Question

Q. A supersonic Jet is moving with a certain velocity, such that vertex of mach cone is 60°. What is the ratio of the velocity of Jet to sound?
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Answer 1

The ratio of the velocity of Jet to velocity of sound is 2 : √3

Explanation:

The relation between angle of mach cone vertex $\alpha$, velocity of sound $v_s$ and velocity of supersonic object $v_o$ is given by

$\sin\alpha=\frac{v_s}{v_o}$

Given that

$\alpha=60^\circ$

Therefore,

$\frac{v_s}{v_o}=\sin 60^\circ$

$\implies \frac{v_s}{v_o}=\frac{\sqrt{3}}{2}$

$\implies \frac{v_o}{v_s}=\frac{2}{\sqrt{3}}$

$\implies v_o: v_s=2:\sqrt{3}$

Therefore, the ratio of the velocity of Jet to velocity of sound is 2 : √3

Hope this answer is helpful.

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Answer 2

Explanation:

sinα=

V

o

V

s

,

V

s

is the velcity of sound in air and V

o

is the velocity of object.

α is the half angle of the cone vertex.

sinα=

V

o

V

s

=

2

1

,

α=30degrees

angle of cone=60degrees