$A$ 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 disturbance in a medium is described by $y(x, t) = 0.02 \cos(50 \pi t + \frac{\pi}{2}) \cos(10 \pi x)$,where $x$ and $y$ are in metres and $t$ is in seconds.

The transverse displacement of a string (clamped at both ends) is given by $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \; m$ and its mass is $3.0 \times 10^{-2} \; kg$. Answer the following:
$(a)$ Does the function represent a travelling wave or a stationary wave?
$(b)$ Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength,frequency,and speed of each wave?
$(c)$ Determine the tension in the string.

Consider the three waves $z_1, z_2$ and $z_3$ as $z_1 = A \sin(kx - \omega t)$,$z_2 = A \sin(kx + \omega t)$ and $z_3 = A \sin(ky - \omega t)$. Which of the following represents a standing wave?

$A$ wave travels on a light string. The equation of the wave is $Y = A \sin (kx - \omega t + 30^o)$. It is reflected from a heavy string tied to an end of the light string at $x = 0$. If $64\%$ of the incident energy is reflected,the equation of the reflected 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 .... $cm$.