Question

A sinusoidal wave travelling in the positive direction of x on a stretched string has amplitude 2.0 cm, wavelength 1 m and wave velocity 5.0 m/s. At x = 0 and t = 0, it is given that displacement y = 0 and $\frac{\partial y}{\partial t}<0$. Express the wave function correctly in the from y = f(x, t) :-

• A. y = (0.04 m) [sin ($\pi m^{-}1)$x - (10$\pi s^{-}1\left)t\right]$
• B. y = (0.02 m) cos 2$\pi$ (x-5t)
• C. y = (0.02 m) [sin (2$\pi m^{-}1)$x - (10$\pi s^{-}1\left)t\right]$
• D. y = (0.02 m) cos $\pi$ $(x-5t+\frac{1}{4})$

Answer 1

The correct option is C y = (0.02 m) [sin (2$\pi m^{-}1)$x - (10$\pi s^{-}1\left)t\right]$

HENCE
y = (0.02 m) [sin (2πm−1)πm−1)x - (10πs−1)t]