Waves Questions and Answers

There is a string of length 3L whose end points are fixed The velocity of transverse wave in the string is v It is desired that the mid point of the string should be a node The minimum excitation frequency to achieve this will be Answer A B Your Attempt 2v 3L v 6L Rate this question Correct answer

In Exercises 17 22 specify a the period and b the amplitude and c identify the viewing window that is shown Caution Don t assume that the tick marks on both axes are at integer values 17 y 1 5 sin 2x 18 y 2 cos 3x MA UM A 19 y 3 cos 2x AAAA 21 y 4 sin amfany 20 y 5 sin 22 y cos x MA AA

Question 1 1 point Which of the following changes could you make to alter the speed of a sound wave as it travels through the air a Increase the pitch of the sound wave b Increase the temperature of the air c Increase the wavelength of the sound wave

22 Two vibrating strings of same length same cross section area and stretched to same tension are made of materials with densities p 2p Each string is fixed at both ends If v represents frequency of the fundamental mode of vibration of the one made with density p and v for another then v v is 2 a 1 2 b 2 c 2 C d 1 28

Three waves producing displacement in the same direction of same frequency and of amplitudes 10 m 4 m and 7 m arrive at a point with successive phase difference of 2 The amplitude of the resultant wave is Question Type Single Correct Type 12 m 2 7 m 3 5 m

12 A taut string at both ends vibrates in its nth overtone The distance between adjacent Node and Antinode is found to be d If the length of the string is L then a L 2d n 1 c L 2dn b L d n 1 d L 2d n 1

A vibrating string of certain length under a tension T resonates with a mode corresponding to the first overtone third harmonic of an air column of length 75 cm inside a tube closed at one end The string also generates 4 beats per second when excited along with a tuning fork of frequency n Now when the tension of the string is slightly increased the number of beats reduces to 2 per second Assuming the velocity of sound in air to be 340 m s the frequency n of the tuning fork in Hz is A 344 B 336 C 117 3 D 109 3

Out of the given four waves 1 2 3 and 4 y asin kx of 1 y a sin t kx 2 y acos kx cot 3 y acos t kx 4 emitted by four different sources S S S3 and S4 respectively interference phenomena would be observed in space under appropriate conditions when Source S emits wave 1 and S emits wave 2 Source S3 emits wave 3 and S4 emits wave 4 Source S emits wave 2 and S4 emits wave 4 S4 emits waves 4 and S3 emits waves 3

8 A tuning fork of frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second are heard The beat frequency reduces if the tension in the string is slightly increased The original frequency of vibration of the string is a 506 Hz b 512 Hz c 518 Hz d 524 Hz

The displacement harmonic wave is y sin 20 y in cm produced by a simple 10 The sin 2000nt T 17 periodic time and maximum velocity of the particles in the medium will respectively be 10 3 s and 330 m s 10 4 s and 20 m s 10 3 s and 200 m s 10 2 s and 2000 m s

The equation of a progressive wave is given by y a sin 628t 31 4x If the distances are expressed in cm and time in seconds then the wave velocity will be 314 cm s 628 cm s 20 cm s 400 cm s

17 A wire is 4 m long and has a mass 0 2 kg The wire is kept horizontally A transverse pulse is generated by plucking one end of the taut tight wire The pulse makes four trips back and forth along the cord in 0 8 sec The tension is the cord will be a 80 N b 160 N c 240 N d 320 N

What happens when the two waves above run into each other a The waves collide and temporarily cancel each other out b The waves reflect off of each other and have no effect on the amplitude c The waves collide and destroy each other d The waves collide and temporarily add their amplitudes together

If the frequency of a wave in a medium is doubled increased by a factor of 2 what will happen to the wavelength a The wavelength will decrease by a factor of 4 b The wavelength will also increase by a factor of 2 Oc The wavelength will decrease by a factor of 2 d The wavelength will remain the same

16 Two mechanical waves y 2 sin 2x 50t 2x Y 4 sin 2 ax 100t propagate in a medium with same speed Choose the correct statement a The ratio of their intensities is 1 16 b The ratio of their intensities is 1 4 c The value of a is 3 units d The value of a is 2 units

According to the Doppler effect what happens to the frequency of a wave if the source is moving toward the receiver a It decreases b It behaves unpredictably c It stays the same d It increases

A couple students are sending waves down a length of string The students want to change the speed of the wave so they change the frequency of the waves but they notice the wave speed remains constant regardless of the frequency Which answer best describes why the students are not getting different speeds a They are not creating waves with large enough amplitude so the waves speed remains constant b The rope has a defect and they must obtain a new rope to get better data Oc As they increase the frequency the wavelength increases too in order to keep the wave speed constant d The speed of the wave only depends on the medium in which it travels so changing frequency has no effect

Q 14 An organ pipe P closed at one end vibrating in its first overtone and another pipe P2 open at the both ends vibrating in its third overtone are in resonance with a given tuning fork The ratic 3 of the length of P to that of P2 is then n

Electric field associated with a light is E 100 sin 6 28 x 10 5 t 3 14 x 10 t V m If this light incident on a metal of work function 2eV find stopping potential 1 3 1 volt 2 2 1 volt 3 5 1 volt 4 None of these orifera faya ut Aufafea E 100 sin 6 28 x 10 5 t 3 14 x 10 t V m 1 3 1 volt 3 5 1 volt fara dari at det for all and 2 2 1 volt 4 None of these

In YDSE both slits produce equal intensities on the screen A 100 transparent thin film is placed in front of one of the slits Now the intensity on the centre becomes 25 of the previous intensity The wavelength of light is 4000 and refractive index 1 5 The minimum thickness of the glass slab is 1 23 x 10 7 m 2 67 x 10 7 m 4 x 10 7 m None of these Marks 4 1

14 A sings with a frequency n and B sings with a frequency 1 8 that of A If the energy remains the same and the amplitude of A is a then amplitude of B will be 1 2a AIIMS 2001 3 4a 2 8a 4 a

On the basis of dimensions decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct FATTER Auta for for a fa ed g feft u facen a fa Affet HUHT 2 y asin 2rt b y a sin vt c y a 21 T sin 2 t d y a 2 sin m COS 2nt

na anla y n 2 21LA Yn In 1 B 0 Two incoherent line sources S and S each emitting monochromatic light of wavelength are placed symmetrically in front of an opaque screen A containing two symmetrically positioned slits In front of screen A another white screen B is placed as shown schematically in the figure Distance between the sources is I and that between the slits is d Distance between the sources and the screen A as well as that between screens A and B is D The distance D is much larger than the distances I and d For what values of the distance between the sources no stationary interference pattern will be observed on the screen B Ans 1 2n 1 AD n 0 1 2 d S 1 S2 d D D

A person B accidentally slips from a large building and screams with a sound of constant frequency n as he falls as shown in the figure The apparent frequency of the sound of the scream as heard by the person A at the top of the building is dependent on time as v is speed of sound 000 000 000

a Two slits 1mm apart are illuminated with a light of wavelength 500 nm What would be the width of each slit to obtain 10 maxima of double slit pattern within the central maxima of the single slit pattern b The velocity of a certain monochromatic light in a given transparent medium is 2 25 x10 m s What is the critical angle of incidence and the polarizing angle for this medium

The function f t describes the distance from center of the shadow of a rider on a ferris wheel at time t f t 20 cos 30 Anwer the following Questions

25 180 A chord attached to a vibrating tuning fork divides it into 6 loops when its tension is 36 N The tension at which it will vibrate in 4 loop is 24 N 36 N 64 N

Two vibrating strings of the same material but length L and 2L have radii 2r and r respectively They stretched under the same tension Both the strings vibrate in their fundamental modes the one of lengt L with frequency u and the other with frequency u The ratio is given by U U 1 1 2 1 2 3 3 2 4 2

An air bubble in glass at a distance 3 cm from a convex surface of diameter 10 cm as shown The distance from surface at which the image of bubble appears is 1 2 5 cm 3 4 cm 1 5 3cm 2 5 cm 4 1 5 cm 1

An organ pipe of length L sounds its fundamental tone at 30 0 Hz The pipe is open on both ends and the speed of sound in air is 343 m s Calculate the length of the pipe Calculate the frequency f1 of the first harmonic Calculate the frequency of the second harmonic Calculate the frequency fs of the third harmonis L f Incred 80 5 7167 incorrect Attempt H H

4 Unpolarized light of intensity 30 0 W cm is incident on two polarizing filters The axis of the first filter is at an angle of 27 counterclockwise from the vertical viewed in the direction the light is traveling and the axis of the second filter is at 65 counterclockwise from the vertical a What is the intensity of the light exiting the first polarizer b What is the intensity of the light exiting the second polarizer

A resistance R inductance L and capacitance C are connected in series to an ac source of voltage v having variable frequency If the TR LCV energy delivered by the source to the circuit during one period if the operating frequency is twice the resonance frequency is R P Find P

2 A solar cell is coated with a transparent thin film of refractive index 1 45 in order to minimize reflective losses from the surface as shown in the figure below Assume that the solar cell refractive index 3 5 Determine the minimum film thickness that produces the least reflection at wavelength of 550 nm 3 M 1 00 M 1 45 43 3 5 Air SAO Si

In an X ray tube for an operating voltage the cut off wavelength is Ag If operating voltage is slightly increased by AV then choose correct statement A changes by An O A changes by 2A Ao Auchanges by Au OA An does not change YOUR ANSWER NOT ATTEMPTED MODERA

In a sine wave the position of different particles at time t 0 is shown in the figure The equation for this wave if it is travelling along positive x axis can be Ya Vox 1 y A sin ot kx 2 y A sin kx ot 3 y Acos ot kx 4 y Acos kx cot

The displacement from the position of equilibrium of a point 4 cm from a source of sinusoidal oscillations is half the amplitude at the moment t T 6 T is the time period Assume that the source was at mean position at t 0 The wavelength of the running wave is A 0 96 m B 0 48 m C 0 24 m D 0 12 m T Then the equation of the

A beam of ordinary light is incident on a system of four polaroids which are arranged in succession such that each polaroid is turned through 30 with respect to the preceding one The percentage of the incident intensity that emerges out from the system is approximately 1 56 2 6 25 3 21 4 14

The magnetic induction and the intensity of magnetic field inside an iron core of an are 1 Wbm 2and 150 Am 1 The relative permeability of electromagnet respectively iron is A 47 B C 106 D 106 67T 10 47 105 67T Answer D

The vibrations of a string fixed at both ends are described by the equation y 5sin 1 57x sin 314t in CGS system What are the wavelengths and the wave speeds of the two transverse waves that combine to give the above vibration If the length of the string is 10 cm how many loops are formed in the vibration

The equation of standing wave is given as y 4 sin 200xt cos 0 05xx where y and x are in centimetres and in seconds then the incorrect statement is 1 The amplitude of the component waves is 2 cm 2 The frequency of the component waves is 100 Hz alate 3 Distance between two successive nodes is 20 cm 4 The speed of the particle at antinode is 6 m s

Light source S1 S2 S3 S4 S5 S6 are in a line and all are coherent with same wavelength X Distance between consecutive sources is a Sources S and S are oscillating in same phase all other sources are oscillating at a phase lag of 2 with both S and S In a wide central region of screen intensity due to all individual sources are same and equal to 1 O is midpoint of S3 and S4 OO is perpendicular to line of sources On screen at P exactly opposite of S4 resultant intensity found is 21 when only S3 and S4 are working and nowhere else between O and P intensity was found to be 21 Now if all sources are working the resultant intensity at P is nI Find n

5 The phase difference between two waves reaching a point is 2 What is the resultant amplitude if the individual amplitudes are 3 mm 4 mm b 6 mm c 7 mm a 5 mm d 1 mm What is the ratio of slit width when amplitudes of light d 8 mm 16

For constructive interference to take place between two monochromatic light waves of wavelength A the path difference should be Question Type Single Correct Type 1 2n 1 2 2n 1 1 3 n

14 Single slit of width d is illuminated by violet light of wavelength 400 nm and the width of the diffraction pattern is measured as y When half of the slit width is covered and illuminated by yellow light of wavelength 600 nm Find the width of diffraction pattern a The pattern vanishes and the width is zero b Y 3 c 3y 1

0 A parallel beam of monochromatic light is incident normally on a narrow slit A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam At the first minimum of the diffraction pattern the phase difference between the rays coming from the two edges of the slit is a Zero b 2 C T d 2n

9 In a double slit experiment the angular width of a fringe is found to be 0 2 on a screen placed Im away The wavelength of light used is 600 nm What will be the angular width of the fringe if the entire experimental apparatus is immersed in water Take refractive index of water to be 4 3 a 0 2 c 0 3 b 0 27 d 0 15

3 2Asine 4 2A sin A sin 0 2 9 If the length of a stretched string is shortened by 20 and the tension is increased by 21 then the frequency Let n initial frequency 1 Increases by 20 5 2 Increases by 37 5 3 Increases by 30 5 4 Decreases by 37 5 A tuning fork of known frequency 256 Hz makes CL 15 To make a st the equation another wave 1 Acos k 3 Acos ot 16 The vibratic conditions a ratio of freq

A particle is confined to move along the x axis under the action of a force F x that is derivable from the potential U x ax bx 1 Find the expression for F x 3ax b ii When the total energy of the particle is zero the particle can be trapped with in the interval x 0 to x x For this case find the values of x Pla iii Determine the maximum kinetic energy that the trapped particle has in its motion Express all answers in terms a and b At what value of x will the kinetic energy be maximum 26 3 Xo X1 X

A tuning fork generates a wave given by y 0 1 sint 0 1 x 2t where x and y in metre and t in second The distance travelled by the wave while the fork completes 30 vibrations is 600 m 20 m 30 m 200 m Marks 1

A tuning fork of frequency n is held near the open end of a tube which is closed at the other end and the length of the tube is adjusted until resonance occurs If the two shortest lengths that produce resonance are L and L2 the speed of the sound is n L2 L n L2 L 2 2n L2 L 2n L2 L