . How far away from a stationary observer will the plane be when the observer hears the sonic boom?

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A jet flying at an altitude of 8.50 km has a speed of Mach 2.00, where the speed of sound is v = 340.00 m/s . How long after the jet is directly overhead, will a stationary observer hear a sonic boom?

θ = 30.02 ° v s = 680.00 m/s tan θ = y v s t , t = 21.65 s

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The shock wave off the front of a fighter jet has an angle of θ = 70.00 ° . The jet is flying at 1200 km/h. What is the speed of sound?

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A plane is flying at Mach 1.2, and an observer on the ground hears the sonic boom 15.00 seconds after the plane is directly overhead. What is the altitude of the plane? Assume the speed of sound is v w = 343.00 m/s .

sin θ = 1 M , θ = 56.47 ° y = 9.31 km

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Questions & Answers

principle of superposition?
Naveen Reply
principle of superposition allows us to find the electric field on a charge by finding the x and y components
Kidus
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
Daniel Reply
gravity pulls towards a mass...like every object is pulled towards earth
Ashok
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find * The angular acceleration
Goodness Reply
what is the formula for pressure?
Goodness Reply
force/area
Kidus
force is newtom
Kidus
and area is meter squared
Kidus
so in SI units pressure is N/m^2
Kidus
In customary United States units pressure is lb/in^2. pound per square inch
Kidus
who is Newton?
John Reply
scientist
Jeevan
a scientist
Peter
that discovered law of motion
Peter
ok
John
but who is Isaac newton?
John
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
Daniel
and the color spectrum
Daniel
what is a scalar quantity
Peter Reply
scalar: are quantity have numerical value
muslim
is that a better way in defining scalar quantity
Peter
thanks
muslim
quantity that has magnitude but no direction
Peter
upward force and downward force lift
adegboye Reply
upward force and downward force on lift
adegboye
hi
Etini
hi
elo
hy
Xander
Hello
Jux_dob
hi
Peter
Helo
Tobi
Yes what about it?
Daniel
what's the answer? I can't get it
Rachel Reply
what is the question again?
Sallieu
What's this conversation?
Zareen
what is catenation? and give examples
sununu
How many kilometres in 1 mile
Nessy
1.609km in 1mile
Faqir
what's the si unit of impulse
Iguh Reply
The Newton second (N•s)
Ethan
what is the s. I unit of current
Roland Reply
Amphere(A)
imam
thanks man
Roland
u r welcome
imam
the velocity of a boat related to water is 3i+4j and that of water related to earth is i-3j. what is the velocity of the boat relative to earth.If unit vector i and j represent 1km/hour east and north respectively
Pallavi Reply
what is head to tail rule?
kinza Reply
Explain Head to tail rule?
kinza
what is the guess theorem
Monu Reply
viva question and answer on practical youngs modulus by streching
Akash Reply
send me vvi que
rupesh
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
Isaac
yoo the ans is 193
Joseph
whats a two dimensional force
Jimoh Reply
what are two dimensional force?
Ahmad
Practice Key Terms 3

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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