Question

A generator at one end of a very long string creates a wave given by
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x+\left(8.00s^{-1}\right)t]$
and a generator at the other end creates the wave
$y=\left(6.0cm\right)\cos \frac{\pi }{2}[\left(2.00m^{-1}\right)x-\left(8.00s^{-1}\right)t]$
For $x\ge 0,$ what is the location of the node having the second smallest value of x?

Answer 1

For any node on th string at any instant of time $y=0$

So by substituting at $t=0,y=0$.

we have $0=\cos \pi x$

solving for x:

$x=n/2$

The second smallest x at which a node exist is $n=3$

at $x=1.5m$