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## Numerical

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A wire of length 30 cm, stretched between rigid supports, has it's nth and (n + 1)th harmonics at 400 Hz and 450 Hz, res...
JEE Main 2022 (Online) 27th July Evening Shift
When a car is approaching the observer, the frequency of horn is $$100 \mathrm{~Hz}$$. After passing the observer, it is...
JEE Main 2022 (Online) 26th July Morning Shift
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are super...
JEE Main 2022 (Online) 25th July Evening Shift
An observer is riding on a bicycle and moving towards a hill at $$18 \,\mathrm{kmh}^{-1}$$. He hears a sound from a sour...
JEE Main 2022 (Online) 25th July Morning Shift
An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car ...
JEE Main 2022 (Online) 30th June Morning Shift
Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfer...
JEE Main 2022 (Online) 24th June Evening Shift
The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the ...
JEE Main 2022 (Online) 25th June Morning Shift
A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to t...
JEE Main 2022 (Online) 26th June Evening Shift
A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrica...
JEE Main 2022 (Online) 28th June Evening Shift
In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonan...
JEE Main 2022 (Online) 29th June Evening Shift
A wire having a linear mass density 9.0 $$\times$$ 10$$-$$4 kg/m is stretched between two rigid supports with a tension ...
JEE Main 2021 (Online) 31st August Morning Shift
A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fo...
JEE Main 2021 (Online) 27th August Evening Shift
Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle...
JEE Main 2021 (Online) 27th August Morning Shift
Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x $$-$$ vt), y2 = A2 sin k...
JEE Main 2021 (Online) 26th August Evening Shift
Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm$$-$$1) x sin(78.5 s$$-$$1)t...
JEE Main 2021 (Online) 26th August Morning Shift
A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. ...
JEE Main 2021 (Online) 26th August Morning Shift
The amplitude of wave disturbance propagating in the positive x-direction is given by $$y = {1 \over {{{(1 + x)}^2}}}$$ ...
JEE Main 2021 (Online) 20th July Morning Shift
The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the ...
JEE Main 2021 (Online) 20th July Morning Shift
A closed organ pipe of length L and an open organ pipe contain gases of densities $$\rho$$1 and $$\rho$$2 respectively. ...
JEE Main 2021 (Online) 16th March Evening Shift
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $$-$$ 0.21 sin (x + 30t) is ...
JEE Main 2021 (Online) 26th February Morning Shift
The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4...
JEE Main 2021 (Online) 25th February Evening Shift
Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having fre...
JEE Main 2021 (Online) 24th February Evening Slot

## MCQ (Single Correct Answer)

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A transverse wave is represented by $$y=2 \sin (\omega t-k x)\, \mathrm{cm}$$. The value of wavelength (in $$\mathrm{cm}... JEE Main 2022 (Online) 26th July Evening Shift Which of the following equations correctly represents a travelling wave having wavelength$$\lambda$$= 4.0 cm, frequenc... JEE Main 2022 (Online) 30th June Morning Shift The equations of two waves are given by : y1 = 5 sin 2$$\pi$$(x - vt) cm y2 = 3 sin 2$$\pi$$(x$$-$$vt + 1.5) cm These ... JEE Main 2022 (Online) 24th June Morning Shift Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses... JEE Main 2022 (Online) 24th June Evening Shift For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 ... JEE Main 2022 (Online) 26th June Evening Shift An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The ... JEE Main 2022 (Online) 27th June Morning Shift If a wave gets refracted into a denser medium, then which of the following is true? JEE Main 2022 (Online) 27th June Evening Shift The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be : JEE Main 2022 (Online) 28th June Morning Shift A longitudinal wave is represented by$$x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$$cm. The maximum parti... JEE Main 2022 (Online) 29th June Morning Shift The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) =... JEE Main 2021 (Online) 22th July Evening Shift A sound wave of frequency 245 Hz travels with the speed of 300 ms$$-$$1 along the positive x-axis. Each point of the wav... JEE Main 2021 (Online) 17th March Evening Shift For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal ? JEE Main 2021 (Online) 17th March Morning Shift A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is field, the... JEE Main 2021 (Online) 26th February Evening Shift A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of th... JEE Main 2021 (Online) 25th February Morning Slot Which of the following equations represents a travelling wave? JEE Main 2021 (Online) 24th February Evening Slot In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spri... JEE Main 2021 (Online) 24th February Morning Slot A sound source S is