1) A shock wave is produced when a sound source moves faster than the speed of sound, causing interference of sound waves. 2) When a source exceeds the speed of sound, a shock wave or sonic boom is created outside the Mach cone from constructive interference. Inside the cone, interference is mostly destructive, reducing sound intensity. 3) A sonic boom from an aircraft produces two booms from the nose and tail, heard separately on the ground after the plane passes. Supersonic flights are restricted over land due to potential damage from sonic booms.

1. SHOCK WAVES
By
Dr M. Arunachalam
Head, Dept. of Physics (Rtd.)
Sri SRNM College, Sattur

2. A shock wave is a wave that is produced
when a sound source moves faster than
the speed of sound. They are produced
due to the interference of sound waves.

3. Types of waves
Waves are widely classified into two types
1. Electro magnetic waves (Eg. Light waves, X-rays)
Require no medium for propagation
2. Mechanical waves (Eg. Sound waves, Ultrasonic
waves) Require an elastic medium for propagation

4. Properties of waves
 Amplitude (A): The maximum displacement of the wave
from the mean position
 Wavelength (λ): Distance between the points which are in
the same phase
 Frequency (n): Number of waves crossing a point in one
second
 Time period (T): Time taken by wave to cross a point
 Speed (c) : The distance travelled by the wave in second

5. Relation connecting speed and
frequency c = n λ
(n)
Speed(c)
(A)

6. Doppler Effect
 When there is a relative motion between the source of
the wave (Eg. Sound waves) and the observer there
exists an apparent change frequency
 Definition: Doppler Effect refers to the change in
wave frequency during the relative motion between a
wave source and its observer.
 Discovered by Christian Johann Doppler

7. Formula
 no = n[(c –v)/(c – u)]
 no – Observed frequency
 n – Actual frequency
 c = Velocity of sound
 u– Velocity of the source
 v = Velocity of the observer

8. Different cases
 Case I: An observer moving away from the stationary
source.
 Case II: An observer moving towards the stationary
source.
 Case III: A source moving away from the stationary
observer.
 Case IV: A source moving towards the stationary
observer.

9. Case IV: A source moving towards the
stationary observer
 In that case the above equation becomes
 no = n[c/(c – u)] (since v = 0)
 From this equation we know that, if the velocity of the source
of sound increases the observed frequency no will increase.
 When the source of waves is moving towards the observer they
will have an upward shift in frequency.

10. Source speed - Four cases
1. u = 0
2. u < c
3. u = c
4. u > c

11. Doppler Effect and High Velocity
 no = n[c/(c – u)]
 Further if the velocity of the source is equal to that of
sound, ie. when c = u
 then the denominator is equal to zero, which means the
frequency is infinite.
 What could this mean? What happens when a source
approaches the speed of sound?

12. Pictorial representation
(a) Source at rest
(u = 0)
(b) The source moving
towards the observer with
a speed u less than that of
speed of sound (u< c)

13. At the speed of sound
 At the speed of sound, this result means that in front
of the source, each successive wave interferes with the
previous one because the source moves forward at the
speed of sound. The observer gets them all at the same
instant, so the frequency is infinite

14. At the speed of sound (Fig.) (u = c)
(c) The source moving towards the
observer with a speed equal to the speed
of sound

15. Compare the figures
(a) the source is at rest (u = 0)
(b)The source is moving with a velocity less
than the speed of sound (u < 0)
(c) The source moves at the speed of sound,
Now each successive wave interfere with the
previous one and the observer observes them
all at the same instant (u = c)
(a) (u = 0)
(b) (u < 0)
(c) (u = c)

16. What happens if the speed of source
exceeds the speed of sound?
 It was once argued by some scientists that such a
large pressure wave would result from the
constructive interference of the sound waves, that
it would be impossible for a plane to exceed the
speed of sound because the pressures would be
great enough to destroy the airplane.

17. speed of source > the speed of sound
waves ie.u > c
 Sound waves from a source that moves faster than the
speed of sound spread spherically from the point where
they are emitted, but the source moves ahead of each wave.
 Constructive interference along the lines shown (a cone in
three dimensions) from similar sound waves is arriving
there simultaneously. This superposition forms a
disturbance called a shock wave out side the cone

18. Pictorial representation (u > c)

19. Angle of Shock wave (θ)
 The angle of the shock wave can be found from the
geometry.
 sinθ =
 ct/ut= c/u
 T - Time taken
 c - Velocity of sound
 U - Velocity of source

20. Constructive interference of sound
 Constructive interference along the lines shown
(a cone in three dimensions) from similar sound
waves is arriving there simultaneously.

21. something interesting happens
 If the source exceeds the speed of sound, no sound is
received by the observer until the source has passed,
so that the sounds from the approaching source are
mixed with those from it when receding. This mixing
appears messy, but something interesting happens—
a shock wave (or sonic boom) is created out side
the cone

22. What about inside?
 Inside the cone, the interference is mostly destructive,
so the sound intensity there is much less than on the
shock wave

23. Sonic Boom
 A sonic boom is the intense sound that occurs as the
shock wave moves along the ground.
 The sound associated with shock waves created by an
object travelling through air at supersonic speeds is
called as a sonic boom. Sonic booms are felt as a
thunder like noise a person on the ground hears when
an aircraft flies over head at super sonic speed (u > c)

24. Schematic illustration

25. Occurrence of Shock Wave
 Shock waves are sound waves. They occur in the
atmosphere when aeroplanes break through the sound
barrier.
 Also during explosive events, like during detonations
or lightning strikes or the passage of a bullet

26. How it behaves
 A shock wave is an extremely thin wavefront that
passes tsunami-like through solids, liquids and
gases at high speeds, driven by molecular collisions
at the nanoscale.
 A compression wave—a sudden spike in pressure
followed by a sudden drop in pressure

27. Properties of Shock Waves
 High speed large amplitude compressibility waves
 Like ordinary waves they carry energy
 They can propagate through a medium (Solid, liquid, gas
or plasma
 Across the shock waves there is always extremely rapid
rise in pressure, temperature and density of flow
 Causes abrupt changes in the characteristics of the
medium
 Causes instantaneous change in density, pressure,
temperature , velocity, Mach number

28. Velocity of Shock waves
 It is the velocity at which the shock wave front
travels.
 It is faster than the speed of sound in the material.
 It is also called Explosive velocity, or detonation
velocity or
 velocity of detonation (VoD)

29. Mach number
 The Mach number is the ratio of the speed of a body to
the speed of sound in the surrounding medium. M = u /c
 u - speed of the body
 C – Speed of sound
 We know that sinθ = ct/ut=c/u
 Hence Mach number is the reciprocal of Sinθ

30. More about Supersonic flights
 An aircraft creates two shock waves, one from its nose and one
from its tail.
 Two distinct booms will be heard.
 Separated by exactly the time it would take the aircraft to pass
by a point.
 Observers on the ground often do not see the aircraft creating
the sonic boom, because it has passed by before the shock
wave reaches them, (see Fig.)

31. Two sonic booms experienced by observers,
created by the nose and tail of an aircraft as the
shock wave sweeps along the ground, are observed
on the ground after the plane has passed by.

32. Impact of supersonic flights
 If the aircraft flies close by at low altitude, pressures
in the sonic boom can be destructive and break
windows as well as rattle nerves. Because of how
destructive sonic booms can be, supersonic flights are
banned over populated areas.