From which condition are the normal modes for the case of small hand drums decided?

$A$ travelling wave represented by $y = A \sin (\omega t - kx)$ is superimposed on another wave represented by $y = A \sin (\omega t + kx)$. The resultant is

$A$ wave represented by the equation $y_1 = a \cos(kx - \omega t)$ is superimposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave is

$A$ string of length $1\,m$ and linear mass density $0.01\,kg/m$ is stretched to a tension of $100\,N$. When both ends of the string are fixed,the three lowest frequencies for standing waves are $f_1, f_2$,and $f_3$. When only one end of the string is fixed,the three lowest frequencies for standing waves are $n_1, n_2$,and $n_3$. Then:

$A$ wave $y = a \sin(\omega t - kx)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is

Which of the following statements is true regarding stationary waves?