$A$ wave $y = a \cos(kx - \omega t)$ superposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10 \, ms^{-1}$. If the minimum time interval between two instants when the string is flat is $0.5 \, s$,the wavelength of the waves is .... $m$

In case of a stationary wave pattern,which of the following statements is $CORRECT$?

Which two of the given transverse waves will produce stationary waves when superimposed?
${z_1} = a\cos(kx - \omega t)$.....$(A)$
${z_2} = a\cos(kx + \omega t)$.....$(B)$
${z_3} = a\cos(ky - \omega t)$.....$(C)$

$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$

$A$ stationary wave is formed with $3$ nodes along the length of a string of $90 \ cm$. The wavelength of the wave is: (in $cm$)