Waves Questions and Answers

A transverse harmonic wave of amplitude 1 0 cm and wavelength 3 0 m is travelling in positive x direction on a stretched string At an instant the particle at x 5 0 m is at y 0 5 cm and is travelling in positive y direction Find the coordinate of the nearest particle x 5 0 m which is at its positive extreme at this instant

6 The wave profile in Figure 15 shows several particles at t 0 The wave has a time period of 8 seconds displacement m 0 3 0 2 0 27 O 3 E 4 distance m 8 Figure 15 a What is the wavelength of this wave in meters b What is the frequency of this wave c What is the phase difference in degrees between points D and E What is the phase difference in VE Pa hete To A

ectromagnetic wave of frequency v 3 0 MHz passes from vacuum into a dielectric medium with relative permittivity 4 0 Then NEET Kar 2013 a wavelength is doubled and frequency is unchanged b wavelength is doubled and frequency becomes half c wavelength is halved and frequency remains unchanged d wavelength and frequency both remain unchanged

A wave travels on a light string The equation of the wave is Y A sin kx oot 30 It is reflected from a heavy string tied to an end of the light string at x 0 If 64 of the incident energy is reflected the equation of the reflected wave is 1 Y 0 8 A sin kx oot 30 180 2 Y 0 8 A sin kx oot 30 180 3 Y 0 8 A sin kx cot 30 4 Y 0 8 A sin kx oot 30

9 At nodes in stationary waves a change in pressure and density are maximum b change in pressure and density are minimum c strain is zero d energy is maximum

In the given arrangement shown in figure a mass M is suspended with the help of string which passes over a light pulley The string is connected to vibrator having constant frequency The vibrator gives transverse oscillation to string When the value of M is either 16 kg or 25 kg standing waves an observed however no standing waves are observed with any mass between these values The largest mass for which standing waves could be observed is n x 102 kg Find the value of n String is very light Virbrator L

A beam of light consisting of two wavelengths 500 nm and 400 nm is used to obtain interference fringes in Young s double slit experiment The distance between the slits is 0 3 mm and the distance between the slits and the screen is 1 5 m Compute the least distance of the point from the central maximum where the bright fringes due to both the wavelengths coincide

The slits S S is illuminated by a light source Semitting light of wavelength The slits are separated by a distance d A plane mirror is placed at a distance D in front of the slits and a screen is placed at a distance 2D behind the slits The screen receives light reflected only by the plane mirror The fringe width

Two tuning forks A and B lying on opposite sides of observer O and of natural frequency 85Hz move with velocity 10 m s relative to stationary observer O Fork A moves away from the observer while the fork B move towards him A wind with a speed 10 m s is blowing towards fork A Find the beat frequency measured by the observer in Hz Take speed of sound in air as 340 m s

A stone thrown into still water creates a circular wave pattern moving radially outwards If r is the distance measured from the centre of the pattern the amplitude of the wave aries as 2006 b r 1 c r a r 1 2 d r 3 2

2 y a cos kx ot superposes on another wave giving a stationary wave having node at x 0 What is the equation of the other wave 1 a cos kx ot 3 a cos kx wt 2 a cos kx ot 4 a sin kx ot

Q 5 Standing waves are established on a string of length L such that A is a node and B is an immediate anti node Oscillation amplitude for point B is ao Let a be the oscillation amplitude for point C Pick the suitable option s for correct value of a and the possible equation s for standing waves on the string Answer A B C D Your Attempt do d 2 X 0 P a ao y a sin x cos wt L 3 Correct answer y a sin 7 sin wt A L 2 5L 6 B C X L Rate this question

23 A child is observing a thin film such as a layer of oil on water shows beautiful colours when illuminated by white light on a rainy day He saw a motorcycle skidding on the oily road The motor cyclist was badly hurt The child signalled a passing by car to stop and help The car driver saw the hurt person and rushed away The child tried to stop other cars but of no avail He asked the hurt person whether he can sit on his bicycle On finding that he can safely do it the child cycled the hurt person to the hospital Answer the following questions a What value was displayed by the child b Comment on the moral values of car driver c Name and define the phenomenon involved d Does appearance of soap bubbles as coloured when seen in sunlight and also light splitted into seven colours by a prism follow the same phenomenon

