Question

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

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

Answer 1

Answer: (A)

$2cm,100cm{s}^{-1}$

$\left(a\right)k=\frac{2\pi }{\lambda }$
$or\lambda =\frac{2\pi }{k}=\frac{6.28}{6.28\left(0.5\right)}=2cm$
$v=\frac{w}{k}=\frac{50\times 6.28}{0.5\times 6.28}=100cm{s}^{-1}$