Waves & Oscillations PYQ

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 :

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 :

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?

If $x=5 \sin \left(\pi t+\frac{\pi}{3}\right) \mathrm{m}$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are

Let $\omega_1, \omega_2$ and $\omega_3$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $x_1, x_2$ and $x_3$ are their respective angular distances in 1 minute then the factor which remains constant $(k)$ is

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

The two-dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ is a/an: A. parabolic path B. elliptical path C. periodic motion D. simple harmonic motion Choose the correct answer from the options given below:

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

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

The $4^{\text {th }}$ overtone of a closed organ pipe is same as that of $3^{\text {rd }}$ overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:

The $x-t$ graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at $t=2s$ is: 

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:

A simple pendulum oscillating in air has a period of $\sqrt{3} \mathrm{~s}$. If it is completely immersed in non-viscous liquid, having density $\left(\frac{1}{4}\right)^{\text {th }}$ of the material of the bob, the new period will be

Two pendulums of length $121\mathrm{cm}$ and $100\mathrm{cm}$ start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

Match List - I with List - II:  Choose the correct answer from the options given below:

Identify the function which represents a nonperiodic motion.

An organ pipe filled with a gas at $27^{\circ} \mathrm{C}$ resonates at $400 \mathrm{~Hz}$ in its fundamental mode. If it is filled with the same gas at $90^{\circ} \mathrm{C}$, the resonance frequency at the same mode will be:

A body is executing simple harmonic motion with frequency $n$, the frequency of its potential energy is

A spring is stretched by $5\mathrm{cm}$ by a force $10N$. The time period of the oscillations when a mass of $2\mathrm{kg}$ is suspended by it is :

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: