Sonic doppler shift in Military Jet Pt2

SONIC DOPPLER SHIFT IN MILITARY JET PT2

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 away from 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 receding away from 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 receding away from 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’ = 500 Hz

This is the frequency of jet noise as registered by the stationary observer in a building when a military jet is receding away from him. We can observe that the frequency reduced to half its original value which means the observer will only hear half of the original frequency.

Difference in frequency = f’ – f₀

                                       = 500 – 1000

                                       = – 500 Hz

Negative sign indicates that apparent frequency is less than original but magnitude is always positive.

CONCLUSION

We thus determined the apparent frequency of jet noise as registered by the observer due to Doppler shift and concluded that the observer will be able to hear only half of the original frequency of jet noise when he watches the jet receding away from him.