Question

A wave is given by the equation y(x, t) = 4.0cos(0.5πx−10 πt) m. The speed of the wave is:

Answer 1

The equation of a wave

$$y(x,t)=A \cos\left(\frac{2\pi}{T} t-\frac{2\pi}{\lambda}x\right)$$

Hence, $T=4\:\rm s, \; \lambda=0.2\:\rm m.$

The speed of wave

$$v=\frac{\lambda}{T}=\frac{0.2}{4}=0.05\:\rm m/s=5\:\rm cm/s.$$