Question

The displacement wave in a string is $y=\left(3\text{cm}\right)\sin 6.28(0.5x-50t)$ where $x$ is in centimeters and $t$ in seconds. The wavelength and velocity of the wave is

• A. $2\text{cm},100{\text{cms}}^{-1}$
• B. $10\text{cm},50{\text{cm}}^{-1}$
• C. $20\text{cm},2{\text{ms}}^{-1}$
• D. $2\text{m},100{\text{ms}}^{-1}$

Answer 1

The correct option is A $2\text{cm},100{\text{cms}}^{-1}$

Given, $y=\left(3\text{cm}\right)\sin 6.28(0.5x-50t)$
As we know that
$k=\frac{2\pi }{\lambda }$
or $\lambda =\frac{2\pi }{k}=\frac{6.28}{6.28\left(0.5\right)}=2\text{cm}$
Also,
$v=\frac{\omega }{k}=\frac{50\times 6.28}{0.5\times 6.28}=100{\text{cms}}^{-1}$