<< Chapter < Page Chapter >> Page >
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)


  • 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?

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!


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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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
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
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 is newtom
and area is meter squared
so in SI units pressure is N/m^2
In customary United States units pressure is lb/in^2. pound per square inch
who is Newton?
John Reply
a scientist
that discovered law of motion
but who is Isaac newton?
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
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
and the color spectrum
what is a scalar quantity
Peter Reply
scalar: are quantity have numerical value
is that a better way in defining scalar quantity
quantity that has magnitude but no direction
upward force and downward force lift
adegboye Reply
upward force and downward force on lift
Yes what about it?
what's the answer? I can't get it
Rachel Reply
what is the question again?
What's this conversation?
what is catenation? and give examples
How many kilometres in 1 mile
1.609km in 1mile
what's the si unit of impulse
Iguh Reply
The Newton second (N•s)
what is the s. I unit of current
Roland Reply
thanks man
u r welcome
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?
what is the guess theorem
Monu Reply
viva question and answer on practical youngs modulus by streching
Akash Reply
send me vvi que
a car can cover a distance of 522km on 36 Liter's of petrol, how far can it travel on 14 liter of petrol.
yoo the ans is 193
whats a two dimensional force
Jimoh Reply
what are two dimensional force?
Practice Key Terms 3

Get the best University physics vol... course in your pocket!

Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 1' conversation and receive update notifications?