Question

The equation of a wave is represented by $y={10}^{4}sin(100t-\frac{x}{10})$ m, then the velocity of wave will be :

• A. 100 m/s
• B. 4 m/s
• C. 1000 m/s
• D. 0.00 m/s

Answer 1

The correct option is C 1000 m/s

General wave equation is $y=Asin(\omega t-kx)$.

So from given wave equation we get :

$\omega =100$

$k=\frac{1}{10}$

We know velocity = frequency x wavelength.

$\omega =2\times \pi \times \nu =100$

So,

$\nu =\frac{100}{2\pi },$

$k=\frac{2\pi }{\lambda }=\frac{1}{10}$

$\lambda =2\pi \times 10$

Therefore,

$v=\nu \times \lambda$

$v=\frac{100}{2\pi }\times 2\pi \times 10m/s$

In above equation $2\pi$ going to cancel out,

$v=1000m/s$.