Question

A progressive wave is represented by [y=Asin2π(0.5t-0.1x).find
Period
Frequency
Wavelength
Velocity of the wave

Answer 1

The wave equation is as follows

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

In our case

$$y(x,t)=A\sin [2\pi(0.5t-0.1x)]$$

So, the period

$$T=2\:\rm{s}$$

The frequency

$$f=\frac{1}{T}=\frac{1}{2}=0.5\:\rm{Hz}$$

The wavelength

$$\lambda=10\:\rm{m}$$

The velocity of the wave

$$v=\frac{\lambda}{T}=\frac{10\:\rm{m}}{2\:\rm{s}}=5\:\rm{m/s}$$