A pipe open at both ends of length 1.5 m is dipped in water at one end such that $2^{\text {nd }}$ overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of sound in air $=330 \mathrm{~m} / \mathrm{s}$ ) (Neglect end correction)

Two uniform wires of same material are vibrating under the same tension. If the $1^{\text {st }}$ overtone of $1^{\text {st }}$ wire is equal to the $2^{\text {nd }}$ overtone of $2^{\text {nd }}$ wire and radius of $1^{\text {st }}$ wire is twice the radius of $2^{\text {nd }}$ wire, the ratio of length of $1^{\text {st }}$ wire to that $2^{\text {nd }}$ wire is

An observer on sea-coast counts 45 waves in one minute. If the wavelength of the waves is 7 m , then the velocity of the waves will be

Two sources of sound are emitting progressive waves $\mathrm{y}_1=4 \sin 710 \pi \mathrm{t}$ and $\mathrm{y}_2=3 \sin 702 \pi \mathrm{t}$. The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and waning are respectively