The equation of a stationary wave is $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin (200 \pi t)$,where $x$ is in $cm$ and $t$ is in $sec$. The separation between consecutive nodes will be .... $cm$.

The given diagram shows a detector placed between a transmitter of sound waves and a metal plate. At three adjacent points,$R, S$ and $T$,the meter shows zero intensity. Which of the following is the frequency of the emitted wave in $Hz$? (Take the velocity of sound as $v = 300 \, m/s$)

$A$ 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:

$A$ wave travelling along a uniform string represented by $Y=A \sin (\omega t-k x)$ is superimposed on another wave travelling along the same string represented by $Y=A \sin (\omega t+k x)$. The resultant is

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

$A$ 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 meters and $t$ is in seconds. Which statement$(s)$ is/are correct?