Waves & Oscillations PYQ — Page 9

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?

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: 

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

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 amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass $=500g$, Decay constant $=20g{s}^{-1}$ then how much time is required for the amplitude of the system to drop to half of its initial value? $(\mathrm{ln}2=0.693)$

A particle executes simple harmonic motion represented by displacement function as $x(t)=A\mathrm{sin}(\omega t+\phi )$. If the position and velocity of the particle at $t=0s$ are $2\mathrm{cm}$ and $2\omega \mathrm{cm}{s}^{-1}$ respectively, then its amplitude is $x\sqrt{2}\mathrm{cm}$ where the value of $x$ 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 uniform thin rope of length $12m$ and mass $6\mathrm{kg}$ hangs vertically from a rigid support and a block of mass $2\mathrm{kg}$ is attached to its free end. A transverse short wave train of wavelength $6\mathrm{cm}$ is produced at the lower and the rope. What is the wavelength of the wave train (in $\mathrm{cm}$ ) when it reaches the top of the rope?

When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion, is described by $y(t)={y}_{0}{\mathrm{sin}}^{2}\omega t$, where '$y$' is measured from the lower end of upstretched spring. Then $\omega$ is :

A wire of length $L$ and mass per unit length $6.0\times {10}^{-3}kg{m}^{-1}$ is put under tension of $540N.$ Two consecutive frequencies that it resonates at are: $420Hz$ and $490Hz.$ Then $L$ in meters is :

A transverse wave travels on a taut steel wire with a velocity of $v$ when tension in it is $2.06\times {10}^{4}N.$ When the tension is changed to $T,$ the velocity changed to $\frac{v}{2}.$ The value of $T$ is close to:

The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale)  Which of the following statements is/are true for this motion? (A) The force is zero at $t=\frac{3T}{4}$ (B) The magnitude of acceleration is maximum at $t=T$ (C) The speed is maximum at $t=\frac{T}{4}$ (D) The $P.E.$ is equal to $K.E.$ of the oscillation at $t=\frac{T}{2}$

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period ${T}_{1}$ and (ii) back and forth in a direction perpendicular to its plane, with a period ${T}_{2}$. The ratio $\frac{{T}_{1}}{{T}_{2}}$ will be :

Two identical strings $X$ and $Z$ made of same material have tension ${T}_{X}$ and ${T}_{Z}$ in then if their fundamental frequencies are $450\mathrm{Hz}$ and $300\mathrm{Hz}$, respectively, then the ratio ${T}_{X}/{T}_{Z}$ is :

Three harmonic waves having equal frequency $v$ and same intensity ${I}_{0}$ , have phase angles $0,\frac{\pi }{4}$ and $-\frac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:

For a transvers wave travelling, along a straight line, the distance between two peaks (crests) is $5\text{ m}$, while the distance between one crest and one trough is $1.5\text{ m}$. The possible wavelengths (in $\text{m}$) of the waves are:

Assume that the displacement (s) of air is proportional to the pressure difference $(\Delta p)$ created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air$(\rho )$ and the frequency (f). If $\Delta p~10Pa,n~300m/s,p~1kg/{m}^{3}$ $f~1000Hz$, then s will be of the order of (take the multiplicative constant to be 1 )

An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross-section, A. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :

In a resonance tube experiment when the tube is filled with water up to a height of $17.0\mathrm{cm}\text{,}$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5\mathrm{cm}\text{.}$ If the velocity of sound in air is $330m{s}^{-1}\text{,}$ the tuning fork frequency is :

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is $300m/s,$ the frequency difference between the fundamental and second harmonic of this pipe is __________ Hz.

A string of length 1 m and mass 5 g is fixed at both ends. The speed of transverse waves on the string is 100 m/s. The fundamental frequency is:

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are ${T}_{h}$ and ${T}_{c}$ respectively, then:

A particle executes simple harmonic motion with an amplitude of $5 cm$ . When the particle is at $4 cm$ from the mean position, the magnitude of its velocity in $SI$ units is equal to that of its acceleration. Then, its periodic time in seconds is: