A progressive wave moving along X-axis is represented by $y=A\sin \left[\frac{2\mathrm{\pi }}{\lambda }\left(vt-x\right)\right]$. The wavelength $\left(\lambda \right)$ at which the maximum particle velocity is $3$ times the wave velocity is:

Sound waves are passing through two routes-one is straight and the other along a semicircular path of radius $r$ and again combined into one pipe and superimposed as shown in the figure. If the velocity of sound waves in the pipe is $v$, then the frequencies of resultant waves of maximum amplitude will be integral multiples of