Chapter 12, Problem 18TE

Does the conical angle of a shock wave open wider, narrow down, or remain constant as a supersonic aircraft increases its speed?

Solution

To determine:

Whether the conical angle of a shock wave open wider, narrow down, or remain constant when supersonic aircraft increases its speed.

Answer:

The conical angle of a shock wave will be narrow down.

Explanation:

When the speed of a source surpasses the speed of sound $(v>c)$ , the wavefront lag following the source in a cone-shaped region with the source at the peak. The edge of the cone forms a supersonic wavefront with an extraordinarily large-amplitude called a shock wave.

Write the expression for the mach angle at the vertex of the shock cone.

$\sin \mu =\frac{c}{v}$

Here,

c is the speed of light

v is the speed of object

Now, when the speed of supersonic aircraft increases, the mach angle got reduced. Therefore, the conical angle of a shock wave will be narrow down.

Conclusion:

Therefore, the conical angle of a shock wave will be narrow down.