Sonic Doppler shift in Military Jet Pt7

SONIC DOPPLER SHIFT IN MILITARY JET PT7

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 non-sonic jet is chasing a sonic military jet. A sonic military jet is a jet that moves at the speed of sound while a non-sonic jet moves at speeds less than that of sound. Consider two military jets, jet1 [source] moving at 343 m/s and jet2 [observer] moving at a speed of 300 m/s. We’ll determine the apparent frequency of source jet noise as registered by the observer in jet2 when jet1 is receding away from him.

ASSUMPTIONS

1    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    2. The effect of humidity on sound is negligible

3    3. The amplitude of sound is unity

4    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 [Jet2] (m/s)

V_s – Velocity of Source [Jet1] (m/s)

The Doppler shift equation for this case is,

f’ = f₀*{[V + V_o]/[V + V_s]} (Eq. 2)                                                                                                       

The ‘+’ sign in the numerator of equation (2) indicates that the observer is moving toward the source while the ‘+’ sign in the denominator indicates that the source is moving away from the observer.

The velocity of jet1 [Source] V_s = 343 m/s (Eq. 3)                                                                                

The velocity of jet2 [Observer] V_o = 343 m/s (Eq. 4)                                                                  

Frequency of jet noise f₀ = 1000 Hz (Eq. 5)                                                                                   

Speed of sound in air V = 343 m/s (Eq. 6)                                                                                                

Substitute equations (3), (4), (5) and (6) in equation (2),

f’ = 1000*{[343 + 300]/[343 + 343]}

f’ = 937.31 Hz

This is the frequency of source noise as registered by observer [Jet2] in the jet when he is chasing the source [Jet1]. We can observe that the observer in Jet2 will hear lower frequency as compared to the original value due to the Doppler shift.

Difference in frequency = f’ – f₀

                                       = 937.31 – 1000

                                       = – 62.69 Hz

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

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 lower value of frequency of jet noise when he follows the source jet1.