Waves Questions and Answers

39 The length of a sonometer wire AB is 110 cm Where should the two bridges be placed from A to divide the wire in 3 segments whose fundamental frequencies are in the ratio o 1 2 3 1 60 cm and 90 cm 2 30 cm and 60 cm 3 30 cm and 90 cm 4 40 cm and 80 cm SIN

27 Figure shows a snapshot for a travelling sine wave along a string Four elemental portions a b c and d are indicated on the string The elemental portion which has maximum potential energy is are d A 1 a 3 c Mem O a b x 2 b 4 b and d

A transverse sinusoidal wave moves along a string in the positive x direction at a speed of 10 cm s The wavelength of the wave is 0 5 m and its amplitude is 10 cm At a particular time t the snap shot of the wave is shown in figure The velocity of P when its displacement is 5 cm is AY 1 3 bis 690 3 m s 50 3T P 01x AA S 1 m s SL 2 X x3 3T 50 m s 3 4 1 m s

200 ms 1 A 10 m long steel wire has mass of 5 g This wire is under a tension of 80 N The speed of transverse wave travelling on it is 300 ms 1 340 ms 1 hr 400 ms 1 m

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

5 Equation of wave is given by y 10 mm sin 2 500 sec t x 0 4 m find wavelength of wave frequency of wave and displacement of a particle at a distance of 0 7 m from origin after 0 01 second

33 180 Mark for Review The amplitude of a wave disturbance propagating in positive x direction is given by at time t 0 and y 02 58 hr mir 1 1 x time t 2 seconds where y and x are in meter The speed of the wave is 2 m s 0 1 m s 1 1 x 1 2 at

Two lens of focal length 15 cm and 10 cm when put in contact act like convex lens They have zero longitudinal chromatic aberration if their dispersive power are in the ratio A B C D w N N w

A wind energy generator generates 1050 w at rated speed of 26 mph at the atmospheric pressure and temperature at 20 deg C calculate the change of output if wind generator is operates altitude of 1800 m temperature 10 deg C wind speed 24 mph atmospheric pressure 0 88 atm Area

sonometer wire of length L and mass mis clamped at both its ends as well as a point at a distance from one of its ends If the minimum frequency a both segments of the wire can resonate together is f the tension in the wire is given by O O 4mL 9f 16 m L 9f2 16mLf2 9 4mLf2 9

Wave on string Wave equation A transverse wave is travelling along a string from left to right The fig represents the shape of the string snap shot at a given instant At this instant a which points have an upward velocity b which points will have downward velocity c which points have zero velocity d which points have maximum magnitude of velocity

A progressive wave is described by the equation y a sin wt 2nx 2 If the maximum particle velocity is equal to four times the wave velocity Then 2 1 T 8 na 11 na

A tuning fork gives 4 beat s with an open organ pipe at 16 C it again gives 4 beat s when temperature increases to 51 C The frequency of tuning fork is Neglect end correction and thermal expansion 20 Hz 140 Hz 80 Hz 136 Hz Solution Answer 2 Hint speed of sound in gases v T

The pressure of an acoustical sinusoidal wave traveling in air where p 1 225 kg m specified by the following function in SI units p 0 2 cos 4 243x 5 657y 7 071z 3400m t Pa etermine b c d The direction of propagation of the wave Its wavelength Its frequency The speed of the wave Intensity of the wave

In a medium a wave represented by equation y 20 cm sin 60 t 40 x propagates The phase difference between two particles separated by a distance 2 cm along the direction of propagation of wave is here t is in second and x is in cm 80T 21 hr min 9

A uniform rope of length 10 m and mass 1 kg hangs vertically from a rigid support A block of mass 1 kg is attached to the free end of the rope A transverse pulse of wavelength A is produced at the lower end of the rope The wavelength of the pulse when it reached the 2 top of the rope is 2 The ratio is

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 loops is 24 N 36 N 64 N 81 N

In a medium a wave represented by equation y 20 cm sin 60nt 40x propagates The phase difference between two particles separated by a distance 2 cm along the direction of propagation of wave is here t is in second and x is in cm 80 21 9

2 A uniform string of fundamental frequency o vibration f is divided into two segments by means of a bridge If f and f are fundamental frequencies of these segments then 1 f f f f f 3 F F 2 2f f f 4 f f 2f

A string is fixed at x and its free end is at x 0 A triangular shape wave pulse is moving along the string with speed v m s in the positive x axis direction Its position at t 0 is shown in the figure a The shape of wave pulse at t 2v A C a 2 2 b ib will be x 0 B D 22 a 2 b 2 2 x 0 2 x 0

A A particle performing S H M about mean position x 0 and at t 0 it is at position x 2 and moving towards the origin Then which of the following is its possible graph between position x and time t X JA is t C A X 1 1 t B X t D X

32 Two points are located at a distance of 10 m and 15 m from the source of oscillation The period of oscillation is 0 05 sec and the velocity of the wave is 300 m sec What is the phase difference between the oscillations of two points 1 6 AIPMT Prelims 2008 2 H 3

L If an electromagnetic wave of frequency 5 MHz travels from vacuum into a dielectric medium of electrical permittivity 4 then its taker 1 r A wavelength is halved and the frequency remains unchanged B wavelength and frequency are both doubled son C wavelength and frequency both remain unchanged D wavelength is doubled but the frequency remains unchanged E wavelength remains unchanged but the frequency is doubled

If the ratio of intensities of two waves is 1 25 then the ratio of their amplitudes will be CPMT 1984 a 1 25 c 26 24 b 5 1 d 1 5

A sequence x n with the z transform X z z z 22 2 3z is applied as an input to linear time invariant system with the impulse response h n 28 n 3 where 8 n 0 10 n o otherwise The output at n 4 is a 6 b zero d 4

2 One insulated conductor from a extension cord has a mass per unit length of A section of this conductor is held under tension between two clamps A subsection is located in a magnetic field of magnitude B directed perpendicular to the length of the cord When the cord carries an AC current of i at a frequency of f it vibrates in resonance in its simplest standing wave vibration state Determine the relationship that must be satisfied between the separation d of the clamps and the tension T in the cord 1 T 4 f d 2 T 2 f d uf d 4 T 3 T f d 2

10 y sin TC For what value of the wavelength the wave velocity is twic the maximum particle velocity a 40 cm b 20 cm c 10 cm d 60 cm 27 T 2TC 2 X

1 100 V 50 Hz 3 150 V 50 Hz 4 200 V TC 4 The phase difference between current and voltage in an AC circuit is then the phase difference is equivalent to the time difference of 1 0 75 s 2 10 5 ms 4 0 25 ms 3 2 5 ms radian If the frequency of AC is 50 Hz

A metal wire of linear mass density of 9 8 g m is stretched with a tension of 10 kg wt between two rigid supports 1 metre apart The wire passes at its middle point between the poles of a bar magnet and it vibrates in resonance when carrying an alternating current of frequency n The frequency n of the alternating source is 2003 1 50 Hz 3 200 Hz 2 100 Hz 4 25 Hz

The relation between angular frequency and wave number k for given type of waves is a ak Bk The wave number k for which the phase velocity equals the group velocity is a 3 c STATSTAT b d a B a NB

12 What is your observation when two source are emitting sound with frequency 499 Hz 501 Hz Frequency of 500 Hz is heard with change in intensity takes place twice 2 Frequency of 500 Hz is heard with change in intensity takes place Once 3 Frequency of 2Hz is heard with change in intensity takes place Once 4 Frequency of 2Hz is heard with change in intensity takes place twice

1 A snapshot of a travelling wave is shown in figure 1 and a snapshot of a standing wave is shown in figure 2 Particles are at their respective extremes The amplitude frequency and the speed of both the waves are the same The string in both the cases is identical If the energy per unit length of system at point A in figure 1 is x and that in figure 2 is x What is value of 1 X2 1 2 1 3 1 1 Fig 1 F d A Fig 2 2 1 2 4 3 1

Two point sound sources S and S are both of same power and send out sound waves in the same phase The wavelength of both the waves 48 IS m The intensity due to S alone at D is 5 25 W m2 The resultant intensity at D is I Find in W m S 0 1 28 3 61 3 km S2 4 km 2 37 4 85 Aa D Medical

A wave pulse is propagating along ve x axis on a string whose one end is attached to a ring which can slide smoothly along a fixed vertical rod Then choose the correct option s A velocity of ring at t 1 5 sec v 2 cm s B velocity of ring at t 1 5 sec v 2 cm s C the shape of string at t 1 5 sec is D the shape of string at t 2 5 sec is 33 2 cm s 1 cm 2 cm 2 cm 2 cm

3 9 2 m s 4 7 6 m s The wavefront of a light beam is given by the equation x 2y 3z c where c is arbitrary constant then the angle made by direction of light with y axis is 1 14 A 14 Water does not wet an oily glass because 1 cos 14 3 cos 2 sin 4 sin

The ratio of maximum to minimum intensity of two interfering waves is 25 9 Find ratio of their individual intensities 1 16 2 8 3 4 4 3

17 In damped ALMS Z015 oscillation mass is 1 kg and 100 N m damping spring constant i boto coefficient 0 5 kg s If the mass is displaced by 10 cm from its mean position than what LUC will be the value of its mechanical energy after 4 seconds e 1 1 0 67 J 2 0 067 J 3 6 7 J 4 0 5 J

about 5 Consider an oscillator which has a charged particle oscillating its mean position with a frequency of 300 MHz The wavelength of electromagnetic waves produced by this oscillator is a 1 m c 100 m b 10 m d 1000 m

In resonance tube experiment if V 300 m s n 500 Hz L 125 cm i Find out maximum order of resonance that can be established ii Maximum number of resonance iii Maximum minimum water level kept at resonance condition

11 iii Maximum minimum water level kept at resonance condition If we increase the tension of streached wire by 5 kg wt then fundamental freq increase with ratio of 2 3 find the initial tension Fill in the blanks for COP and OOP

38 A sonometer wire of density d and radius a is held between two bridges at a distance L apart The wire has a tension T The fundamental frequency of the wire will be gno pri no a 150 a n 2L od T c n 1 2 2 Td b n Ta 1 2 Td 1 z d n T a d T a d 21 44 15

Board Competitive Exams 44 travelling wave in a string is represented by T y 3 sin t 2 T 1 X 4 The phase difference between two particles separated by a distance 4 cm is Take x and y in cm and t in seconds T 1 rad 2 3 rad c 2 OT rad 4 4 O 21

10 A sonometer wire fixed at one end has a mass M hanging from the other end The length of the wire 70 cm produces fundamental vibrations when plucked The mass is now submerged in water and the length had to be decreased by 5 cm to produce the same fundamental vibrations The density of the mass M is A 7 25 x 10 kg m C 4 00 x 10 kg m kg m B 6 00 10 kg m x D 2 10 kg m

have a different frequencies and same amplitude b different frequencies c different frequencies same amplitude an same phase d different frequencies and same phase

The standing wave in a medium is expressed as y 0 2 sin 0 8x cos 3000t m The distance between any two consecutive points of minimum or maximum displacement is 1 m 2 3 E O 6 3 E 2 R 4 3 4 None of these

A string of mass 10 gram and length 1 m is stretched between two rigid supports It vibrates with its fundamental node of 50 Hz Tension in string is 1 50 N 2 100 N 4 10 N 3 150 N

8 The potential energy of a particle of mass 100 g moving along x axis is given by U 5x x 4 where x is in metre The period of oscillation is 1 0 2 s 3 S 2 0 1 s 1 4 S T

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9kg is suspended from the wire When this mass is replaced by mass M the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges Then find the value of square root of M Femm 1 5 2 10 3 25 4 None

Q13 A string consists of two parts attached at x 0 The right part of the string x 0 has mass per unit length and the left part of the string x 0 has mass per unit length The string tension is T If a wave of unit amplitude travels along the left part of the string as shown in the figure what is the amplitude of the wave that is transmitted to the right part of the string Hy Hp A 1 B 2 1 C 2 1 M M D 1 1

A thin wire of length of 99 cm is fixed at both ends as shown in the figure The wire is kept under a tension and is divided into three segments of lengths 1 1 and I as shown in figure When the wire is made to vibrate the segments vibrate respectively with their fundamental frequencies in the ratio 1 2 3 Then lengths 1 12 13 of the segments respectively are in cm 1 4 1 13 A a 27 54 18 c 54 27 18 18 27 54 b d 27 9 14 B