Waves & Oscillations PYQ — Page 7

A body is performing simple harmonic with an amplitude of $10\mathrm{cm}$. The velocity of the body was tripled by air Jet when it is at $5\mathrm{cm}$ from its mean position. The new amplitude of vibration is $\sqrt{x}\mathrm{cm}$. The value of $x$ is _____ .

The potential energy of a particle of mass $4\mathrm{kg}$ in motion along the $x$-axis is given by $U=4(1-\mathrm{cos}4x)J$. The time period of the particle for small oscillation $(\mathrm{sin}\theta \simeq \theta )$ $(\frac{\pi }{K})s$. The value of $K$ is _____ .

The motion of a simple pendulum executing S.H.M. is represented by the following equation $y=A\mathrm{sin}(\pi t+\phi )$, where time is measured in second. The length of pendulum is

If a wave gets refracted into a denser medium, then which of the following is true?

Two light beams of intensities in the ratio of $9:4$ are allowed to interfere. The ratio of the intensity of maxima and minima will be :

A bob of mass $m$ suspended by a thread of length $\ell$ undergoes simple harmonic oscillations with time period $T.$ If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by ${(\frac{1}{3})}^{rd}$ of the original length, then the time period of the simple harmonic oscillations will be:

Two waves are simultaneously passing through a string and their equations are : ${y}_{1}={A}_{1}\mathrm{sin}k(x-vt),{y}_{2}={A}_{2}\mathrm{sin}k(x-vt+{x}_{0}).$ Given amplitudes ${A}_{1}=12\mathrm{mm}$ and ${A}_{2}=5\mathrm{mm}$, ${x}_{0}=3.5\mathrm{cm}$ and wave number $k=6.28{\mathrm{cm}}^{-1}.$ The amplitude of resulting wave will be _____ $\mathrm{mm}.$

A block of mass $1\mathrm{kg}$ attached to a spring is made to oscillate with an initial amplitude of $12\mathrm{cm}$. After $2$ minutes the amplitude decreases to $6\mathrm{cm}$. Determine the value of the damping constant for this motion. (take $\mathrm{ln}2=0.693$ )

Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l.$ What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?

Two travelling waves produces a standing wave represented by equation. $y=(1.0\mathrm{mm})\mathrm{cos}[(1.57{\mathrm{cm}}^{-1})x]\mathrm{sin}[(78.5{s}^{-1})t]$. The node closest to the origin in the region $x>0$ will be at $x=......(\text{in}\mathrm{cm}).$

An object of mass $0.5\mathrm{kg}$ is executing simple harmonic motion. It amplitude is $5\mathrm{cm}$ and time period (T) is $0.2s$. What will be the potential energy of the object at an instant $t=\frac{T}{4}s$ starting from mean position. Assume that the initial phase of the oscillation is zero.

A sound wave of frequency $245\mathrm{Hz}$ travels with the speed of $300{ms}^{-1}$ along the positive x-axis. Each point of the wave moves to and fro through a total distance of $6\mathrm{cm}$. What will be the mathematical expression of this travelling wave?

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4%$, will be ___ $%$.

The mass per unit length of a uniform wire is $0.135g{\mathrm{cm}}^{-1}$. A transverse wave of the form $y=-0.21\mathrm{sin}(x+30t)$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is $x\times {10}^{-2}N$. Value of $x$ is (Round-off to the nearest integer)

Time period of a simple pendulum is $T$. The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{\alpha }{12}T$. The value of $\alpha$ is $______$.

A tuning fork is vibrating at $250\mathrm{Hz}$. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _____$\mathrm{cm}$. (Take speed of sound in air as $340{ms}^{-1}$ )

A particle performs simple harmonic motion with a period of $2$ second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{a}s.$ The value of $a$ to the nearest integer is

In the given figure, a mass $M$ is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is $k.$ The mass oscillates on a frictionless surface with time period $T$ and amplitude $A.$ When the mass is in equilibrium position, as shown in the figure, another mass $m$ is gently fixed upon it. The new amplitude of oscillation will be: 

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is: 

Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants ${K}_{1}$ and ${K}_{2}$ respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of $A$ and $B$ is

Which of the following equations represents a travelling wave?

A pendulum bob has a speed of $3m{s}^{-1}$ at its lowest position. The pendulum is $50\mathrm{cm}$ long. The speed of bob, when the length makes an angle of $60^{\circ}$ to the vertical will be $(g=10m{s}^{-2})$ ______ $m{s}^{-1}$.

A tuning fork $A$ of unknown frequency produces $5\mathrm{beats}{s}^{-1}$ with a fork of known frequency $340\mathrm{Hz}$. When fork $A$ is filed, the beat frequency decreases to $2\mathrm{beats}{s}^{-1}$. What is the frequency of fork $A$ ?

In the reported figure, two bodies $A\mathrm{and}B$ of masses $200g$ and $800g$ are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ $\mathrm{rad}{s}^{-1}$ when $k=20N{m}^{-{1}^{}}$.