A wave is given by the equation
` y = 10 sin 2 pi (100 t - 0.02 x) + 10 sin 2 pi (100 t + 0.02 x)`
Find the loop length , frequency , velocity and maximum amplitude of the stationary wave produced.

Explanation

We know the equation of a stationary wave is given by
`y = A Sin [(2pi)/(lambda)(vt-x)] + Asin[(2pi)/(lambda)(vt + x)]`
` = 2 A cos" (2pix)/(lambda)(sin)(2pivt)/(lamda)`
= ` R sin" (2pi)/(lambda)vt`
Here `R = 2 A cos" (2pix)/(lambda)` is the amplitude of medium particle situated at a distance x.
The given equation can be expressed as
`y = 10sin [(2pi)/(50)(5000 t - x)] + 10sin[(2pi)/(50)(5000 t + x)]`
`2 xx 10cos ((2pix)/(50)) sin((2pi)/(50)5000t)` Comparing it with standard equation of stationary wave, we get wavelength
`lambda = 50 units`
Wave velocity ` v = 5000 units`
Thus amplitude `R = 2xx 10 cos (2pix)/(50)`
and maximum amplitude `R_(max) = 2xx 10 = 20 units`
As wave velocity is ` v = 5000 units`
Frequency `(v)/(lambda) = (5000)/(5) = 100 units`
and loop length is
`(lambda)/(2) = (50)/(2)` = 25 units.