JEE Main Physics — Waves & Oscillations previous year questions with solutions.
A set of $20$ tuning forks is arranged in a series of increasing frequencies. If each fork gives $4$ beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _____ $\mathrm{Hz}$.
The metallic bob of simple pendulum has the relative density $5$. The time period of this pendulum is $10s$. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}s$. The value of $x$ will be _____ .
The velocity of sound in a gas, in which two wavelengths $4.08m$ and $4.16m$ produce $40$ beats in $12s$, will be
A tunning fork of frequency $340\mathrm{Hz}$ resonates in the fundamental mode with an air column of length $125\mathrm{cm}$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is _____ $\mathrm{cm}$. (Velocity of sound in air is $340{\mathrm{ms}}^{-1}$)
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 _____ $\mathrm{cm}.$
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 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
When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be
The time period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by :
As per given figures, two springs of spring constants $K$ and $2K$ are connected to mass $m$. If the period of oscillation in figure (a) is $3s$, then the period of oscillation in figure (b) will be $\sqrt{x}s$. The value of $x$ is _____ . 
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)
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is $20\mathrm{cm}$. The length of the open organ pipe is _____ $\mathrm{cm}$
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 _____ .
The speed of a transverse wave passing through a string of length $50\mathrm{cm}$ and mass $10g$ is $60m{s}^{-1}$. The area of cross-section of the wire is $2.0{\mathrm{mm}}^{2}$ and its Young's modulus is $1.2\times {10}^{11}N{m}^{-2}$. The extension of the wire over its natural length due to its tension will be $x\times {10}^{-5}m$. The value of $x$ is _____ .
An observer is riding on a bicycle and moving towards a hill at $18\mathrm{km}{h}^{-1}$. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is $640\mathrm{Hz}$ and velocity of the sound in air is $320m{s}^{-1}$, the beat frequency between the two sounds heard by observer will be _____ $\mathrm{Hz}$.
In the wave equation $y=0.5\mathrm{sin}\frac{2\pi }{\lambda }(400t-x)m$ the velocity of the wave will be :
A wire of length $30\mathrm{cm}$, stretched between rigid supports, has it's ${n}^{\mathrm{th}}$ and ${(n+1)}^{\mathrm{th}}$ harmonics at $400\mathrm{Hz}$ and $450\mathrm{Hz}$, respectively. If tension in the string is $2700N$, it's linear mass density is _____ $\mathrm{kg}{m}^{-1}$.
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of $20.0\mathrm{cm}$ for a tuning fork of frequency $400\mathrm{Hz}$ is used. The velocity of the sound at room temperature is $336{ms}^{-1}$. The third resonance is observed when the air column has a length of _____ $\mathrm{cm}$
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?
The equations of two waves are given by : ${y}_{1}=5\mathrm{sin}2\pi (x-vt)\mathrm{cm}$ ${y}_{2}=3\mathrm{sin}2\pi (x-vt+1.5)\mathrm{cm}$ These waves are simultaneously passing through a string. The amplitude of the resulting wave is :
Time period of a simple pendulum in a stationary lift is $T$. If the lift accelerates with $\frac{g}{6}$ vertically upwards then the time period will be (Where $g=$ acceleration due to gravity)
In figure (A), mass $2m$ is fixed on mass $m$ which is attached to two springs of spring constant $k$. In figure (B), mass $m$ is attached to two spring of spring constant $k$ and $2k$. If mass $m$ in (A) and (B) are displaced by distance $x$ horizontally and then released, then time period ${T}_{1}$ and ${T}_{2}$ corresponding to (A) and (B) respectively follow the relation. 
The equation of a particle executing simple harmonic motion is given by $x=\mathrm{sin}\pi (t+\frac{1}{3})m$. At $t=1s$, the speed of particle will be (Given: $\pi =3.14$)
The displacement of simple harmonic oscillator after $3$ seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is