The figure shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ among $1, 2,$ and $3$ are in phase with point $X$?

$A$ $20 \ cm$ long string,having a mass of $1.0 \ g$,is fixed at both the ends. The tension in the string is $0.5 \ N$. The string is set into vibrations using an external vibrator of frequency $100 \ Hz$. Find the separation (in $cm$) between the successive nodes on the string.

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{\pi x}{3} \cos 40\pi t$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The separation between two adjacent nodes is..... $cm$.

When a string is stretched between two rigid supports,kept under a certain tension,and vibrated,what is the nature of the standing wave formed?

Two identical progressive waves moving in opposite directions superimpose to produce a stationary wave. The wavelength of each progressive wave is $\lambda$. The wavelength of the stationary wave is

$A$ wave of frequency $100 \, Hz$ is sent along a string towards a fixed end. When this wave travels back after reflection,a node is formed at a distance of $10 \, cm$ from the fixed end of the string. The speed of the incident (and reflected) wave is .... $m/s$.