Waves Questions and Answers

An interference is observed due to two coherent sources A and B having phase difference zero separated by a distance 42 along the y axis where is the wavelength of the source If the distance of 3rd maxima on x axis from B is n find the value of n A

A ray of light strikes a transparent rectangular slab of refractive index 2 at an angle of incidence of 45 The angle between the reflected and refracted rays is a 75 b 90 c 105 d 120 c 14 A ve inde refra

The displacement of the medium in a sound wave is given by the equation y Acos ax bt where A a b are positive constants The wave is reflected by an obstacle situated at x 0 The intensity of the reflected wave is 0 64 times that of the incident wave A the wavelength of the incident wave is 27 a and its frequency is b 2 B the equation for the reflected wave is n 0 8 A cos ax bt C in the resultant wave formed after reflection the maximum particle speeds in the medium is 1 8bA D in the resultant wave formed after reflection the minimum particle speeds in the medium is zero Answer A CD

19 In a Young s double slit experimental arrangement shown here if a mica sheet of thickness t and refractive index u is placed in front of the slit S then the path difference S P S P is S Slit Screen 1 Decreases by 1 t 2 Increases by 1 t 3 Does not change

A stretched string of length 4 m vibrates in 6 loops The distance between consecutive antinodes is 113 3 6 m 4 m

The displacement of a wave disturbance propagating in the positive x direction is given by y 1 1 x at time t C and y 1 1 x 1 at t 2 seconds where x and y are in metres The shape of the wave disturbance does no is change during the propagation The velocity of the wave is 1 2 5 m s 1 62 1 2 0 25 m s 3 0 5 m s 4 5 m s quation Y Y sin ft x 2 The maximum particle velocity is equal to f

6 Two waves passing through a region are represented by y 1 0 cm sin 3 14 cm x 157 s t and y 1 5 cm sin 1 57 cm x 314 s t Find the displacement of the particle at x 4 5 cm at time t 5 0 ms

18 180 Mark for Review 1 02 57 hr min Which among the following statements is incorrect In interference all maxima are equally intense but in diffraction they are of varying intensity Interference occurs when two or more wavefronts from coherent sources overlap In diffraction the region of minimum intensity may not be perfectly dark In interference as well as in diffraction fringe

Particle nature of light is exhibited by O Diffraction and interference O Diffraction and refraction

A wire of linear density 8 x 10 3 kg m and length 2 m is stretched by a weight of 20 kg The fundamental frequency of vibration of the wire is O 6 29 Hz O4 Hz 39 52 Hz hr min 0 98 Hz

ma Young s double slit experiment 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600 nm is used If the whole set up is mmersed in a liquid of refractive index 4 3 the number of fringes observed in the same segment of the screen is 6 16

b The displacement y of a point on a vibrating stretched string at a distance x from one end at time t is given by a y 0 y at x Show that one solution of this equation is y Asin A p c and a are constants sin pt a where 5 marks

A chord attached to rigid supports is vibrating into 6 loops when its tension is 36 N The tension at which i will vibrate in 4 loops is frequency is same O 24 N O 36 N O 64 N 81 N

The displacement represented by y x t a cos kx wt represents 1 Transverse wave propagating in x direction Transverse wave propagating in x direction 3 Longitudinal wave propagating in x direction 4 Longitudinal wave propagating in x direction

When two coherent waves interfere there is 1 Loss in energy 2 Gain in energy 3 Redistribution of energy which changes with time 4 Redistribution of energy which does not change with time

How many number of maximas are formed on a finite screer in Young s double slit experiment given slit screen separation as 1 meter separation between slits 3 mm and wavelength used is 0 5 mm 5 6 9 11

In the arrangement shown in the figure below an object of mass m 2 0 kg hangs from a cord around a light pulley The length of the cord between point P and the pulley is L 2 0 m Ignore the mass of the vertical section of the cord Vibrator L m a When the vibrator is set to a frequency of 160 Hz a standing wave with six loops is formed What must be the linear mass density of the cord 00522 X Use the wavelength illustrated in the diagram and the other given information to calculate the wave speed and then from the wave speed find the linear mass density of the cord kg m b How many loops if any will result if m is changed to 72 0 kg Enter 0 if no loops form loops 6 low many loons if any will result if mic changed Entor 0 if Joong

A string of length 0 5 m and mass 20 gm is tied both ends When it vibrates in its 4th harmonic it produce equal number of beats per second when vibrated together with two tuning forks of frequencies 620 Hz and 580 Hz Find the tension in the string in N

3 Speed of a transverse wave on a straight win mass 6 0 g length 60 cm and area of cross sectio 1 0 mm is 90 ms 1 If the Young s modulu of wire is 16 x 1011 Nm 2 the extension of win over its natural length is 1 0 02 mm 2 0 04 mm 3 0 03 mm 4 0 01 mm

