Sonic Doppler shift in Military Jet Pt3

SONIC DOPPLER SHIFT IN MILITARY JET PT3

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 an observer [pilot] in a sonic military jet is moving toward a stationary source. A sonic military jet is a jet that moves at the speed of sound. Consider an observer in a military jet moving at a speed of 343 m/s toward the source. We’ll determine the apparent frequency of the source as registered by the observer in the jet.

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 [Jet] (m/s)

V_s – Velocity of Source (m/s)

Since the source is stationary,

V_s = 0 (Eq.2)                                                                                                                                            

Substitute equation (2) in equation (1),

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

The ‘+’ sign in the numerator of equation (3) indicates that the observer is moving toward the source.

The velocity of jet V_o = 343 m/s (Eq.4)                                                                                                  

Frequency of source 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’ = 2000 Hz

This is the frequency of source noise as registered by observer in the military jet when approaching the source. We can observe that the frequency increased to twice its original value which means the observer will hear twice the original frequency of noise.

Difference in frequency = f’ – f₀

                                       = 2000 – 1000

                                       = 1000 Hz

CONCLUSION

We thus determined the apparent frequency of source noise as registered by the observer due to Doppler shift and concluded that the observer will be able to hear twice the original frequency of sound when he is moving toward the source.