# Waves · Physics · JEE Main

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## Numerical

JEE Main 2024 (Online) 1st February Morning Shift
A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is c...
JEE Main 2024 (Online) 30th January Evening Shift
A point source is emitting sound waves of intensity $$16 \times 10^{-8} \mathrm{~Wm}^{-2}$$ at the origin. The difference in intensity (magnitude only...
JEE Main 2024 (Online) 30th January Morning Shift
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 th...
JEE Main 2024 (Online) 27th January Evening Shift
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 funda...
JEE Main 2023 (Online) 15th April Morning Shift
The fundamental frequency of vibration of a string stretched between two rigid support is $50 \mathrm{~Hz}$. The mass of the string is $18 \mathrm{~g}... JEE Main 2023 (Online) 13th April Evening Shift In an experiment with sonometer when a mass of $$180 \mathrm{~g}$$ is attached to the string, it vibrates with fundamental frequency of $$30 \mathrm{~... JEE Main 2023 (Online) 12th April Morning Shift For a certain organ pipe, the first three resonance frequencies are in the ratio of$$1:3:5$$respectively. If the frequency of fifth harmonic is$$40... JEE Main 2023 (Online) 11th April Morning Shift The equation of wave is given by $$\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)$$ where $$x$$ and $$Y$$ are in $$\mathrm{m}$$ and $$\mathrm{t}$$... JEE Main 2023 (Online) 10th April Morning Shift A transverse harmonic wave on a string is given by $$y(x,t) = 5\sin (6t + 0.003x)$$ where x and y are in cm and t in sec. The wave velocity is _______... JEE Main 2023 (Online) 8th April Evening Shift A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz ... JEE Main 2023 (Online) 8th April Morning Shift An organ pipe $$40 \mathrm{~cm}$$ long is open at both ends. The speed of sound in air is $$360 \mathrm{~ms}^{-1}$$. The frequency of the second harmo... JEE Main 2023 (Online) 6th April Morning Shift A person driving car at a constant speed of $$15 \mathrm{~m} / \mathrm{s}$$ is approaching a vertical wall. The person notices a change of $$40 \mathr... JEE Main 2023 (Online) 31st January Evening Shift The displacement equations of two interfering waves are given by y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega ... JEE Main 2023 (Online) 29th January Morning Shift Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is... JEE Main 2023 (Online) 25th January Evening Shift A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the obse... JEE Main 2023 (Online) 25th January Morning Shift The distance between two consecutive points with phase difference of 60$$^\circ$$in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave... JEE Main 2022 (Online) 28th July Morning Shift The frequency of echo will be __________ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill fro... JEE Main 2022 (Online) 27th July Evening Shift A wire of length 30 cm, stretched between rigid supports, has it's nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the s... JEE Main 2022 (Online) 26th July Morning Shift When a car is approaching the observer, the frequency of horn is$$100 \mathrm{~Hz}$$. After passing the observer, it is$$50 \mathrm{~Hz}$$. If the o... JEE Main 2022 (Online) 25th July Evening Shift Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitu... JEE Main 2022 (Online) 25th July Morning Shift An observer is riding on a bicycle and moving towards a hill at$$18 \,\mathrm{kmh}^{-1}$$. He hears a sound from a source at some distance behind him... JEE Main 2022 (Online) 30th June Morning Shift An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of 72 kmh$$-$$1 i... JEE Main 2022 (Online) 29th June Evening Shift In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air co... JEE Main 2022 (Online) 28th June Evening Shift A tunning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When... JEE Main 2022 (Online) 26th June Evening Shift A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the freq... JEE Main 2022 (Online) 25th June Morning Shift The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pip... JEE Main 2022 (Online) 24th June Evening Shift Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave... JEE Main 2021 (Online) 31st August Morning Shift A wire having a linear mass density 9.0$$\times$$10$$-$$4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates a... JEE Main 2021 (Online) 27th August Evening Shift A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be __________ cm. (Tak... JEE Main 2021 (Online) 27th August Morning Shift Two cars X and Y are approaching each other with velocities 36 km/h and 72 km/h respectively. The frequency of a whistle sound as emitted by a passeng... JEE Main 2021 (Online) 26th August Evening Shift Two waves are simultaneously passing through a string and their equations are : y1 = A1 sin k(x$$-$$vt), y2 = A2 sin k(x$$-$$vt + x0). Given ampli... JEE Main 2021 (Online) 26th August Morning Shift A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a freq... JEE Main 2021 (Online) 26th August Morning Shift Two travelling waves produces a standing wave represented by equation,y = 1.0 mm cos(1.57 cm$$-$$1) x sin(78.5 s$$-$$1)t. The node closest to the orig... JEE Main 2021 (Online) 20th July Morning Shift The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. The... JEE Main 2021 (Online) 20th July Morning Shift The amplitude of wave disturbance propagating in the positive x-direction is given by$$y = {1 \over {{{(1 + x)}^2}}}$$at time t = 0 and$$y = {1 \ov... JEE Main 2021 (Online) 16th March Evening Shift A closed organ pipe of length L and an open organ pipe contain gases of densities $$\rho$$1 and $$\rho$$2 respectively. The compressibility of gases a... JEE Main 2021 (Online) 26th February Morning 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 produced in it, where x is in ... JEE Main 2021 (Online) 25th February Evening Shift The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%. JEE Main 2021 (Online) 24th 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 frequency of 676 Hz. The beat fre... JEE Main 2020 (Online) 8th January Morning Slot A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is ... ## MCQ (Single Correct Answer) JEE Main 2024 (Online) 31st January Morning Shift 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 $$60 \m... JEE Main 2023 (Online) 11th April Evening Shift A car P travelling at$$20 \mathrm{~ms}^{-1}$$sounds its horn at a frequency of$$400 \mathrm{~Hz}$$. Another car$$\mathrm{Q}$$is travelling behind... JEE Main 2023 (Online) 10th April Evening Shift For a periodic motion represented by the equation$$y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$$the amplitude of the motion is... JEE Main 2023 (Online) 8th April Morning Shift The engine of a train moving with speed$$10 \mathrm{~ms}^{-1}$$towards a platform sounds a whistle at frequency$$400 \mathrm{~Hz}$$. The frequency ... JEE Main 2023 (Online) 1st February Morning Shift A steel wire with mass per unit length$$7.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$$is under tension of$$70 \mathrm{~N}$$. The speed of trans... JEE Main 2023 (Online) 29th January Morning Shift A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of$$30 \mathrm{~m} / \mathrm{s}$$. If both... JEE Main 2023 (Online) 24th January Morning Shift A travelling wave is described by the equation$$y(x,t) = [0.05\sin (8x - 4t)]$$m The velocity of the wave is : [all the quantities are in SI unit]... JEE Main 2022 (Online) 28th July Morning Shift In the wave equation$$ y=0.5 \sin \frac{2 \pi}{\lambda}(400 \mathrm{t}-x) \,\mathrm{m} $$the velocity of the wave will be: JEE Main 2022 (Online) 26th July Evening Shift A transverse wave is represented by$$y=2 \sin (\omega t-k x)\, \mathrm{cm}$$. The value of wavelength (in$$\mathrm{cm}$$) for which the wave velocit... JEE Main 2022 (Online) 30th June Morning Shift Which of the following equations correctly represents a travelling wave having wavelength$$\lambda$$= 4.0 cm, frequency v = 100 Hz and travelling in... JEE Main 2022 (Online) 29th June Morning Shift A longitudinal wave is represented by$$x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)$$cm. The maximum particle velocity will be four time... JEE Main 2022 (Online) 28th June Morning Shift The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be : JEE Main 2022 (Online) 27th June Evening Shift If a wave gets refracted into a denser medium, then which of the following is true? JEE Main 2022 (Online) 27th June Morning Shift An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequ... JEE Main 2022 (Online) 24th June Morning Shift The equations of two waves are given by : y1 = 5 sin 2$$\pi$$(x - vt) cm y2 = 3 sin 2$$\pi$$(x$$-$$vt + 1.5) cm These waves are simultaneously passi... JEE Main 2021 (Online) 22th July Evening Shift The motion of a mass on a spring, with spring constant K is as shown in figure.The equation of motion is given by x(t) = A sin$$\omega$$t + B cos$$\om... JEE Main 2021 (Online) 17th March 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 wave moves to and from through a ... JEE Main 2021 (Online) 26th February Evening Shift A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2... JEE Main 2021 (Online) 25th February Morning Shift A student is performing the experiment of resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed... JEE Main 2021 (Online) 24th February Evening Shift Which of the following equations represents a travelling wave? JEE Main 2020 (Online) 6th September 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 observer is standing at a fin... 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 480 Hz, when it gets reflected f... JEE Main 2020 (Online) 5th September Morning Slot Assume that the displacement(s) of air is proportional to the pressure difference ($$\Delta$$p) created by a sound wave. Displacement (s) further dep... JEE Main 2020 (Online) 5th September Morning Slot In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When t... JEE Main 2020 (Online) 4th 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 when he hears it after it gets r... JEE Main 2020 (Online) 4th September Morning Slot For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one t... JEE Main 2020 (Online) 3rd September Morning 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 attached to its free end. A transve... JEE Main 2020 (Online) 2nd September Morning Slot Two identical strings X and Z made of same material have tension TX and TZ in them. If their fundamental frequencies are 450 Hz and 300 Hz, respective... JEE Main 2020 (Online) 9th January Evening Slot A wire of length L and mass per unit length 6.0 × 10–3 kgm–1 is put under tension of 540 N. Two consecutive frequencies that it resonates at are : 420... JEE Main 2020 (Online) 9th January Morning Slot Three harmonic waves having equal frequency $$\nu$$ and same intensity $${I_0}$$, have phase angles 0, $${\pi \over 4}$$ and $$- {\pi \over 4}$$ r... JEE Main 2020 (Online) 8th January Evening 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 is changed to T, the velocity... JEE Main 2020 (Online) 7th January Evening Slot A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less... JEE Main 2020 (Online) 7th January Morning 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. If the Young's modulus of wire ... 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 S2 with a constant speed u m/... 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 method. Resonance is observed to ... JEE Main 2019 (Online) 12th April Evening Slot A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of... 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 + $$\phi$$). Its snapshot at t = 0 is ... JEE Main 2019 (Online) 12th April Morning Slot A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar... 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 Hz and 11 Hz, is : JEE Main 2019 (Online) 10th April Evening Slot A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. W... JEE Main 2019 (Online) 10th April Morning Slot A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequenc... 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–1 with respect to the ground. ... JEE Main 2019 (Online) 9th April Evening 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. The speed of the wave and it... 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 atmospheric temperature is 0°C... JEE Main 2019 (Online) 9th April Morning 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 = 0.3 sin(0.157x) cos(200pt). T... JEE Main 2019 (Online) 8th April Morning 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 same material. It is vibrating ... JEE Main 2019 (Online) 12th January Evening 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 tuning fork of frequency 512 H... JEE Main 2019 (Online) 12th January Morning Slot A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the f... JEE Main 2019 (Online) 11th January Morning 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 time are measured in SI units... 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 by the observer is ƒ1. If the s... JEE Main 2019 (Online) 10th 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 vibration using an external vibr... JEE Main 2019 (Online) 9th January Evening Slot A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at ... JEE Main 2019 (Online) 9th January Morning Slot A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of tran... 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 tension of the string B s slight... JEE Main 2018 (Online) 16th April 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 next resonating length should... JEE Main 2018 (Offline) A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $$\times$$ 103 kg/... JEE Main 2018 (Online) 15th April Evening Slot 5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or... JEE Main 2018 (Online) 15th April Morning Slot A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is th... 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 displacement is given by y(x, t) = 0.5 s... JEE Main 2017 (Online) 9th April Morning Slot In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2 . The two ... JEE Main 2017 (Online) 8th 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$$\rho$$1 . They are joined together... JEE Main 2017 (Offline) An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of ... JEE Main 2016 (Online) 10th April Morning Slot 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 car is moving, is able to hea... JEE Main 2016 (Online) 9th 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 of frequency 540 Hz. Calculat... 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 lowest end. It starts moving up the... JEE Main 2016 (Offline) A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamen... JEE Main 2015 (Offline) A train is moving on a straight track with speed $$20\,m{s^{ - 1}}.$$ It is blowing its whistle at the frequency of $$1000$$ $$Hz$$. The percentage ch... JEE Main 2014 (Offline) A pipe of length $$85$$ $$cm$$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies li... JEE Main 2013 (Offline) A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\%$$. What is the fundamental frequenc... AIEEE 2012 A cylindrical tube, open at both ends, has a fundamental frequency, $$f,$$ in air. The tube is dipped vertically in water so that half of it is in wat... AIEEE 2011 The transverse displacement $$y(x, t)$$ of a wave on a string is given by $$y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt}... AIEEE 2010 The equation of a wave on a string of linear mass density$$0.04\,\,kg\,{m^{ - 1}}$$is given by$$$y = 0.02\left( m \right)\,\sin \left[ {2\pi \left...
AIEEE 2009
Three sound waves of equal amplitudes have frequencies $$\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$$ They superpose to give beats. The numb...
AIEEE 2009
A motor cycle starts from rest and accelerates along a straight path at $$2m/{s^2}.$$ At the starting point of the motor cycle there is a stationary e...
AIEEE 2008
While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $$1... AIEEE 2008 A wave travelling along the$$x$$-axis is described by the equation$$y(x, t)=0.005\cos \,\left( {\alpha \,x - \beta t} \right).$$If the wavelen... AIEEE 2007 A sound absorber attenuates the sound level by$$20dB$$. The intensity decreases by a factor of AIEEE 2006 A whistle producing sound waves of frequencies$$9500Hz$$and above is approaching a stationary person with speed$$vm{s^{ - 1}}.$$The velo... AIEEE 2006 A string is stretched between fixed points separated by$$75.0cm.$$It is observed to have resonant frequencies of$$420Hz$$and$$315H...
AIEEE 2005
When two tuning forks (fork $$1$$ and fork $$2$$) are sounded simultaneously, $$4$$ beats per second are heated. Now, some tape is attached on the pro...
AIEEE 2005
An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the app...
AIEEE 2004
The displacement $$y$$ of a particle in a medium can be expressed as, $$y = {10^{ - 6}}\,\sin$$ $$\left( {100t + 20x + {\pi \over 4}} \right)$$ $$m... AIEEE 2003 A metal wire of linear mass density of$$9.8g/m$$is stretched with a tension of$$10kg$$-$$wt$$between two rigid supports$$1$$metre apar... AIEEE 2003 The displacement$$y$$of a wave travelling in the$$x$$-direction is given by$$$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,... AIEEE 2003 A tuning fork of known frequency $$256$$ $$Hz$$ makes $$5$$ beats per second with the vibrating string of a piano. The beat frequency decreases to $$2... AIEEE 2002 length of a string tied to two rigid supports is$$40cm$$. Maximum length (wavelength in$$cm$$) of a stationary wave produced on it is AIEEE 2002 A tuning fork arrangement (pair) produces$$4$$beats/sec with one fork of frequency$$288cps.$$A little wax is placed on the unknown fork and i... AIEEE 2002 Tube$$A$$has bolt ends open while tube$$B$$has one end closed, otherwise they are identical. The ratio of fundamental frequency of tube$$A$$and ... AIEEE 2002 A wave$$y=a\sin \left( {\omega t - kx} \right)$$on a string meets with another wave producing a node at$$x=0.$\$ Then the equation of the unkno...
AIEEE 2002
When temperature increases, the frequency of a tuning fork
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