moving along a straight track with speed v, and is emitting, sound of frequency v0 (see figure). An... JEE Main 2020 (Online) 6th September Morning Slot Two coherent sources of sound, S1 and S2, produce sound waves of the same wavelength,$$\lambda $$= 1 m, in phase. S1 a... JEE Main 2020 (Online) 5th September Evening Slot A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 48... JEE Main 2020 (Online) 5th September Evening Slot The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz wh... JEE Main 2020 (Online) 4th September Evening Slot A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attac... JEE Main 2020 (Online) 3rd September Morning Slot An amplitude modulated wave is represented by the expression vm = 5(1 + 0.6 cos 6280t) sin(211 × 104 t) volts The minimu... JEE Main 2020 (Online) 2nd September Morning Slot For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distan... JEE Main 2020 (Online) 4th September Morning Slot Three harmonic waves having equal frequency$$\nu $$and same intensity$${I_0}$$, have phase angles 0,$${\pi \over 4}...
JEE Main 2020 (Online) 9th January Morning Slot
A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension...
JEE Main 2020 (Online) 8th January Evening Slot
A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes ...
JEE Main 2020 (Online) 7th January Evening Slot
Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. I...
JEE Main 2020 (Online) 7th January Morning Slot
A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ?...
JEE Main 2019 (Online) 12th April Evening Slot
A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube met...
JEE Main 2019 (Online) 12th April Evening Slot
Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards...
JEE Main 2019 (Online) 12th April Evening Slot
A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travellin...
JEE Main 2019 (Online) 12th April Morning Slot
A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $$\omega$$t + $$\phi ... JEE Main 2019 (Online) 12th April Morning Slot A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequen... JEE Main 2019 (Online) 10th April Evening Slot The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 H... JEE Main 2019 (Online) 10th April Evening Slot A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source ... JEE Main 2019 (Online) 10th April Morning Slot The displacement of a damped harmonic oscillator is given by x(t ) = e–0.1t cos (10$$\pi $$t + f). Here t is in seconds.... JEE Main 2019 (Online) 10th April Morning Slot A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode... JEE Main 2019 (Online) 9th April Evening Slot Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms–... JEE Main 2019 (Online) 9th April Evening Slot A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is Y =... JEE Main 2019 (Online) 9th April Morning Slot The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2, corresponds to the sound produced by a vibrating blade on a day when ... JEE Main 2019 (Online) 9th April Morning Slot A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for eve... JEE Main 2019 (Online) 8th April Evening Slot A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the s... JEE Main 2019 (Online) 8th April Morning Slot A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A ... JEE Main 2019 (Online) 12th January Evening Slot Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and... JEE Main 2019 (Online) 11th January Morning Slot A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vi... JEE Main 2019 (Online) 10th January Morning Slot In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To r... JEE Main 2019 (Online) 10th January Morning Slot A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered b... JEE Main 2019 (Online) 10th January Morning Slot A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician... JEE Main 2019 (Online) 9th January Evening Slot A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masse... JEE Main 2019 (Online) 9th January Evening Slot Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximu... JEE Main 2019 (Online) 9th January Morning Slot The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the... JEE Main 2018 (Online) 16th April Morning Slot Two sitar strings, A and B, playing the note 'Dha' are slightly out of tune and produce beats of frequency 5 Hz. The te... JEE Main 2018 (Online) 16th April Morning Slot 5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sono... JEE Main 2018 (Online) 15th April Evening Slot A tuning fork vibrates with frequency$$256Hz$$and gives one beat per second with the third normal mode of vibrati... JEE Main 2018 (Online) 15th April Morning Slot A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of gra... JEE Main 2018 (Offline) A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is th... JEE Main 2018 (Offline) In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs ... JEE Main 2017 (Online) 9th April Morning Slot A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displaceme... JEE Main 2017 (Online) 9th April Morning Slot Two wires W1 and W2 have the same radius r and respective densities$$\rho $$1 and$$\rho $$2 such that ρ2 = 4$$\rho ...
