Waves Questions and Answers

58 In Young s double slit experiment the fringe pattern is observed on screen placed at a distance D The slits are illuminated by light of wavelength 2 The distance from the central point 3 where intensity becomes th of the maxima will 4 be 1 3 AD 6d D 2d 2 4 D d 2ND 3d

50 The slits in a Young s double slit experiment have equal width and the source is placed symmetrically with respect to the slits The intensity at the central fringe is lo If one of the slits is closed the intensity at this point will be The value of a is

47 Two sound sources are moving in opposite directions with velocities and v v Both are moving away from a stationary observer The frequency of both the sources is 900 Hz What is the value of V V in m s so that the beat frequency observed by the observer is 6 Hz Speed of sound 300 m s Given that v and v v

28 Two identical waves each of intensity lo superpose at a point in space Then they are said to be destructively interfering if the resultant I is A equal to zero B equal to 210 C greater than 2lo D less than 200

A sinusoidal wave travelling on a rope has a period of 0 025 s speed of 30 m s and an amplitude of 0 021525 m At t 0 the element of the string has zero displacement and is moving in the x direction Find the following wave characteristics a frequency f b angular frequency w c wave number k d wavelength e Write the wave function

Complete destructive interference occurs when waves are out of phase by a 1 wavelength b wavelength c wave length d Multiple wavelengths e None of the above Which of the following statements in incorrect a x ray wavelengths are comparable to lattice spacings b x ray diffraction can be carried out in a laboratory environment c x ray diffraction is non destructive d x ray diffraction always requires a single crystal sample e Intensity of x ray diffraction peaks is related to structure factor Which of the following statements is correct Cu K alpha radiation has a wavelength of 1 54 nm b Electron wavelength in transmission electron microscopy is smaller than x ray wavelength a C XRD of an amorphous solid gives sharp peaks d Cubic close packing repeats in the order of ababab Systematic absences occur in all tuma e

Maxwell s theory of electromagnetic waves was experimentally tested by Oersted Tesla min sec Hertz

Consider two identical plane waves having the same phase shift one is propagating in x direction while the other is propagating in y direction One can say they will have constructive interfernce Select one O True O False

28 Which of the following statement is false for the properties of electromagnetic waves a Both electric and magnetic field vectors attain the maxima and minima at the same place and sam time b The energy in electromagnetic waves is divided equally between electric and magnetic field vecto c Both electric and magnetic field vectors are parallel to each other and perpendicular to the directic of propagation of wave d These waves do not require any material medium for propagation vision on 500 MHE

7 i In biprism experiment the eye piece was placed at a distance of 120 cm from the source The distance between two virtual images was found to be 0 075 cm Find the wavelength of light source if eye piece is moved through a distance of 1 88 cm for 20 fringes crossed the field of view 6

On observing light from three different stars P Q and R it was found that intensity of violet colour is maximum in the spectrum of P the intensity of green colour is maximum in the spectrum of R and the intensity of red colour is maximum in the spectrum of Q If Tp To and TR are the respective absolute temperatures of P Q and R then it can be concluded from the above observations that O Tp Ta Tr O Tp Ta Tr

Q 12 A particle is oscillating according to the equation X 7 cos 0 5 nt where t is in second The point moves from the position of equilibrium to maximum displacement in time 1 4 0 second bng 2 2 0 second 3 1 0 second 4 0 5 second

in a pipe closed at one end is made to vibrate in its third overtone by a tuning fork of frequency 660 Hz The speed of sound in air is 330 m s end correction is negligible Let Po denote the mean pressure at any point in pipe What is the maximum pressure at the open end of the pipe Po Read Less 29 2

Eleven tuning forks are arranged in an ascending order of frequencies If each tuning fork produces 8 beats per second with the previous one If the frequency of last fork is an octave of the first the frequency of 10th fork from beginning will be

The device for the demonstration of sound interference has first two identical upper and lower acoustic ducts At what minimum distance in meters is it necessary to lower the lower acoustic circuit in order to maximally weaken the sound of the horn B at the frequency v 100 Hz Take speed of sound to be 340 m s inside the ducts Jwww B Jums

A plane progressive sound wave of frequency 160 Hz is moving along vector 31 4j Find phas difference between point A 1 0 2 and point B 3 1 4 is Given velocity of sound 320 m s A Eld B B O C 2 D 3r

Two waves represented by the following equations are travelling in the same medium y 5 sin 2m 75t 0 25x y 10 sin 2 150t 0 50x The intensity ratio 1 12 of the two waves is 1 1 2 2 1 4 3 1 8 4 1 16

The same progressive wave is represented by two graphs I and II Graph I shows how the displace ment y varies with the distance x along the wave at a given time Graph II shows how y varies with time t at a given point on the wave The ratio of measurements AB to CD marked on the curves represents M A N

How can the wave velocity decrease when the density increases because when the density increases the particles come closer and therefore the wave should travel faster Also in solids sound travels the fastest because of its high density So shouldn t this be true that the way velocity increases with increasing density

A plane progressive simple harmonic sound wave of angular frequency 680 rad s moves with speed 340 m s in the direction which makes equal angle with each x y and z axis The phase difference 0 0 of the oscillations of the particle in the medium located at the positions 0 0 3 and 0 0 2 3 is assume cos 0 A 2 radian B 3 radian C 4 radian D 6 radian

The original frequency of the note produced by a sonometer is n The sonometer wire is reduced in length to half of its original value and its tension increases four times The frequency becomes 2n O 4n O 3n On Marks 4 1

the place of the listener Speed of sound in air 320 m s 12 51 tuning fork are arranged in a series in such a way that each fork produce five beats sec with neighbouring tunning fork If frequency of last is six time of first then determine frequency of first 11th 17th 27th 33th and last tunning fork REFLECTION OF WAVES STATIONARY WAVES STANDING WAVES IN STRINGS 5

Figure shows a snapshot of a vibrating string at t 0 The particle P is observed moving up with velocity 20 3 cm s The tangent at P makes an angle 60 with the x axis Select correct option s ua hea yg s Tef qu h P 20 3 cm s 34 3 na sem g n diga da 1 puz zyrftu x 360 u Afa ga 1 a facu facut ce qu B 4 1 5 D P 60 A negative x axis Correct Answer 3 5 5 5 2 x in 10 m x 10 m Velocity of wave is 20 cm s along ffu ain c 20 cm s Correct Answer Angular frequency of wave is 31 4 rad s 31 4 rad s Velocity of wave is 20 cm s along positive x axis cafe din c 20 cm s Frequency of wave is 10 rad s 10 rad s

If the speed of the wave shown in the figure is 330 m s in the given medium then the equation of the wave propogating in the positive x direction will be all quantities are in MKS units YA m V 0 25 m 0 05 m

other at a particular point Amplitude and frequency of both the waves are equal The ratio of intensities when both waves reach in the same phase and they reach with the phase difference of 90 will be

2 A wave of wavelength 400 nm superimposes with another wave coherent with first of same wavelength If the path difference between the waves is 300 nm then the resultant intensity due to superposition will be 1 Maximum 2 Minimum 3 Between minimum and maximum oximum wavelength 21

Plot the corresponding reference circle for each of the following simple harmonic motions Indicate the initial t 0 position of the particle the radius of the circle and the angular speed of the rotating particle For simplicity the sense of rotation may be fixed to be anticlockwise in every case x is in cm and t is in s a x 2 sin 3t 1 3 b x cos 6 t x 3 sin 2nt 4 c

30 An isotropic stationary source is emitting waves 6 of frequency n and wind is blowing due north An observer A is one north of the source while observer B is on south of the source If both the observers are stationary then 1 frequency received by A is greater than n 2 frequency received by B is less than n 3 frequency received by A is equal to that received by B 4 frequencies received by A and B cannot be calculated unless velocity of waves in still air and velocity of wind are known 30 fat fa and the aff a 4 ABRT feat ad 1 Aferd safe fr 2 B 3 Afera en Buffa EFTER n A f B n sifat and at a af fear anyan na an

Which of the following statements is are correct for mechanical standing wave on a stretched wire A Elastic potential energy of a small element at antinode is constant and minimum B Elastic potential energy of a small element at node is constant and maximum C Total energy of an element is constant D Total kinetic energy between two consecutive nodes become maximum twice in one time peri

2 Assume the sun rises at 5 30 a m 6 a m and 6 30 a m in Kolkata Bhopal and Ahmedabad respectively You re in a helicopter that took off vertically from Bhopal and has remained at a constant altitude without moving forward or backward After half an hour where will you 44 344 ch ac d Huld 32 344101 as 5 30 aut as 6 aut 3FR yar a y Salchite HUM 3R 35H H 34 Aga jus yas 6 30 34R URFI 3T c Gi 3TU ch i O Kolkata Bhopal Ahmedabad Shopal Kolkata

Question how to determine the direction of progression of a wave

3 4 5 mm 4 6 mm Two light wave from coherant sources superpose 2 at point A with phase difference 0 at point B with phase difference of x 2 Calculate ratio of resultant intensities of point A B 2 2 1 4 1 4 1 1 1 3 4 1 3 4 5 mm a far TIT 1 1 1 3 4 1 4 6 mm 0 fi B x 2 tir fra funnet at gula 2 2 1 4 1 4

Two particles of medium disturbed by the wave 41 propagation are at x 0 and x 1 cm The respective displacements in cm of the particles can be given by the equations y 2 sin 3xt y 2 sin 3xt 8 The wave velocity is 1 16 cm s 2 24 cm s 3 12 cm s 4 8 cm s When a wave travels in a medium the particle 42 x 1 16 cm s 3 12 cm s 0x 1cm f fe face a y 2 in 3at y 2 sin 3xt n 8 at 2 24 cm s 4 8 cm s

5 The equation of the stationary wave is cos 2x COS 2 ct y 2A sin Which of the following statements is wrong A The unit of ct is same as that of B The unit ofx is same as that of C The unit 2nc is same as that of 2 x t D The unit of c is same as that of x 2

a A string is stretched and fastened to two points at distance L apart is displaced into the form y x 0 3 x x from which it is released at t 0 Write suitable partial differential equation with initial and boundary condition Justify your choice

4 9 m s A police car moving at 22 m s chase a motorcyclist The police man sounds his horn at 176 Hz while both of them move towards a stationary siren of frequency 165 Hz Calculate the speed of the motorcyclist if he does not observe any beats Velocity of sound in air 330 m s 1 33 m s 3 Zero 2 22 m s 4 11 m s

The strings of a guitar have a length of 0 627 m The lowest E string has a mass of 3 32 g and has a tension of 226 N What is the speed of waves on this string 1 Point 207 m s 43 000 m s 43 m s 6 5 m s

Which of the following is an example of a transverse wave only 1 Point sound waves in fluids wave produced by strumming the strings of a guitar wave motion in a slinky waves produced by striking a piece of wood with a hammer

What is the frequency of this wave 1 Point y m period 0 25 S 0 25 Hz 4 s 4 Hz Time s Vi 1s

5 Which of the following statements accurately describes how mechanical waves are able to transmit energy efficiently 1 Point Mechanical waves are able to act at a distance and don t require a medium where energy is lost Mechanical waves are able to absorb the thermal energy from the random motion of the particles in the medium After a wave has passed through a medium the particles return to their original location so no energy is lost by the wave Mechanical waves displace each particle of the medium by the same distance so that energy is distributed through out

If the Mach number is 0 81 and the speed of the airplane measured by radar is 850 km h what is the local temperature of the air 1 Point 3200 C 248 C 25 C 66 C

A wave has a speed of 2100 m s and a period of 0 01818 s What is its approximate wavelength 1 Point 38 m 115 500 m 2045 m 2155 m

The oscillatory motion of a simple pendulum is represented by 0 t 0 15rad cos 2 56t Which one of the following is closest to the length of the pendulum a 0 15 m Ob 0 25 m Oc 1 5 m Od 6 4 m

2 Sketch a possible graph of the wave and give a formula that matches your graph a a wave that is 8 4 nanometers from top to bottom and has a frequency of 10 Hertz

You and a partner sit on the floor and stretch out a coiled spring to a length of 7 2 meters You shake the coil so you have 1 antinode between the two of you Your partner measures the time for 10 vibrations and finds that its takes 16 3 seconds to make 10 vibrations What is the speed of the wave two part question

5b A student makes a claim that a piece of wood on top of an ocean wave stays in the same location only moving up and down as the wave passes It is energy that moves toward the shore Do you accept or reject this student s claim Explain your answer 3 points

A wave is present in a slinky A coil of the slinky makes 12 complete up and down cycles of vibration in a total time of 4 seconds The period of this wave is seconds and the frequency is Hertz Do not answer in fractions

Jennie waves the end of a skipping rope up and down 4 0 times every second What is the period of the waves produced in the rope O2 0 s 0 13 s 4 0 s 0 25 s

What quantity does the distance marked z represent y z A A O wavelength O frequency O amplitude X

You have an air column open at both ends of length 1 2m in air at 30 C Calculate the frequency of the second harmonic