A wave 10 sin ax bt is reflected from dense medium at an origin If 81 of energy is reflected then the equation of reflected wave is 8 1 sin ax bt 8 1 sin ax bt 9 sin ax bt A B C D Y Y y y 10 sin ax bt

X a sin ot X2 a sin wt If in the resultant wave the frequency and amplitide remains equals to amplitude of superimposing waves Then phase diff between them 2 3 TU 2 3 4 B

In Maxwell s distribution curve if we increase the temperature and molecular weight both by the same factor the curve A Spreads out Becomes mor stoonor d

Which of the given functions is a wave function displacement y x position t time A a b are constants 1 y A sin ax bt y A sin ax bt Sa Somboa ari niw galyuci y A sin ax bt X A coslavy h 2 2 3 3 4

7 A uniform thread of linear mass density 2 0 g m passes through a fixed ideal pulley At its ends the thread is stacked into two heaps that do not interfere motion of the thread A beetle of mass m 80 g tries to manage itself at a constant height on the thread by adjusting its speed relative to the thread At some steady speed of the thread the beetle succeeds in doing so Find this steady speed of the thread Acceleration due to gravity is g 10 m s Amg 20m s

An acoustic wave given by y Asin wt kx is sent down a long string Upon reflection from one end the equation of reflected wave becomes A sin wt kx The resultant wave in the string will be 2 A A pure standing wave with amplitude A 2 B A combination of a standing wave with amplitude 2A and a traveling wav amplitude A C A traveling wave with amplitude D A combination of a standing wave with amplitude A and a traveling wave o 3 A 2

A 5 kg weight suspended vertically by a string vibrates with amplitude of 7 5 cm and a frequency of 60 oscillations per minute Find i Spring constant ii Maximum tension induced in spring iii Maximum velocity of the weight

When the diffraction pattern from a certain slit illuminated with laser light lambda 6330 angstrom is projected on a screen 150cmfrom the slit the second minima on each side are seperated by 8cm This tells us that the slit is approximately 0 005 cm wide the slit is approximately 0 05 cm wide a is approximately 7 5 a is the slit width a A is approximately 750

6 7 8 9 10 In the diagram the phase difference between points A and D is 2 A B D 1 x X 2 C 2 1 8 2 A 3 8 x 3 22 The velocity of a wave propagating along a stretched string is 10 m s and its frequency is 100 Hz The phase difference between the particles situated at a distance of 2 5 cm on the string will be 1 8 2 4 A x 4 If the frequency of a wave is 100 Hz then the particles of the medium cross the mean position in one second 1 100 times 3 400 times 3 3 8 4 2 The relation between frequency n wavelength and velocity of propagation v of the wave is 1 n v 2 n 2 v 4 n v 3 n 1 v 2 200 times 4 50 times Two sound waves are represented by the following equations Y 10 sin 3x t 0 03x and Y 5 sin 3x t 0 03x 3 cos 3nt 0 03x Then the ratio of their amplitudes is given by 1 1 1 3 2 1 T X 2 1 2 4 2 5 11 The correct relation between phase difference 8 and path difference A is 2 2 8 A 2 4 8 2

Sound waves from different source are interfering and pressure at some point in space is given as P Posin 200 t 2 os 3 t 3 The frequency of one source is above 100Hz and other source is below 100Hz Beat frequency is 3 Hz Beat frequency is 200 Hz Beat frequency can be 3 Hz as well as 200 Hz

block with a speaker bolted to it is connected to a spring having spring constant k 45 0 N m as shown in the figure below The total mass of the block and speak 00 kg and the amplitude of this unit s motion is 0 610 m The speaker emits sound waves of frequency 442 Hz Assume the speed of sound in air is 343 m s wwwwww a Determine the highest frequency heard by the person to the right of the speaker Give your answer correct to 1 Hz Hz b Determine the lowest frequency heard by the person to the right of the speaker Give your answer correct to 1 Hz

05 34 IlmA VIV t ms 10 15 20 12 The given graph shows variation with time in the source voltage Vand steady state current I drawn by a series RLC circuit Which of the following statements is are correct a Current lags the voltage f Resistance in the circuit is 250 3 22 c If capacitive reactance is 742 inductance in the circuit is approximately 560 mH d Average power dissipation in the circuit is 20 3 W

21 In a stretched string 1 Only transverse waves can exist 2 Only longitudinal waves can exist 3 Both transverse and longitudinal waves can exist 4 None of these

Light of wavelength 624 nm is incident perpendicularly on a soap film n 1 33 suspended in air What are the a least and b second least thicknesses of the film for which the reflections from the film undergo fully constructive interference

Intensity of a sound wave gets reduced by 20 on passing through a slab The reduction in intensity on passage through two such consecutive slabs is Question Type Single Correct Type 1 40 2 36 3 30

During propagation of a plane progressive mechanical wave which one is INCORRECT Question Type Single Correct Type 1 all the particles are vibrating in the same phase 2 amplitude of all the particles is equal 3 particles of the medium executes S H M wave velocity depends upon the nature of the

