The displacement of a particle of a string carrying a travelling wave is given by $y = (3\text{ cm}) \sin 6…
The displacement of a particle of a string carrying a travelling wave is given by $y = (3\text{ cm}) \sin 6.28 (0.50x - 50t)$ ($x \rightarrow$ in cm, $t \rightarrow$ in second). What would be the speed of the wave? [UK PMT 2015]
$200\text{ cms}^{-1}$
$150\text{ cms}^{-1}$
$100\text{ cms}^{-1}$
$50\text{ cms}^{-1}$
Solution
The displacement of the particle is given by
$y = 3 \sin 6.28 (0.50x - 50t)$
$\text{Speed of wave}, v = \frac{\text{Coefficient of } t}{\text{Coefficient of } x} = \frac{50}{0.50} = 100\text{ cm s}^{-1}$