A wave on a string passes the point x = 0 with amplitude A angular frequency $\omega ,$ and average power P. As the wave travels down the string it gradually looses energy. 

At the point $x=l$, the average power is $\frac{P_0}{2},$ , then at $x=l$

As the wave propagates down the string, the frequency of wave remains same, even though the energy of wave is decreasing, this is because of the fact that frequency is the property of source. And decrease in energy causes the decrease in amplitude of wave.

From $P_{\text{average }}=\frac{\mu v{A}^2{\omega }^2}{2}$, we can find amplitude at $x=l.$