SONIC DOPPLER SHIFT IN MILITARY JET
INTRODUCTION
We know that Doppler Effect
or Doppler shift occurs between a source and observer when they are in relative
motion with respect to each other. In this case we’ll determine the Doppler
shift that occurs when a sonic military jet is moving toward a stationary
observer in a building. A sonic military jet is a jet that moves at the speed
of sound. Consider a military jet moving at a speed of 343 m/s approaching an
observer who is inside a building. We’ll determine the apparent frequency of
the jet’s noise as registered by the observer.
ASSUMPTIONS
1. The
atmospheric air has standard temperature and pressure conditions
·
Temperature T = 298 K or 25°C or 77°F
·
Pressure = 1 bar = 105 N/m2
2. The
effect of humidity on sound is negligible
3. The
amplitude of sound is unity
4. The
air molecules do not move with respect to source and observer
CALCULATION
The
equation for Doppler shift is given by,
f’
= f0*{[V ± Vo]/[V ± Vs]} (Eq. 1)
f0
– Original frequency (Hz)
f’
– Apparent or observed frequency (Hz)
V
– Velocity of Sound in air at standard temperature and pressure conditions
(m/s) {V = 343 m/s}
Vo
– Velocity of observer (m/s)
Vs
– Velocity of Source [Jet] (m/s)
Since the observer is
stationary,
Vo = 0 (Eq. 2)
Substitute equation (2)
in equation (1),
f’ = f0*{[V]/[V
– Vs]} (Eq. 3)
The ‘–’ sign in the
denominator of equation (3) indicates that the source is approaching the
observer.
The velocity of jet Vs
= 343 m/s (Eq. 4)
Frequency of jet
exhaust noise f0 = 1000 Hz (Eq. 5)
Speed of sound in air V
= 343 m/s (Eq. 6)
Substitute equations
(4), (5) and (6) in equation (3),
f’ = 1000*{343/[343 –
343]}
f’
= ∞
Hz
This is the frequency
of sound as registered by the stationary observer in a building when a military
jet approaches him. The ∞
value indicates that time is 0. It means that the object [jet] is traveling
with sound waves, hence an observer will never hear any sound as there exists
no sound to an observer. However the observer will hear sound when the jet
moves away from him which we’ll discuss in the next post.
Difference in frequency
= f’ – f0
= ∞ – 1000
= ∞ Hz [does not exist]
CONCLUSION
We thus determined
the apparent frequency as registered by the observer due to Doppler shift and
concluded that the observer will not be able to hear anything even though he’ll
be able to see a jet approaching him.
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