NEET UG 2018 — Waves & Oscillations

A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20m{s}^{-2}$ at a distance of $5m$ from mean position. The time period of oscillation is

The fundamental frequency in an open organ pipe is equal to the third harmonic of closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

A tuning fork is used to produce resonance in glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of ${27}^{ o}C$ two successive resonances are produced at $20\mathrm{cm}$ and $73\mathrm{cm}$ of column length. If the frequency of the tuning fork is $320\mathrm{Hz}$, the velocity of sound in air at ${27}^{ o}C$ is