NEET UG 2010 — Waves & Oscillations

A transverse wave is represented by $y=A \sin (\omega t-k x)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

A particle moves in $x-y$ plane according to rule $\mathrm{x}=\mathrm{a} \sin \omega \mathrm{t}$ and $\mathrm{y}=\mathrm{a} \cos \omega \mathrm{t}$. The particle follows

The period of oscillation of a mass $M$ suspended from a spring of negligible mass is $\mathrm{T}$. If along with it another mass $M$ is also suspended, the period of oscillation will now be

The displacement of a particle along the $x$ axis is given by $\mathrm{x}=\mathrm{a} \sin ^2 \omega \mathrm{t}$. The motion of the particle corresponds to

A tuning fork of frequency $512 \mathrm{~Hz}$ makes 4 beats/seconds with the vibrating string of a piano. The beat frequency decreases to 2 beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was