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A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle σof the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the sonic boom? Neglect the variation of the speed of sound with altitude.

Short Answer

Expert verified

a) Angle of the shock-wave cone is α=36.03c

b) Time taken is 2.94s

Step by step solution

01

Step 1:

Given data:

The shock wave is produced by a sound source that moves faster than sound

sinα=vvS

Here,

vspeed of sound

vsspeed of source

localid="1664344351725" αangle of shock wave

02

Step 2:

a) As the Mach number =vSv=1.7

sim=vvS=11.7α=sin-111.7=36.03o

Hence, the angle of the shock-wave cone isα=36.03°

03

Step 3:

b) Time-taken is

Tanα=tan36.03°=dvSt=0.727

On putting the values;

t=dvs×0.727=1250m0.727×1.7×344m/s=2.94s

Hence, the time taken is 2.94s

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