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 .... $cm$.

Explain the reflection of a wave at a rigid support.

$A$ progressive wave travelling in the positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by

$A$ stationary wave is represented by $y = 12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two successive antinodes is (in $cm$)

$A$ 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 .... $cm$.

For a stationary wave,$Y = 10 \sin \left( \frac{\pi x}{15} \right) \cos (48 \pi t) \text{ cm}$,the distance between a node and the successive antinode is (in $\text{ cm}$)