Question

The displacement of a particle of a string carrying a travelling wave is given by $y=3\sin \left[6.28\right(0.50x-50t\left)\right]$
$(x\to \text{in cm},y\to \text{cm},t\to \text{in second})$.
What would be the speed of the wave?

• A. $200{\text{cm s}}^{-1}$
• B. $150{\text{cm s}}^{-1}$
• C. $100{\text{cm s}}^{-1}$
• D. $50{\text{cm s}}^{-1}$

Answer 1

The correct option is C $100{\text{cm s}}^{-1}$

Displacement of a particle on string(carrying a travelling wave) is given,
$y=3\sin \left[6.28\right(0.5x-50t\left)\right]$
where $x,y$ are in $\text{cm}$, $t$ is in seconds.
Comparing with equation of progressive wave,
$y=A\sin (kx-\omega t)$
We get
$k=6.28\times 0.5;\omega =6.28\times 50$
We know that $k=\frac{2\pi }{\lambda }$
$\Rightarrow \frac{2\times 3.14}{\lambda }=6.28\times 0.5$
$\Rightarrow \lambda =2\text{cm}$
and $\omega =2\pi f$
$\Rightarrow 2\pi f=6.28\times 50$
$\Rightarrow 6.28f=6.28\times 50$
$\Rightarrow f=50\text{Hz}$
Speed of wave is,
$v=f\lambda$
$\therefore v=50\times 2=100{\text{cm s}}^{-1}$