Sonic doppler shift in Military Jet

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 ± V_o]/[V ± V_s]} (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}

V_o – Velocity of observer (m/s)

V_s – Velocity of Source [Jet] (m/s)

Since the observer is stationary,

V_o = 0 (Eq. 2)                                                                                                                                        

Substitute equation (2) in equation (1),

f’ = f₀*{[V]/[V – V_s]} (Eq. 3)                                                                                                                

The ‘–’ sign in the denominator of equation (3) indicates that the source is approaching the observer.

The velocity of jet V_s = 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.