$A$ wave is represented by the equation $y = 10 \sin 2\pi(100t - 0.02x) + 10 \sin 2\pi(100t + 0.02x)$. The maximum amplitude and loop length are respectively:

$A$ string vibrates according to the equation $y = 5 \sin \left( \frac{2\pi x}{3} \right) \cos (20\pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $sec$. The distance between two adjacent nodes is .... $cm$.

The equation of a stationary wave is $Y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$. The distance between two consecutive nodes in metres is

$A$ 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:

$A$ standing wave with a number of loops is produced on a string fixed at both ends. Which one of the following statements is correct?

$A$ 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: