NEET UG 2020 — Waves & Oscillations

The length of the string of a musical instrument is $90\mathrm{cm}$ and has a fundamental frequency of $120\mathrm{Hz}$. Where should it be pressed to produce fundamental frequency of $180\mathrm{Hz}?$

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

Identify the function which represents a periodic motion

In a guitar, two strings $A$ and $B$ made of same material are slightly out of tune and produce beats of frequency $6\mathrm{Hz}$. When tension in $B$ is slightly decreased, the beat frequency increases to $7\mathrm{Hz}$. If the frequency of $A$ is $530\mathrm{Hz}$, the original frequency of $B$ will be: