Two sound waves having displacements $x_1=2 \sin (1000 \pi t)$ and $x_2=3 \sin (1006 \pi t)$, when interfere, produce

When the listener moves towards stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted note is ' $F_1$ '. When observer moves away from the source with velocity ' $\mathrm{V}_1$ ', apparent frequency is ' $F_2$ '. If V is the velocity of sound in air and $\frac{F_1}{F_2}=2$ then $\frac{V}{V_1}$ is

When the string is stretched between two rigid supports, under certain tension and vibrated

A musical instrument X produces sound waves of frequency n and amplitude A. Another musical instrument $Y$ produces sound waves of frequency $\frac{n}{3}$. The waves produced by $x$ and $y$ have equal energies. The amplitude of waves produced by Y will be