22 A transverse wave is travelling along a string in the positive x axis then identify the points which have negative particle velocity 1 A 3 C toe B A 2 B 4 D

Contraction on heating Some rubber like substances contract on heating because transverse vibration of atoms of substance domin over longitudinal vibration which is responsible for expansion

12 Interference was observed in interference chamber when air was present Now the chamber is evacuated and if the same light is used a careful observer will see a no interference b interference with bright bands c interference with dark bands d interference in which width of the fringe will be slightly increased JAFMC 2006 CBSE PMT 19921

For progressive wave y 2cm sin 3t 4x Statement 1 The particle at x 0 is moving towards positive y axis at t 0 Statement 2 The particle at x 8m is in phase with particle at x 1m Statement 3 The acceleration of particle at x mat t sec is increasing in magnitude Statement 4 The velocity of particle at x m is in direction of propagation of wave at all times The correct statement are 8 6 O1 and 3 O 1 2 and 3 Q1 2 3 and 4

In an organ pipe with one end closed a standing wave is formed If the wave speed of longitudinal wave is v in the air contained by organ pipe and length of pipe is then equal of wave can be represented by TV A y A sin COS 27 t t if closed end is origin 27 t if closed end is origin COS B AP TCX BA T 20 C y A cos BA T 20 D AP 16 20 COS TCX 20 COS TCX 20 COS TCX 20 TV 2l COS t if open end is origin TTV 2l t if open end is origin

A composition string is made up by joining two strings of different masses per unit length and 4 The composite string is under the same tension A transverse wave pulse Y 6 mm sin 5t 40x where t is in seconds and x in meters is sent along the lighter string towards the joint The joint is at x 0 The equation of the wave pulse reflected from the joint is A 2 mm sin 5t 40x B 4 mm sin 40x 5t D 2 mm sin 5t 10x 2 mm sin 5t 40x In the previous question the percentage of power transmitted to the heavier string through the joint is approximately A 33 B 89 V1 Ai Ay 2 yr 2 sin st yox MVW Az Pr T C 67 D 75 J Ft 5m i JA 24 A F ST A 6 2 6 10 8 4 4 Pi

Which of the following statement s are true about a stationary wave No particle will move with same amplitude All particles between two successive nodes reach their extreme position together in phase Displacement and velocity nodes co exist O Velocity nodes and pressure nodes co exist

Q8 A parallel beam of fast moving electrons is incident normally on a narrow sit A fluorescent screen is placed at a large distance from the slit If the speed of the electrons is increased which of the following statements is correct a The angular of width width of the central maximum of the diffraction pattern will increase b The angular width of the central maximum will decrease c The angular width of the central maximum will be unaffected d Diffraction pattern is not observed on the screen in the case of electrons

u 2 13 11 A wall is moving with velocity u and a source of sound moves with velocity shown in the figure Assuming that the sound travels with velocity 10u The ratio of incident sound wavelength on the wall to the reflected sound wavelength by the wall is equal to A 9 11 B 11 9 S u 2 C 4 5 wot onille in the same direction as D 5 4

The electric field of strength 5kV m and magnetic field of induction 0 25T are crossed and velocity v of a charged particle is also perpendicular to both If the charged particle crosses both the fields undeflected the value of v in m s is A 1 25 10 B 2 x 10 C 1 25 x 104 D 2 104

Speed of a wave pulse on a 8 m long string fixed at both ends is 20 m s The frequency associated with the third overtone of the string is 2 Hz 3 Hz 5 Hz hr m 4 Hz

10 Four different independent i y a sinot iii y a cost 2 waves are represented by ii y a sin2wt iv Y a sin wot of TC 3 With which of two waves interference is possible 1 i ii 2 i iv 3 iii iv 4 Not possible with any combination 16

