Waves Questions and Answers

1 A wave in a string has an amplitude of 2 cm The wave travels in the positive direction of x axis with a speed of 128 m s and it is noted that 5 complete waves fit in 4 m length of the string The equation describing the wave is AIPMT Prelims 2009 1 y 0 02 m sin 15 7x 2010t 2 y 0 02 m sin 15 7x 2010t 3 y 0 02 m sin 7 85x 1005t 4 v 0 02 m sin 7 85x 1005t

3 A uniform rope of length L and mass m hangs vertically from a rigid support A block of mass m is attached to the free end of the rope A transverse pulse of wavelength is produced at the lower end of the rope The wavelength of the pulse when it reaches the top of the rope is 22 The ratio 2 is 1 NEET 2016 a c m m m m m m b d m Vm m m

Light appears to travel in straight lines since CPMT 1987 89 90 2001 RPMT 1997 AIIMS 1998 2002 KCET 2002 BHU 2002 DCE 2003 a It is not absorbed by the atmosphere b It is reflected by the atmosphere c Its wavelength is very small dy Its velocity is very large

T 12 A uniform rope of mass 0 1 kg and length 2 45 m hangs from a rigid support The time taken by the transverse wave formed in the rope to travel through the full length of the rope is Assume g 9 8 m s a 0 5 s b 1 6 s c 1 2 s d 1 0 s

1 When a vibrating tuning fork is placed on a sound box of a sonometer 8 beats per second are heard when the length of the sonometer wire is kept at 101cm or 100cm Then the frequency of the tuning fork is Consider that the tension in the wire is kept constant a 1616 Hz b 1608 Hz 1600 Hz c 1632 Hz d AMCFT 44

You have learnt that a travelling wave in one dimension is represented by a function y f x t where x and must appear in the combination x vt or x vt i e y F x vt Is the converse true Examine if the following functions for y can possibly represent a travelling wave x vt b exp x vt x d a c log x vt x 1 x vt

If the sound heard by observer whose equation is given as y 8sin10nt cos t at x 0 The number of beat frequency heard by observer is 2k then the value of k is 5

of a particle which represents SHM A y sinot cos ot B y sin ot C y 5 cos 3 t 4 3ot D y 1 wt w t 1 Only A A Maiss 2 Only D does not represent SHM 3 Only A and C motion J P

4 4 A wave has a frequency of 120Hz Two points at a distance of 9m apart have phase difference of 1080 The velocity of the wave is 1 340m s 3 330m s 2 300m s 4 360m s

The intensity of a plane progressive wave of frequency 1 kHz is 10 10 watt m If the density of air is 1 3 kg m and the speed of sound is equal to 340 m s then the pressure amplitude of the wave is about 1 3 x 10 5 N m 3 3 x 10 6 N m 2 3 x 104 N m 4 3 x 10 3 N m

Two tunning forks of frequency 520 Hz anc 524 Hz are vibrated together The time interva between successive maximum and minimum intensity is 1 3 100 IN S 8 1 S 2 2 1 4 4 1s

represented by the equation y a cos kx wt is superposed with another wave to form a stationary wave such that the point x 0 is a node The equation of the other wave is Da 1 a sin kx wt 3 a sin kx wt 2 a cos kx wt 4 a cos kx wt

2 A string is rigidly tied at two ends and its equation of vibration is given by y cos 2 t sin 2x Then the length of string can not be 1 1 m 3 5 m 2 5 3 2 4 2 m

030 50 A rod AB of length L is hung from two identical wires 1 and 2 A block of mass m is hung at point O of the rod as shown in figure The value of x so that a tuning fork excites the fundamental mode in wire 1 and the second harmonic in wire 2 is L P the value of P is Wire 1 0 Wire 2

A Write an expression for a linearly polarized harmonic plane wave of scalar amplitude Eo propagating along a line in the xy plane at 45 to the x axis and having the xy plane as its plane of vibration 3 marks

Two superimposing waves are represented by equation y 2 sin2r 10t 0 4x and y 4 sin 2r 20t 0 8x Y2 The ratio of max to min is 1 36 4 3 1 4 2 25 9 4 4 1

4 5 6 7 speed of 15 m s What is the speed U with respect to mirror 17 5 m s 4 45 m s Figure shows two plane mirrors parallel to each other and an object O placed between them Then the distance of the first three images from the mirror M will be in cm 1 5 10 15 2 5 15 30 3 5 25 35 4 5 15 25 3 30 m s 215 m s 1 12 feet 10 M 5cm O 15cm A ray gets succesively reflection from two mirrors inclined at an angle of 40 If the angle of incidence on the first mirror is 30 then the net deviation of this ray after two reflections 1 40 2 280 3 80 A tall man of height 6 feet want to see his fell image Then required minimum length of the mirror will be M 2 3 feet 4 240 T 11 An c a co a dis sho 41 2 12 A sc cm The and enc 1 13 The WH So 1 14 An Co an XUX 2 3

4 The de Broglie wavelength of a particle movir with a velocity of 2 x 108 ms 1 is equal to th wave length of photon What will be ratio kinetic energy of the moving particle to that energy of a photon 1 1 2 3 3 11 2 2 3 4 1

5 To make a stationary wave having node at x 0 the equation y Acos wt kx is superimposed to another wave of equation 1 Acos kx cof 3 Acos wt kx 2 Asin kx wt 4 Acos kx cot

A source of frequency 340 Hz is kept above a vertical cylindrical tube closed at lower end The length of the tube is 120 cm Water is slowly poured in just enough to produce resonance Then the minimum height veloc ity of sound 340 m s of the water level in the tube for that resonance is a 0 75 m c 0 95 m b 0 25 m d 0 45 m

At antinodes 1 Pressure is maximum and velocity is minimum 2 Pressure is minimum and velocity is maximum 3 Pressure and velocity both are maximum 4 Pressure and velocity both are minimum

3 A point source emits sound equally in all directions in a non absorbing medium Two points P and Q are at distance of 2 m and 3 m respectively from the source The ratio of the intensities of the waves at P and Q is AIPMT Prelims 2005 1 9 4 3 3 2 2 2 3 4 4 9

Two wires are in unison If the tension in one of the wires is increased by 2 5 beats are produced per second The initial frequency of each wire is 1 400 Hz 2 1000 Hz 3 500 Hz 4 200 Hz

A string is stretched along x axis The shape of the string is given by the curve 9 y unit s 9 2x 24x 90 at t 0 and y 2x 4 11x 65 at t 1 unit The speed of pulse is

For a particle which is undergoing simple harmonic motion the square of velocity v2 is plotted against the square of displacement x The curve will be 1 An ellipse 2 A straight line 3 A circle

3 0 8 mm 5 The interference pattern shifts downward by 4mm when a polystyrene sheet of refractive index 1 8 is place in front of the lower slit If wavelength used is 683 nm separation between slits is 2 mm and separation between slits and screen is 10 cm then thickness of sheet 1 0 1 mm 3 0 3 mm 2 0 2 mm he 4 0 4 mm

D A tuning fork of frequency 440 Hz is attached to a long string of linear mass density 0 01 kg m kept under a tension of 49 N The fork produces transverse waves of amplitude 0 50 mm on the string a Find the wave speed and the wavelength of the waves b Find the maximum speed and acceleration of a particle of the string c At what average rate is the tuning fork transmitting energy to the string

A standing wave is produced on a string fixed at one end and free at other The length of string must be an a odd integral multiple of 2 b 2 c integral multiple of d integral multiple of 4 integral multiple of 4

A heavy rope is suspended from a rigid suppor wave pulse is set up at the lower end then a the pulse will travel with uniform speed b the pulse will travel with increasing speed c the pulse will travel with decreasing speed d the pulse cannot travel through the rope

A light ray falling at an angle of 45 with the surface of a clean slab of ice of thickness 1 00 m is refracted into it at an angle of 30 Calculate the time taken by the light rays to cross the slab Speed of light in vacuum 3 x 10 ms 8 1

If the wire is gently tapped in vertical direction half way between the pulleys what is the lowest frequency at which it will vibrate transversely The mass per unit length of the wire is 0 02 kg m and it has a length of 0 2 m between pulleys 1 m and its mass is 10 kg Volume of block is 200 1 250 Hz 3 62 5 Hz Q Water 2 125 Hz 4 500 Hz

It has been observed that velocity of longitudinal and transverse mechanical waves in this earth are 8 km s and 5 km s respectively If the time interval between P wave and S wave as noted by a seismograph is 1 minute then the distance of epicentrequake from the seismograph is 1 800 km 3 200 km 2 400 km 4 600 km

a stationary wave represented by y 2acos kx sin wt the intensity at a certain point maximum when 1 cos kx is maximum 2 cos kx is minimum 3 sin wt is maximum 4 sin at is minimum

at a point 10 m from the point source is 20 dB then the sound level at distance 20 m from the same source will be about a 18 dB b 16 dB c 14 dB d 12 dB 9 Four sources of sound each of sound level 20 dB are sounded together in phase The resultant intensity level will be log10 2 0 3 1 1 100g 0 a 40 dB b 26 dB c 22 dB d 13 dB A 4A I 16A Putr

22 The frequency of the second overtone of the open pipe is equal to the frequency of the first overtone of the closed pipe The ratio of lengths of the closed pipe to that of open pipe is 2 1 3 1 2 1 3 2 2 4 1 1

A wave pulse propagating in positiv 1 1 x 1 by y at t 0 and y Eat 1 Yx 1 t 2sec when n and y are in metre The shape of distruband do not change Then welocity of

Problem 17 A string is under tension so that its length is increased by times its original length The ratio of n fundamental frequency of longitudinal vibrations and transverse vibrations will be 1 1 n 3 n 1 2 n 1 4 n 1

Problem 6 A string of length 0 4 m and mass 10 2 kg is tightly clamped at its ends The tension in the string is 1 6N Identical wave pulses are produced at one end at equal intervals of time At The value of At which allows constructive interference between successive pulses is 1 0 05 sec 2 0 10 sec 3 0 20 sec 4 0 40 sec

Two organ pipes A closed and B open of same cross section but different lengths are connected so as to make a longer pipe If their respective fundamental frequencies are 5 Hz and 10 Hz then the fundamental frequency after joining them will be 1 7 Hz 3 2 5 Hz 2 5 Hz 4 2 Hz

For a wave propagating in a medium identify th property that is dependent of others 1 Velocity 2 Wavelength 3 Frequency 4 Both 1 and 2

2 Which of the following statement is true about stationary waves 1 All particle except particles at node execute SHM 2 All particles except particles at node come to their mean positions at the same time 3 All particles at antinodes have same velocity at mean position 4 All of these

sound waves are given by y Asin 2 2rnt G 2 y A sin 22 2 nt 2 12E1 1 6 V S E do stomsiba 1 2 Bl 8 3 When superposed find value of x x fc constructive interference dynalot gaived 3

23 The vibrations of a string of length 60 cm and fixed at both the ends are represented by the equation TEX y 4 sin cos 96nt 15 In which harmonic mode is the string vibrating a Fundamental b Third c Fourth d Fifth UT 19851

d particle B is moving downward Fig 10 32 shows four progressive waves A B C and D with their phases expressed with respect to the wave A It can be calculated from the figure S that B A TC 2 C TT D 3 2 2T of FIGURE 10 32 a the wave C is ahead by a phase angle of 1 2 and the wave B lags behind by a phase angle of 2 b the wave C lags behind by a phase angle of rt 2 and the wave B is ahead by a phase angle of 2 c the wave C is ahead by phase angle of it and the wave B lags behind by a phase angle of d the wave C lags behind by a phase angle of T and the tu n

m VK 2 25K 1 2 4K 43 A curve is plotted represent the dependence of the ratio of the received frequency f to the frequency fo emitted by the source on the ratio of the speed of observer Vab to the speed of sound Vsound in a situation in which an observer is moving towards a stationary sound source The curve is best represented by 3 4

8 A string is stretched between fixed points separated by 75 0 cm It is observed to have resonant frequencies of 420 Hz and 315 Hz There are no other resonant frequencies between these two The lowest resonant frequencies for this string is 1 105 Hz S 2 155 Hz 3 205 Hz 4 10 5 Hz

A polaroid examines two adjacent plane polari sed beams A and B whose planes of polarisation ar mutually perpendicular In the first position of the analyser beam B shows zero intensity From thi position a rotation of 300 shows that the two bear have same intensity The ratio of intensities of th two beams I and I will be A 1 1 3 2 3 1 3 3 1 4 1 3

are shown in the diagram What is the frequency and the phase relationship between the voltages M 0 Jes Iam Frequency in Hz Phase lead of N over M in radians Ap 1 0 4 14 3 25 2 L 0 4 0 6 0 8 t in sec 2 2 5 2 4 2 5 4 KAX 2 to

A metallic rod of length 1 m is rigidly clamped at its mid point Longitudinal stationary waves are set up in such a way that there are two nodes on either side of the mid point The amplitude of an antinode is 2x10 m Write the equation of motion at a point 2 cm from the mid point and those of constituent waves in the rod Y 2x10 N m ando 8x 10 kg m

1 5 4 N A rope of length L and mass m hangs freely from the ceiling The velocity of transverse wave as a function of position x along the rope is proportional to 4 Application Mx 2 x V 1 to 3 x 4 x The speed of sound in hydrogen at NTP is 1270 m s Then the speed in a mixture of hydrogen and oxygen MALAH da b in m s will be v 5 1270 125