Question

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

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

Answer 1

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

General expression for transverse wave on a string is
$y=A\sin (kx-\omega t)$

Comparing with the given equation,
$k=\frac{2\pi }{\lambda }=6.28\times 0.5$
or $\lambda =\frac{2\pi }{k}=\frac{6.28}{6.28\left(0.5\right)}=2\text{cm}$
& $\omega =6.28\times 50{\text{rad s}}^{-1}$
$\Rightarrow v=\frac{\omega }{k}=\frac{50\times 6.28}{0.5\times 6.28}=100{\text{cm s}}^{-1}$