Statement I Disturbance in a medium is represented by equation y Statement II Any disturbance represented by y A Brict D is wave 3 2x 3t 3which represent a wave O Statement 1 is True Statement 2 is True Statement 2 is a correct explanation for Statement 1 Statement 1 is True Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1 Statement 1 is True Statement 2 is False O Statement 1 is False Statement 2 is True

A wave is represented by the equation y 10 sin2n 100t 0 02x 10 sin2 100t 0 02x The maximum amplitude and loop length are respectively 1 20 units and 30 units 2 20 units and 25 units 3 30 units and 20 units 25 units and 20 units 1

When vapour condenses into liquid 1 it absorbs heat 2 It liberates heat 3 Its temperature increases 4 Its temperature decreases A travelling wave passes a point of observation At this point the time interval between successive crests is 0 2 s and 1 the wavelength is 5m 2 the frequency is 5 Hz 3 the velocity of propagation is 5m s 4 the wavelength is 0 2m A tuning fork makes 256 vibrations per second in air When the velocity of sound is 330 m s ther

Q A standing wave y A sin TX cos 1000nt is maintained in a taut string where y and x are 3 expressed in meters The distance between the successive points oscillating with the amplitude A 2 across a node is equal to A 2 5cm B 25cm 5cm D 10cm N t o x 0 A 2 2 5cm A IN 2 S co 2 5 umm N sin 20 xx 12 Sin 2057x 1 2 20 An 3 FG 6 x 40 2 5cm

and sounded together with a tuning fork of frequency 100 Hz produces one beat then the frequency of the other tuning fork is 1 102 2 98 3 99 4 101 The equation of a transverse wave is given by y 10sinz 0 01x 2r where x and y are in cm and t is in seconds It frequency is 1 10s 2 2s 3 15 4 0 01s A particle executing simple harmonic motion along y axis has its motion described by the equation deinfet The amplitude of the simple harmonic motion in

The wave function for the wave pulse is y x t C x vt with C 4 cm at x 0 the displacem y x t is observed to decrease from its maximum value to half of its maximum value in time t 2 x 10 s A y x t represents the motion of travelling pulse moving along positive X direction B y x t does not represent the motion of a travelling pulse C Speed of wave pulse is 20 m s D Speed of wave nule i 10 m s

When a particle of mass m is attached to a vertical spring of spring constant k and released its motion is described by 2 y t y sin wt where y is measured from the lower end of upstretched spring Then wis A B C D 1 2 Yo b 0 Yo 2g VYo g

Part A The amplitude of a standing sound wave in a long pipe closed at the left end and open at the right end is sketched below The vertical axis is the maximum displacement of the air and the horizontal axis is along the length of the pipe What is the harmonic number for the mode of oscillation illustrated x Submit Answer Tries 0 10 Part B The length of the pipe is 0 410 m What is the pitch frequency of the sound Assume that the speed of sound is 310 m s Submit Answer Tries 0 10 Part C

The equation of transverse displacement of a string clamped at both ends is 2 X y 0 06 sin 3 cos 120nt where x y are in meters and t is in second The length of the IMPORTANT FORM string is 1 5 m and its mass is 3 x 10 kg Then A wavelength frequency and speed of progressive wave are 3 m 60 Hz and 180 m s respectively B tension in the string is 648 N C amplitude at a distance x 0 375 m is 4 2 cm D wavelength frequency and speed of progressive waye are 3 m 80 Hz and 240 m s

A string fixed at both ends has a standing wave mode for which the distances between adjacent nodes is 18 cm For the net consecutive standing wave mode distance between adjacent nodes is 16 cm The minimum possible length of the string is A B 144 cm Correct Answer 204 cm 288 cm

Example The increase in energy of a fallen photon was first observed in 1960 by Pound and Rebka at Harvard In their work H was 22 5 m Find the change in frequency of a photon of red light whose original frequency is 7 3 x 10 Hz when it falls through 22 5 m Solution

iv A transmitting antenna at the top of a tower has a height of 32 m and that of the receiving antenna is 50m Wha is the maximum distance between them for satisfactory communication in line of sight mode Radius of the earth 6 4 x 10 m A 45 5 Km B 40 5 Km C 35 Km D 32 Km

