Waves & Oscillations PYQ — Page 7

A radar sends an electromagnetic signal of electric field $({E}_{0})=2.25V{m}^{-1}$ and magnetic field $({B}_{0})=1.5\times {10}^{-8}T$ which strikes a target on line of sight at a distance of $3\mathrm{km}$ in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time $t=0$ from radar, then after how much time echo will reach to the radar?

A particle executes simple harmonic motion. Its amplitude is $8\mathrm{cm}$ and time period is $6s$. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is _____ $s$

A mass $0.9\mathrm{kg}$, attached to a horizontal spring, executes SHM with an amplitude ${A}_{1}$. When this mass passes through its mean position, then a smaller mass of $124g$ is placed over it and both masses move together with amplitude ${A}_{2}$. If the ratio $\frac{{A}_{1}}{{A}_{2}}$ is $\frac{\alpha }{\alpha -1}$, then the value of $\alpha$ will be _____ .

A longitudinal wave is represented by $y=10\mathrm{sin}2\pi (nt-\frac{x}{\lambda })\mathrm{cm}$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to

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 _____ .

Which of the following equations represents a travelling wave?

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

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 _____ $\mathrm{mm}.$

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 $x=......(\text{in}\mathrm{cm}).$

Two simple harmonic motions are represented by the equations ${x}_{1}=5\mathrm{sin}(2\pi t+\frac{\pi }{4})$ and ${x}_{2}=5\sqrt{2}(\mathrm{sin}2\pi t+\mathrm{cos}2\pi t).$ The amplitude of the second motion is _____ times the amplitude in the first motion.

Two simple harmonic motion, are represented by the equations ${y}_{1}=10\mathrm{sin}(3\pi t+\frac{\pi }{3});{y}_{2}=5(\mathrm{sin}3\pi t+\sqrt{3}\mathrm{cos}3\pi t)$ Ratio of amplitude of ${y}_{1}$ to ${y}_{2}=x:1$. The value of $x$ 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

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 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 $T$. The time taken to complete $\frac{5}{8}$ oscillations starting from mean position is $\frac{\alpha }{12}T$. The value of $\alpha$ 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 :

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:

The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36m$ and covers $30^{\circ}$ in $0.1s$. The perpendicular projection $P$ from $A$ on the diameter $MN$ represents the simple harmonic motion of $P$. The restoration force per unit mass when $P$ touches $M$ will be : 

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)

The function of time representing a simple harmonic motion with a period of $\frac{\pi }{\omega }$ is :

The amplitude of wave disturbance propagating in the positive $x$-direction is given by $y=\frac{1}{(1+x{)}^{2}}$ at time $t=0$ and $y=\frac{1}{1+(x-2{)}^{2}}$ at $t=1s$, where $x$ and $y$ are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be $m{s}^{-1}.$

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? $(\mathrm{ln}2=0.693)$

The phase difference between two points separated by 1 m on a wave of wavelength 4 m is: