Question

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

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

Answer 1

Answer: (A)

$\frac{3}{2}\pi$

From the wave equations, we know that
$v_{max}=a\omega$
$v=n\lambda$
$\frac{v_{max}}{v}=\frac{a\omega }{n\lambda }=\frac{a\left(2\pi n\right)}{n\lambda }=\frac{2\pi a}{\lambda }=\frac{2\pi a}{\frac{2\pi }{K}}$
$=Ka=\frac{\pi }{2}\times 3=\frac{3\pi }{2}$