Question

The equation of a progressive wave is $y=0.05\sin (200t-\frac{x}{2})$where $x,y$ are in metres and $t$ in seconds, then

a ) velocity of wave is $100m{s}^{-1}$

b) maximum velocity of particle in the wave is $10m{s}^{-1}$
c) wavelength of wave is $4\pi m$

• A. only a and c are true
• B. only b and c are true
• C. only a and b are true
• D. a,b,c are true

Answer 1

Answer: (B)

only b and c are true

particle velocity $v=\frac{dy}{dx}=200\times 0.05\cos (200t-\frac{x}{2})$
$=10\cos (200t-\frac{x}{2})$
$\therefore$ maximum value is $10m{s}^{-1}$
$k=\frac{2\pi }{\lambda }=\frac{1}{2}\Rightarrow \lambda =4\pi$
Velocity of wave $=\frac{w}{k}=\frac{200}{\frac{1}{2}}=400m{s}^{-1}$