Question

The equation of a transverse wave on a stretched string is given by $y=0.05\sin 2\pi (\frac{t}{0.002}-\frac{x}{0.1})$, where $x$ and $y$ are expressed in metre and $t$ in second. The speed of the wave is

• A. $100{\text{ms}}^{-1}$
• B. $50{\text{ms}}^{-1}$
• C. $200{\text{ms}}^{-1}$
• D. $400{\text{ms}}^{-1}$

Answer 1

The correct option is B $50{\text{ms}}^{-1}$

Given, the displacement equation
$y=0.05\sin 2\pi (\frac{t}{0.002}-\frac{x}{0.1})$
Comparing it with equation of progressive wave,
$y=A\sin 2\pi (\frac{t}{T}-\frac{x}{\lambda })$
We get
$T=0.002\text{s};\lambda =0.1\text{m}$
Hence Speed of the wave,
$\Rightarrow v=\frac{\lambda }{T}=\frac{0.1}{0.002}$
$\therefore v=50{\text{ms}}^{-1}$