For the stationary wave $y = 4 \sin \left(\frac{\pi x}{15}\right) \cos (96 \pi t)$,the distance between a node and the next antinode is

The equation of a standing wave in a string fixed at both ends is given as $y = 2A \sin kx \cos \omega t$. The amplitude and frequency of a particle vibrating at the midpoint between an antinode and a node are respectively:

$A$ wave $y = a \cos (kx + \omega t)$ superimposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

Length of a string tied to two rigid supports is $40 \ cm$. The maximum wavelength (in $cm$) of a stationary wave produced on it is ... $cm$.

$A$ 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 .... $cm$.

$A$ stationary wave is formed having $4$ nodes along the $120 \,cm$ length of the string. The wavelength of the wave is (in $\,cm$)