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Chapter 2: Q57E (page 541)

A jet plane flies overhead at Mach 1.70 and at a constant altitude of 1250 m. (a) What is the angle 蟽of 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 伪=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

sin伪=vvS

Here,

v鈫�speed of sound

vs鈫�speed of source

localid="1664344351725" 伪鈫�angle of shock wave

02

Step 2:

a) As the Mach number =vSv=1.7

sim=vvS=11.7伪=sin-111.7=36.03o

Hence, the angle of the shock-wave cone is伪=36.03掳

03

Step 3:

b) Time-taken is

罢补苍伪=tan36.03掳=dvSt=0.727

On putting the values;

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

Hence, the time taken is 2.94s

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