Answer to Question #86202 in Mechanics | Relativity for Pankaj

Question

the oscillation of two points X1and X2 at X=0 and X=1m respectively are modelled as follows : Y1=0.2 sin 3πt and Y2= 0.2 sin (3πt+ 8π) calculate the wavelength and speed of the associate wave

Answer 1

Let's look at common wave equation:

$$y=A\cdot\text{sin}(\omega t+\frac{2\pi}{\lambda} x).$$

Determine the wavelength:

$$\frac{2\pi}{\lambda} x=8\pi, \to \lambda=0.25\text{ m}.$$

$$\omega=2\pi\nu=3\pi, \to \nu=1.5\text{ Hz}.$$

The speed:

$$v=\lambda \nu=0.375\text{ m/s}.$$