1 Two trains are approaching each other each sounding a horn of frequency n 1000 Hz with velocities this case i calculate the frequency of the second V 10 m s1 and 20 m s 1 respectively In passenger of the first train and the whistle relative to frequency of the first whistle relative to a passenger of the second train ii What will be these two frequencies after the two trains cross each other Velocity of sound 340 m s 1 i 1094 Hz 1091 Hz ii 917 Hz 914 Hz

A fisherman notices that his boat is moving up and down periodically without any horizontal motion owing to waves on the surface of the water It takes a time of 2 90 s for the boat to travel from its highest point to its lowest a total distance of 0 680 m The fisherman sees that the wave crests are spaced a horizontal distance of 5 50 m apart Part A How fast are the waves traveling

of angular momentum 0 21 In a single slit diffraction pattern the distance between first minima on the right and first minima on R the left of central maximum is 4 mm The screen on which the pattern is displaced is slit and wavelength of light used is 6000 Calculate width of the slit and width of the central 2 m from the maximum 22 Draw a nent dir

A parallel beam of fast moving electrons is incident normally on a narrow slit A fluorescent screen is placed at a large distance from the slit If the speed of the electrons is increased which of the following statements is correct A B skipped C The angular width of the central maximum of the diffraction pattern will increase The angular width of the central maximum will decrease The angular width of the central maximum will be unaffected D Diffraction pattern is not observed on the screen in the case of electrons M

A snap shot of transverse wave travelling towards righ on a string is shown in figure then which of the following option is correct y A B C D E B and D points have maximum energy Point C has minimum energy Point E is going downward x Point A is going upward

string is fixed at a and its free end is at x 0 A triangular shape wave plus is moving along the string with Deed v m s in the positive x axis direction Its position at t 0 is shown in the figure he shape of wave pulse at t a 2v a will be a 2 y X 0

ev Con applied to A is increased The diffracted beam will elow Suppose the voltage have the maxima at a I value of 0 that NCERT Exemplar HT ww A Electron gun Movable collector Electron beam To galvanometer Diffracted electron beam a will be larger than the earlier value b will be the same as the earlier value c will be less than the earlier value d will depend on the target Nickel target 56 Vacuum chamber

An organ pipe resonates at successive frequencies of 50 Hz 150 Hz 250 Hz etc speed of sound 340 m s The pipe is Neglect end correction Open at both ends and of length 3 4 m Open at both ends and of length 6 8 m Closed at one end open at the other and of length 1 7 m Closed at one end open at the other and of length 3 4 m

A rope of length I and mass per unit length is suspended vertically If mass M is suspended from bottom of the rope Then time for a transverse wave to travel the rope is Answer Your Attempt A ME Mg B 2 C Correct answer 2 M l M Rate this qu

A wave y A cos t kx passes through a medium If V is the particle velocity and a is the particle acceleration then 1 y V and a all are in the same phase 3 a leads y by a phase angle of 2 2 y lags behind V by a phase angle of 4 V leads a by a phase angle of 2 3r

122 A string of length hangs freely from a rigid support under its own weight Find the time required by transverse waves to travel from lower end to upper end A T A I C T g NVX terliw to spe mu VX AS 0 B 2 shoe g 16121 D 1 2n g V VAOF

Equation of a wave travelling along x axis on a string is given as y 3 sin 3 14x 314t where x and y in cm and tin second Maximum velocity of particle is 9 4 ms 1 12 3 ms 1 6 2 m s 8 5 m s

45 Two sinusoidal waves given below are superposed Y A sin kx wt Y A sin kx ot 1 y 2 y 6 The equation of resultant wave is 4 y TU A 3 6 A 3 sin kx wt 3 A 3 sin kx wt sin kx wt 3 y A 3 sin kx wt T cost 3 Em