Waves & Oscillations PYQ — Page 5

Which graph represents the difference between total energy and potential energy of a particle executing $\mathrm{SHM}$ vs its distance from mean position?

For a periodic motion represented by the equation $y=sin\omega t+cos\omega t$ the amplitude of the motion is

The maximum potential energy of a block executing simple harmonic motion is $25J$. A is amplitude of oscillation. At $\frac{A}{2}$, the kinetic energy of the block is

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______. 

The fundamental frequency of vibration of a string between two rigid support is $50\mathrm{Hz}$. The mass of the string is $18g$ and its linear mass density is $20g{m}^{-1}$. The speed of the transverse waves so produced in the string is _______ $m{s}^{–1}$.

In an experiment with sonometer when a mass of $180g$ is attached to the string, it vibrates with fundamental frequency of $30\mathrm{Hz}$. When a mass $m$ is attached, the string vibrates with fundamental frequency of $50\mathrm{Hz}$. The value of $m$ is ______ $g$.

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:

For particle $P$ revolving round the centre $O$ with radius of circular path $r$ and regular velocity $\omega$, as shown in below figure, the projection of $OP$ on the $x$-axis at time $t$ 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 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 ______$\mathrm{cm}$.

The equation of wave is given by $Y={10}^{-2}\mathrm{sin}2\pi (160t-0.5x+\frac{\pi }{4})$, where $x$ and $Y$ are in $m$ and $t$ in $s$. The speed of the wave is _______ $\mathrm{km}{h}^{-1}$.

The velocity of a particle executing SHM varies with displacement ($x$) as $4{v}^{2}=50–{x}^{2}$. The time period of oscillations is $\frac{x}{7}s$. The value of $x$ is ______. [Take $\pi =\frac{22}{7}$]

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1\mathrm{kg}$, the angular frequency is ${\omega }_{1}$. When the mass block is $2\mathrm{kg}$ the angular frequency is ${\omega }_{2}$. The ratio $\frac{{\omega }_{2}}{{\omega }_{1}}$ 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

The amplitude of a particle executing SHM is $3\mathrm{cm}$. The displacement at which its kinetic energy will be $25%$ more than the potential energy is: ______ $\mathrm{cm}$.

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

The general displacement of a simple harmonic oscillator is $x=A\mathrm{sin}\omega t$. Let $T$ be its time period. The slope of its potential energy ($U$) – time ($t$) curve will be maximum when $t=\frac{T}{\beta }$. The value of $\beta$ is ______.

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 _____ $\mathrm{cm}$

Sound travels in a mixture of two moles of helium and $n$ moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be

A transverse wave is represented by $y=2\mathrm{sin}(\omega t-kx)\mathrm{cm}$. The value of wavelength (in $\mathrm{cm}$) for which the wave velocity becomes equal to the maximum particle velocity, will be

A simple pendulum has time period T. If its length is increased by 21% the new time period is:

The speed of sound in air at 0°C is 332 m/s. The speed at 20°C is approximately:

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 _____ $I$.

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 :