Question

For a given wave , maximum particle velocity is $5$ times the wave velocity corresponding to the equation,
$y=A\sin (5t-0.05x)$ in which $A$ , $x$ are in metres and $t$ is in seconds. The value of $A$ is

Answer 1

We know that ,
Maximum particle velocity $\left(v_p\right)=\omega A$
and wave velocity $v=\frac{\omega }{k}$
Given ,
Equation of wave , $y=A\sin (5t-0.05x)$
Comparing this with,
$y=A\sin (\omega t-kx)$ we get,
$\omega =5\text{rad/s}$ and $k=0.05{\text{m}}^{-1}$
From the data given in the question ,
$\omega A=5\times \frac{\omega }{k}$
$\Rightarrow A=\frac{5}{k}=\frac{5}{0.05}=100\text{m}$