A transverse wave is travelling through a string of a mass per unit length 100 g m The tension in the string is 10 N If the equation of the wave is y 2 cm sin 20t 2x where x t are in m and second the linear energy density of a point when it passes through mean position is O 1 6 x 10 2 J m O 1 6 x 104 J m O 1 6 J m Zero t

In a standing wave on a string rigidly fixed at both ends 1 all the particles must be at their positive extremes simultaneously once in half of the time period 2 all the particles must be at their positive extremes simultaneously once in a time period 3 in one time period all the particles are simultaneously at rest twice 4 all the particle are never at rest simultaneously

Parallel beam of light of wavelength 500nm falls on two narrow slits placed a distance d 25 x 10 4 cm apart at an angle 30 relative to the slits On the lower slit a transparent material 15 10 3 cm wide is placed Its refractive index is 7 The interference pattern appears on a screen a distance from the slits d O 30 The angular position of central maximum is 30 below certain line The order of minima closest to 8 0 is 26 Screen If the transparent material from the lower slits is removed then number of maximas that will pass through 8 0 position on screen is 50 If the transparent material from the lower slits is removed then number of maximas that will pass through 8 0 position on screen is 25 D

165 Two waves each of intensity io and wavelength 0 2 m starts from sources A and B and meet at point P as shown in the figure If AP 0 5 m BP 0 8 m then intensity at Pis A B 1 210 2 10 3 10 2

4 In all of the above conditions 159 A y travelling wave pulse is given m then 20 4 x 4 1 The pulse is travelling along negative x axis 2 The speed of pulse is 4 m s 3 The amplitude of pulse is 5 m 4 All of these by

same ng in open pe is d per de is asing ives 3 e last Hz duces may be a 420 Hz c 440 Hz b 430 Hz d 450 Hz 94 A train standing in a station yard blows a whistle c frequency 400 Hz in still air The wind starts blowing in the direction from the yard to the station with speed of 10 ms Which of the following statemen is correct Speed of sound in still air is 340 ms a The frequency of sound as heard by an obserw standing on the platform is 400 Hz b The speed of sound for the observer standing the platform is 330 m s c The frequency of sound as heard by the obser standing on the platform will increase d The frequency of sound as heard by the obser unding on the platform will decrease

5 s For waves propagating in a medium identify the property that is independent of the others 1 Velocity defenes in medin 2 Wavelength 3 Frequency 4 All these depend on each other

A horizontal beam of laser light of wavelength 517 nm passes through a narrow slit that has width 0 0570 mm The intensity of the light is measured on a vertical screen that is 2 70 m from the slit T Part A What is the minimum uncertainty in the vertical component of the momentum of each photon in the beam after th through the slit Express your answer with the appropriate units Apy 01 Part B A Value Submit Request Answer Units LA Use the result of part A to estimate the width of the central diffraction maximum that is observed on the screen Express your answer to two significant figures and include the appropriate units O BOND

Gravitational field at the centre of the semicircle formed by a thin wire AB of mass M and length is 2 GM 1 along x axis e 3 4 GM l Y 2 GM A O along y axis 2 GM e along x axis along y axis B x X T

A composite string is made up by joining two strings of different masses per unit length and 4 respective The composite string is under the same tension A transverse wave pulse y 6 mm sin 5t 40x where t in seconds and x in meters is sent along the lighter string towards the joint The joint is at x 0 The equati of the wave pulse reflected from the joint is 2 mm sin 5t 40x 4 mm sin 40x 5t 2 mm sin 5t 40x 2 mm sin 5t 10x

In a sonometer experiment the string of length under tension vibrates in second overtone between two bridges The amplitude of vibration is maximum at L 2L 5L a LLL b 336 8 4 2 L L 5L c LL d MHT CET

Example 15 2 A wave travelling along a string is described by y x t 0 005 sin 80 0 x 3 0 t in which the numerical constants are in SI units 0 005 m 80 0 rad m and 3 0 rad s Calculate a the amplitude b the wavelength and c the period and frequency of the wave Also calculate the displacement y of the wave at a distance x 30 0 cm and time t 20 s

A string is stretched along the x axis There is a transverse disturbance along the string x t 4 sin cos 10 t cm where x is measured in centimeter and t in seconds Assume the velocities and amplitudes are equal for the two waves The velocity in cm s of the two waves moving towards each other which create this disturbance is

The time period of a spring pendulum on earth is T If it is taken on the moon and made to oscillate the period of vibration will be 1 Less than T 3 More than T 2 Equal to T 4 None of these Z NODE02 BOAI BO TARGET PHY ENGW

A thin string is held at one end and oscillated vertically so that y x 0 t 8 sin 4t cm Neglect the gravitational force The string s density is 0 2 m tension is 1N The string through a bath filled with 1kg water Due to friction heat is transferred to the bath The heat transfer efficiency is 50 and its The power transfer to the bath is 0 0 01145 watt