Question

The equation of a simple harmonic wave is given by $y=3\text{sin}\frac{\pi }{2}(50t-x)$
where $x$ and $y$ are in metres and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is

• A. $\frac{2}{3}\pi$
• B. $\frac{3}{2}\pi$
• C. $3\pi$
• D. $2\pi$

Answer 1

The correct option is B $\frac{3}{2}\pi$

Given: $y=3\text{sin}\frac{\pi }{2}(50t-x)$
$V_{\text{{max}}}=A\omega ;V_w=\frac{\omega }{k}$
$\frac{V_{max}}{V_{\omega }}=Ak$

From the given equation:$A=3;k=\pi /2$

$\frac{V_{max}}{V_{\omega }}=Ak$
$\Rightarrow \frac{V_{max}}{V_{\omega }}=\frac{3}{2}\pi$
Hence, option $\left(C\right)$ is correct.