Waves & Oscillations PYQ — Page 5

For a certain organ pipe, the first three resonance frequencies are in the ratio of $1:3:5$ respectively. If the frequency of fifth harmonic is $405\mathrm{Hz}$ and the speed of sound in air is $324m{s}^{–1}$ the length of the organ pipe is _____ $m$.

Choose the correct length $(L)$ versus square of time period $({T}_{2})$ ) graph for a simple pendulum executing simple harmonic motion.

At a given point of time the value of displacement of a simple harmonic oscillator is given as $y=A\mathrm{cos}(30^{\circ}).$ If amplitude is $40\mathrm{cm}$ and kinetic energy at that time is $200J,$ the value of force constant $1.0\times {10}^{x}N{m}^{–1}$. The value of $x$ is _____.

An organ pipe $40\mathrm{cm}$ long is open at both ends. The speed of sound in air is $360m{s}^{-1}$. The frequency of the second harmonic is _$________\mathrm{Hz}.$

A wire of density $8\times {10}^{3}\mathrm{kg}{m}^{-3}$ is stretched between two clamps $0.5m$ apart. The extension developed in the wire is $3.2\times {10}^{-4}m$. If $Y=8\times {10}^{10}N{m}^{-2}$, the fundamental frequency of vibration in the wire will be _____ $\mathrm{Hz}$

A travelling wave is described by the equation $y(x,t)=[0.05\mathrm{sin}(8x-4t)]m$. The velocity of the wave is: [All the quantities are in SI unit]

A transverse harmonic wave on a string is given by $y(x,t)=5\mathrm{sin}(6t+0.003x)$ where $x$ and $y$ are in $\mathrm{cm}$ and $t$ in $\mathrm{sec}$. The wave velocity is _________ $m{s}^{-1}$.

A steel wire with mass per unit length $7.0\times {10}^{–3}\mathrm{kg}{m}^{–1}$ is under tension of $70N$. The speed of transverse waves in the wire will be:

A simple pendulum with length $100\mathrm{cm}$ and bob of mass $250g$ is executing S.H.M of amplitude $10\mathrm{cm}$. The maximum tension in the string is found to be $\frac{x}{40}N$. The value of $x$ is _____.

A rectangular block of mass $5\mathrm{kg}$ attached to a horizontal spiral spring executes simple harmonic motion of amplitude $1m$ and time period $3.14s$. The maximum force exerted by spring on block is ___ $N$.

A particle of mass $250g$ executes a simple harmonic motion under a periodic force $F=(–25x)N$. The particle attains a maximum speed of $4m{s}^{-1}$ during its oscillation. The amplitude of the motion is ______$\mathrm{cm}$.

A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

A particle executes simple harmonic motion between $x=–A\text{and}x=+A$. If time taken by particle to go from $x=0$ to $\frac{A}{2}$ is $2s$; then time taken by particle in going from $x=\frac{A}{2}$ to $A$ is:

A particle executes SHM of amplitude$A$. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:

A particle executes S.H.M. of amplitude $A$ along $x$-axis. At $t=0$, the position of the particle is $x=\frac{A}{2}$ and it moves along positive $x$-axis. The displacement of particle in time $t$ is $x=A\mathrm{sin}(\omega t+\delta )$, then the value $\delta$ will be

A mass $m$ attached to free end of a spring executes SHM with a period of $1s$. If the mass is increased by $3\mathrm{kg}$ the period of oscillation increases by one second, the value of mass $m$ is ________ $\mathrm{kg}$.

A guitar string of length $90\mathrm{cm}$ vibrates with a fundamental frequency of $120\mathrm{Hz}$. The length of the string producing a fundamental of $180\mathrm{Hz}$ will be _____ $\mathrm{cm}$

A block of mass $2\mathrm{kg}$ is attached with two identical springs of spring constant $20N{m}^{-1}$ each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $\frac{\pi }{\sqrt{X}}$ in SI unit. The value of $X$ is______. 

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is _____ (degree)

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $y=(10\mathrm{cos}\pi x\mathrm{sin}\frac{2\pi t}{T})\mathrm{cm}$. The amplitude of the particle at $x=\frac{4}{3}\mathrm{cm}$ will be _____ $\mathrm{cm}.$

Two massless springs with spring constants $2k$ and $9k$, carry $50g$ and $100g$ masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

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 :

Two light beams of intensities $4I$ and $9I$ interfere on a screen. The phase difference between these beams on the screen at point $A$ is zero and at point $B$ is $\pi$. The difference of resultant intensities, at the point $A$ and $B$, will be _____ $I$.