NEET UG 2014 — Waves & Oscillations

The oscillation of a body on a smooth horizontal surface is represented by the equation, $X=A\mathrm{cos}⁡(\omega t)$, where $X=$ displacement at time $t$, $\omega =$ frequency of oscillation, $a=$ acceleration at time $t$ and $T=$ time period. Which one of the following graph shows correctly the variation $a$ with $t$ ?

The number of possible natural oscillations of air column in a pipe closed at one end of length $85 cm$ whose frequencies lies below $1250 Hz$ are: (velocity of sound $=340 {ms}^{-1}$)

If ${n}_{1}, {n}_{2}$ and ${n}_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by: