Waves & Oscillations PYQ — Page 9

A closed organ pipe of length $L$ and an open organ pipe contain gases of densities ${\rho }_{1}$ and ${\rho }_{2}$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{{\rho }_{1}}{{\rho }_{2}}}$, where $x$ is _______. (Round off to the Nearest Integer)

Two identical springs of spring constant $2k$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is : 

Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upwards with an acceleration $\frac{g}{2}$, the time period of pendulum will be :

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance $\frac{R}{2}$ from the earth's centre, where $R$ is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.  The potential energy $U(x)$ versus time $(t)$ plot of the particle is correctly shown in figure:

A particle is making simple harmonic motion along the $X$-axis. If at a distances ${x}_{1}$ and ${x}_{2}$ from the mean position the velocities of the particle are ${v}_{1}$ and ${v}_{2}$, respectively. The time period of its oscillation is given as:

${T}_{0}$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period 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 :

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:

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:

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:

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 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?

Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m.$ The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is: 

A pendulum is executing simple harmonic motion and its maximum kinetic energy is $\mathrm{K}_{1}$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $\mathrm{K}_{2}$