Question

1. Set up a standing wave pattern and calculate the wave speed using v=f(wavelength) and V= Square root of (Ftension/ u). You only need to do this for one pattern.

Answer 1

The standing wave is a composite wave which is composed from two equal and opposite waves every one has the same speed and wavelength.

So, mathematically it can be expressed by:

y(x,t)= A sin( 2 pi x/ lambda - wt) + A sin (2 pi x/ lambda + wt),

This form can be reduced to the form where time and position are separated:

y(x,t)= 2A sin (2 pi x/ lambda ) cos wt

Because of separation of the time and position, the wave is no longer propagating which means that it does not contain a phase relation like the travelling waves for example sin (2 pi x/ lambda - wt).

Accordingly one can not define for it a phase speed like the elementary wave. Here one can define for it a group velocity which describes the velocity of the envelope which in case of stationary wave is not moving resulting in zero group velocity or wave velocity