Question

The equation of a wave travelling on a stretched string is $y=4\sin 2\pi (\frac{t}{0.02}-\frac{x}{100})$ , here $x,y$ are in cm and $t$ in seconds.

The ratio of maximum particle velocity and wavelength is

• A. $\pi$
• B. $2\pi$
• C. $3\pi$
• D. $4\pi$

Answer 1

Answer: (D)

$4\pi$

Given:

$y=4Sin2\pi (\frac{t}{0.02}-\frac{x}{100})$

maximum particle velocity $v=Aw$
wavelength $\lambda =\frac{2\pi }{K}$

$\therefore \frac{v}{\lambda }=\frac{4\left(\frac{2\pi }{0.02}\right)}{\frac{2\pi }{2\pi }\times 100}=\frac{4\left(2\pi \right)}{2}$

Ratio $=4\pi$