$A$ wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed 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 fixed at both ends vibrates in a resonant mode with a separation of $2.0 \, cm$ between consecutive nodes. For the next higher resonant frequency,this separation is reduced to $1.6 \, cm$. The length of the string is .... $cm$.

In a stationary wave,if the distance between a consecutive node and antinode is $5 \ cm$,then find the distance between two consecutive antinodes. (in $cm$)

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

The displacement of a string is given by,
$y(x, t) = 10 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$
where $x$ and $y$ are in $m$ and $t$ is in $sec$. The length of the string is $1.5 \ m$ and its mass is $3 \times 10^{-2} \ kg$.
Select the correct statement$(s)$ below:
$(A)$ It represents a progressive wave of frequency $60 \ Hz$.
$(B)$ It represents a standing wave of frequency $60 \ Hz$.
$(C)$ It is the result of two waves of wavelength $3 \ m$,frequency $60 \ Hz$ each travelling with a speed of $180 \ m/s$ in opposite directions.
$(D)$ Reflection occurs from a free end.

What will be the change in phase of a wave due to reflection from a rigid support?