JEE Main 2024 — Waves & Oscillations

A point source is emitting sound waves of intensity $16\times {10}^{-8}W{m}^{-2}$ at the origin. The difference in intensity (magnitude only) at two points located at a distances of $2m$ and $4m$ from the origin respectively will be ________$\times {10}^{-8}W{m}^{-2}$.

A particle performs simple harmonic motion with amplitude $A$. Its speed is increased to three times at an instant when its displacement is $\frac{2A}{3}$. The new amplitude of motion is $\frac{nA}{3}$. The value of $n$ is _____.

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$, where $x=$_________.

An object of mass $0.2 \mathrm{~kg}$ executes simple harmonic motion along $\mathrm{x}$ axis with frequency of $\left(\frac{25}{\pi}\right) \mathrm{Hz}$. At the position $x=0.04 \mathrm{~m}$ the object has kinetic energy $0.5 \mathrm{~J}$ and potential energy $0.4 \mathrm{~J}$. The amplitude of oscillation is _____$\mathrm{cm}$.

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$ and $16 \mathrm{~ms}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}, \mathrm{~m}$ where $x$ is ________

Two open organ pipes of lengths $60 \mathrm{~cm}$ and $90 \mathrm{~cm}$ resonate at $6^{\text {th }}$ and $5^{\text {th }}$ harmonics respectively. The difference of frequencies for the given modes is _______ $\mathrm{Hz}$. (Velocity of sound in air $=333 \mathrm{~m} / \mathrm{s}$ )

A plane progressive wave is given by $y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$. The frequency of the wave is :

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60\mathrm{cm}$, the length of the closed pipe will be :

A particle of mass $0.50 \mathrm{~kg}$ executes simple harmonic motion under force $F=-50\left(\mathrm{Nm}^{-1}\right) x$. The time period of oscillation is $\frac{x}{35} \mathrm{~s}$. The value of $x$ is _______ (Given $\pi=\frac{22}{7}$ )

A mass $m$ is suspended from a spring of negligible mass and the system oscillates with a frequency ${f}_{1}.$ The frequency of oscillations if a mass $9m$ is suspended from the same spring is ${f}_{2}.$ The value of $\frac{{f}_{1}}{{f}_{2}}$ is _____ .

A particle executes simple harmonic motion with an amplitude of $4\mathrm{cm}$. At the mean position, velocity of the particle is $10\mathrm{cm}{s}^{-1}$. The distance of the particle from the mean position when its speed becomes $5\mathrm{cm}{s}^{-1}$ is $\sqrt{\alpha }\mathrm{cm}$, where $\alpha =$______.

A closed organ pipe $150\mathrm{cm}$ long gives $7$ beats per second with an open organ pipe of length $350\mathrm{cm}$, both vibrating in fundamental mode. The velocity of sound is ______ $m{s}^{-1}$.

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $\left(\frac{a-1}{a}\right)$ then the value of $\mathrm{a}$ is ________

In simple harmonic motion, the total mechanical energy of given system is $E$. If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is: 

A particle is doing simple harmonic motion of amplitude $0.06 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum velocity of the particle is _______ $\mathrm{cm} / \mathrm{s}$.

The equation of a progressive wave is y = 5sin(100πt - 0.4πx). The velocity of the wave is:

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4m$, then the time period of small oscillations will be _________$s$. $[$take $g={\pi }^{2}m{s}^{-2}$]

A tuning fork resonates with a sonometer wire of length $1m$ stretched with a tension of $6N.$ When the tension in the wire is changed to $54N,$ the same tuning fork produces $12$ beats per second with it. The frequency of the tuning fork is _______ $\mathrm{Hz}.$

The displacement of a particle executing SHM is given by $x=10 \sin \left(w t+\frac{\pi}{3}\right) m$. The time period of motion is $3.14 \mathrm{~s}$. The velocity of the particle at $t=0$ is ______$\mathrm{m} / \mathrm{s}$.

The speed of sound in oxygen at S.T.P. will be approximately: (Given, $R=8.3J{K}^{-1},\gamma =1.4)$

A sonometer wire of resonating length $90 \mathrm{~cm}$ has a fundamental frequency of $400 \mathrm{~Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600 \mathrm{~Hz}$ under same tension _____$\mathrm{cm}$.

The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5K}}$, where the value of $\alpha$ is _______. 

A simple harmonic oscillator has an amplitude $A$ and time period $6\pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from$x=A$ to $x=\frac{\sqrt{3}}{2}A$ will be $\frac{\pi }{x}s$, where $x=_______.$

In a closed organ pipe, the frequency of fundamental note is $30\mathrm{Hz}$. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to $110\mathrm{Hz}$. If the organ pipe has a cross-sectional area of $2{\mathrm{cm}}^{2}$, the amount of water poured in the organ tube is ________$g$. (Take speed of sound in air is $330m{s}^{-1}$ )