Can two waves of the same frequency and amplitude travelling in the same direction give rise to a stationary wave after superposition?

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the velocity and amplitude of the component travelling waves. 

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the node closest to the origin in the region $x>0.$

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the antinode closest to the origin in the region $x>0.$

Two travelling waves of equal amplitudes and equal frequencies move in opposite direction along a string. They interfere to produce a standing wave having the equation. 

$=A\cos kx\sin \omega t$ 

in which $A=1.0 \mathrm{mm}, k=1.57{ \mathrm{cm}}^{-1}$and $\omega =78.5{ \mathrm{s}}^{-1}.$ 

Find the amplitude of the particle at $x=2.33 \mathrm{cm}.$

Two sinusoidal waves combining in a medium are described by the wave functions 

$y_1=(3.0 \mathrm{cm})\mathrm{sin\pi }(\mathrm{x}+0.60\mathrm{t})$
$y_2=(3.0 \mathrm{cm})\mathrm{sin\pi }(\mathrm{x}-0.60\mathrm{t})$

where $x$ is in centimetres and $t$ is in seconds. Determine the maximum transverse position of an element of the medium at

$x=0.250 \mathrm{cm}$

Two sinusoidal waves combining in a medium are described by the wave functions 

$y_1=(3.0 \mathrm{cm})\mathrm{sin\pi }(\mathrm{x}+0.60\mathrm{t})$
$y_2=(3.0 \mathrm{cm})\mathrm{sin\pi }(\mathrm{x}-0.60\mathrm{t})$

where $x$ is in centimetres and $t$ is in seconds. Determine the maximum transverse position of an element of the medium at

$x=0.500 \mathrm{cm}$

Two sinusoidal waves combining in a medium are described by the wave functions 

$y_1=(3.0 cm)\sin \pi (x+0.60t)$
$y_2=(3.0 cm)\sin \pi (x-0.60t)$

where $x$ is in centimetres and $t$ is in seconds. Determine the maximum transverse position of an element of the medium at

$x=1.50 cm$.