Question

A transverse wave is given by $A\sin \left(tx\right)$ where A and t are constants. The ratio of wave velocity to maximum particle velocity is

• A. $A$
• B. $\frac{1}{A}$
• C. $1$
• D. none of the above

Answer 1

The correct option is D none of the above

$y=A\sin \left(tx\right)$

Wave velocity $=\frac{\omega }{k}$

Maximum particle velocity $=V_{max}=\omega \sqrt{A^2}=\omega A$

$\Rightarrow \frac{Wavevelocity}{V_{max}}=\frac{\omega /k}{\omega A}=\frac{1}{kA}$

Here, $k=t$ (where $t=$ constant)

$\therefore Ratio=\frac{1}{tA}$

So, option $D$ is correct