Question

The equation of a travelling wave is, $y=60\cos (1800t-6x)),$ where $y$ is in $\text{microns}$, $t$ in $\text{sec}$ and $x$ in $\text{metres}$. The ratio of maximum particle velocity to velocity of wave propagation is

• A. $3.6$
• B. $3.6\times {10}^{-6}$
• C. $3.6\times {10}^{-11}$
• D. $3.6\times {10}^{-4}$

Answer 1

The correct option is D $3.6\times {10}^{-4}$

Maximum particle velocity, $(v_P{)}_{\text{max}}=\omega A$
Wave velocity, $v=\frac{\omega }{k}$
From given wave equation,
$\omega =1800,k=6$
$A=60\text{micron}=60\times {10}^{-6}\text{m}$
$\Rightarrow$ Required ratio $=\frac{\omega A}{\frac{\omega }{k}}=kA$
$\Rightarrow \text{Required ratio}=60\times {10}^{-6}\times 6$
$\therefore \text{Required ratio}=3.6\times {10}^{-4}$