Question

A wave is represented by the equation $y=$ $(0.02\, m) \sin (5 \pi x-20 t)$. The minimum distance between the two particles always having the same speed is. (Assume $x$ and $t$ are in SI units)

• A. $0.02 \, m$
• B. $0.4\, m$
• C. $0.8 \, m$
• D. $0.2 \, m$

Answer 1

Answer: (D)

Given, wave equation, $y=0.02 \sin (5 \pi x-20 t) m$
As we know that,
Minimum distance between two particles
$=\frac{\text { Wavelength }(\lambda)}{2}$
and according to wave equation,
Wave number, $k=5 \pi m^{-1}$
Angular frequency, boldsymbol $\omega=20$ rads $^{-1}$
Since, $k=\frac{2 \pi}{\lambda}$
$\therefore \lambda=\frac{2 \pi}{k}=\frac{2 \pi}{5 \pi}$
$=\frac{2}{5}=0.4 m$
$\therefore$ Minimum separation between two particles
$=\frac{0.4}{2}=0.2 m$