Looking for classes? Ksquare Career Institute, Bengaluru →
The equation of a simple harmonic wave is given by $y = 3\sin\frac{\pi}{2}(50t - x)$ 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
$2\pi$
C
$\frac{3}{2}\pi$
D
$3\pi$
Detailed Solution
Comparing with $y = A\sin(\omega t - kx)$: $A = 3$ m, $\omega = 25\pi$ rad/s, $k = \frac{\pi}{2}$ $m^{-1}$
Maximum particle velocity: $v_{max} = A\omega$
Wave velocity: $v_w = \frac{\omega}{k}$
$\frac{v_{max}}{v_w} = \frac{A\omega}{\omega/k} = Ak = 3\times\frac{\pi}{2} = \frac{3}{2}\pi$
Maximum particle velocity: $v_{max} = A\omega$
Wave velocity: $v_w = \frac{\omega}{k}$
$\frac{v_{max}}{v_w} = \frac{A\omega}{\omega/k} = Ak = 3\times\frac{\pi}{2} = \frac{3}{2}\pi$