Question

The equation of a plane progressive wave by y = 2 $sin(5\pi t-0.5\pi x)$. The speed of the wave [x and y are in metre and t is in second] is

• A. 10 ms⁻¹
• B. 5 ms⁻¹
• C. 0.5 ms⁻¹
• D. 2.5 ms⁻¹

Answer 1

The correct option is A

10 ms⁻¹

Compare the equation with standard form y = $\alpha sin(\omega x-kx)$

$\omega =5\pi rad{s}^{-1}k=0.5\pi rad{m}^{-1}$. Wave velocity

$v=\frac{\omega }{k}=\frac{5\pi }{0.5\pi }=10m{s}^{-1}$