NEET UG 2008 — Physics Waves & Oscillations

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency $\omega(t)$ and average amplitude $A(t)$ of the system change with time $t$. Which one of the following options schematically depicts these changes correctly?

Two identical point masses P and Q , suspended from two separate massless springs of spring constants $\mathrm{k}_1$ and $\mathrm{k}_2$, respectively, oscillate vertically. If their maximum speeds are the same, the ratio $\left(A_Q / A_P\right)$ of the amplitude $A_Q$ of mass $Q$ to the amplitude $A_P$ of mass $P$ is :

A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic energies at the displacement

The displacement of a travelling wave $y=C \sin \frac{2 \pi}{\lambda}$ (at $-x$ ) where $t$ is time, $x$ is distance and $\lambda$ is the wavelength, all in S.I. units. Then the frequency of the wave is