JEE Main 2017 (Online) 8th April Morning Slot
A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium...
JEE Main 2017 (Offline)
A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy...
JEE Main 2016 (Online) 10th April Morning Slot
Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle...
JEE Main 2016 (Online) 9th April Morning Slot
A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half o...
JEE Main 2016 (Offline)
A uniform string of length $$20$$ $$m$$ is suspended from a rigid support. A short wave pulse is introduced at its lowes...
JEE Main 2016 (Offline)
A train is moving on a straight track with speed $$20\,m{s^{ - 1}}.$$ It is blowing its whistle at the frequency of $$10... JEE Main 2015 (Offline) A pipe of length$$85cm$$is closed from one end. Find the number of possible natural oscillations of air column in... JEE Main 2014 (Offline) A sonometer wire of length$$1.5m$$is made of steel. The tension in it produces an elastic strain of$$1\% $$. Wh... JEE Main 2013 (Offline) A cylindrical tube, open at both ends, has a fundamental frequency,$$f,$$in air. The tube is dipped vertically in wate... AIEEE 2012 The transverse displacement$$y(x, t)$$of a wave on a string is given by$$y\left( {x,t} \right) = {e^{ - \left( {a{x^2...
AIEEE 2011
The equation of a wave on a string of linear mass density $$0.04\,\,kg\,{m^{ - 1}}$$ is given by $$y = 0.02\left( m \r... AIEEE 2010 A motor cycle starts from rest and accelerates along a straight path at$$2m/{s^2}.$$At the starting point of the motor... AIEEE 2009 Three sound waves of equal amplitudes have frequencies$$\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$$They sup... AIEEE 2009 A wave travelling along the$$x$$-axis is described by the equation$$y(x, t)=0.005\cos \,\left( {\alpha \,x - \bet...
AIEEE 2008
While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condi...
AIEEE 2008
A sound absorber attenuates the sound level by $$20$$ $$dB$$. The intensity decreases by a factor of
AIEEE 2007
A string is stretched between fixed points separated by $$75.0$$ $$cm.$$ It is observed to have resonant frequencies of ...
AIEEE 2006
A whistle producing sound waves of frequencies $$9500$$ $$Hz$$ and above is approaching a stationary person with speed $... AIEEE 2006 An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the ... AIEEE 2005 When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, so... AIEEE 2005 The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin$$ $$\left( {100t + 20x + ... AIEEE 2004 A tuning fork of known frequency$$256Hz$$makes$$5$$beats per second with the vibrating string of a piano. The b... AIEEE 2003 The displacement$$y$$of a wave travelling in the$$x$$-direction is given by$$$y = {10^{ - 4}}\,\sin \left( {600t - ...
AIEEE 2003
A metal wire of linear mass density of $$9.8$$ $$g/m$$ is stretched with a tension of $$10$$ $$kg$$-$$wt$$ between two r...
AIEEE 2003
When temperature increases, the frequency of a tuning fork
AIEEE 2002
A wave $$y=a$$ $$\sin \left( {\omega t - kx} \right)$$ on a string meets with another wave producing a node at $$x=0.$$ ...
AIEEE 2002
Tube $$A$$ has bolt ends open while tube $$B$$ has one end closed, otherwise they are identical. The ratio of fundamenta...
AIEEE 2002
A tuning fork arrangement (pair) produces $$4$$ beats/sec with one fork of frequency $$288$$ $$cps.$$ A little wax is pl...
AIEEE 2002
length of a string tied to two rigid supports is $$40$$ $$cm$$. Maximum length (wavelength in $$cm$$) of a stationary wa...
AIEEE 2002

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