Question

shock waves and sonic boom
if $\frac{u}{source}> \frac{v}{sound}$ 340 m/s
$sin\theta=\frac{h}{x}=\frac{vt}{ut}=\frac{v}{u}$
$u > v$
$m = \frac{1}{sin\theta}=\frac{u}{v}>1$
when $u = v$, $m = 1$
$u = 2v$, $m = 2$
mark number

Explanation:

Step1: Identify the key - concepts

The problem involves the relationship between the speed of a source ($u$) and the speed of sound ($v = 340\ m/s$), and the formation of shock - waves and sonic booms. The Mach number ($M$) is defined as $M=\frac{u}{v}$, and the angle of the shock - wave cone $\theta$ is related to the speeds by $\sin\theta=\frac{v}{u}$.

Step2: Analyze the cases

When $u = v$, $M = 1$ (the source is moving at the speed of sound). When $u=2v$, $M = 2$ (the source is moving at twice the speed of sound). The formula $\sin\theta=\frac{v}{u}$ shows that as the speed of the source $u$ increases relative to the speed of sound $v$, the angle $\theta$ of the shock - wave cone decreases.

Answer:

The Mach number $M$ is a key parameter in understanding shock - waves and sonic booms. When $u>v$, shock - waves are formed. The angle of the shock - wave cone $\theta$ is given by $\sin\theta=\frac{v}{u}$, and $M=\frac{u}{v}$. When $u = v$, $M = 1$ and when $u = 2v$, $M=2$.