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PHYSICS CRASH COURSE (AIEEE/PET/PMT-2014) SARASWATIEDUCATIONAL INSTITUTEWaves -1

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1. A travelling wave passes a point of observation.

At this point, the time interval betweensuccessive crests is 0.2 seconds and

[MP PMT 1990]

(a) The wavelength is 5 m

(b) The frequenc is 5Hz

(c) The velocit of propagation is 5 m!s

(d) The wavelength is 0.2 m

2. The equation of a transverse wave is given b

)201.0(sin10 txy = wherex andyare in cmand tis in second. "ts

frequenc is[MP PET 1990; MNR 1986; RPET 2003]

(a) 1sec10 (b)

1sec2

(c)1

sec1 (d)1

sec01.0

3. A wave is represented b the equation

+=

304.07sin7

xty

xis in metresand tis in seconds. The speed of

the wave is[MP PET 1996; AMU (Engg.) 1999]

(a) #$5 m!sec (b) %& m!sec

(c) %& m!sec (d) 0.2' m!sec

4. The equation of a wave is given as)300012sin(07.0 txy = . here xis in metre and

tin sec, then the correct statement is[UPSEAT 2003]

(a) smvm /250,/1 == (b) smvma /300,07.0 ==

(c) smvn /200,1500 == (d) one

5. The equation of a wave is )2005.0(sin2 txy = ,wherex andyare e*pressed in cm and t in sec.

The wave velocit is[MP PMT 1986]

(a) #00 cm!sec (b) 200 cm!sec

(c) +00 cm!sec (d) %00 cm!sec

6. quation of a progressive wave is given b

+=

02.04.0c!s2.0

xty

The distance is e*pressed in cm and time in

second. hat will be the minimum distancebetween two particles having the phase

difference of !2

(a) % cm (b) ' cm

(c) 25 cm (d) #2.5 cm

7. The equation of a wave travelling on a string is

=

""

2sin4

xty

. "f x and y are in cm, then

velocit of wave is [MP PET 1990]

(a) -% cm!secin xdirection

(b) +2 cm!secin xdirection

(c) +2 cm!secin /xdirection

(d) -% cm!secin /xdirection

8. The equation of a progressive wave is given b)4.312"sin( xtay =

"f the distances are e*pressed in cms and time iseconds, then the wave velocit will be

[DPMT 1999]

(a) +#% cm!sec (b) -2' cm!sec

(c) 20 cm!sec (d) %00 cm!sec

9. Two waves are given b )sin(1 kxtay = an)c!s(2 kxtay = The phase difference between th

two waves is [MP PMT 1993; SCRA 1996; CET 1998;

(a) 4

(b)

(c) "

(d) 2

10. A plane wave is represented b

)5.12314sin(2.1 ytx +=

herexandyare distances measured along inxan

ydirection in meters and tis time in seconds. Thiwave has

[MP PET 1991]

(a) A wavelength of 0.25 m and travels in / ve

direction

(b) A wavelength of 0.25 m and travels in / ve

direction

(c) A wavelength of 0.5 m and travels in ve

direction

(d) A wavelength of 0.5 m and travels in vedirection

11. A transverse wave is described b the equatio

=

xftYY 2sin0

. The ma*imum particle velocit

is four times the wave velocit if

[IIT 1984; MP PMT 1997; EAMCET; 1998

CSE PMT 2000; A!MC 2000; MP PMT"PET 1998; 01

#CET 1999$ 04; P%. PET 2001; DPMT 200

(a) 40Y=

(b) 20Y=

(c) 0Y=

(d) 02 Y=

12. A wave represented b the given equatio

++=

31510sin

txAY

, wherexis in meter and ti

in second. The e*pression represents [IIT 1990]

(a) A wave travelling in the positive X directio

with a velocit of #.5 m!sec

(b) A wave travelling in the negative X directiowith a velocit of #.5 m!sec

(c) A wave travelling in the negative X directio

with a wavelength of 0.2 m

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(d) A wave travelling in the positive Xdirection

with a wavelength of 0.2 m

13. A plane wave is described b the equation

=

210

4c!s3

t

xy

. The ma*imum velocit of

the particles of the medium due to this wave is[MP PMT 1994]

(a) +0 (b) 23

(c) +!% (d) %0

14. The path difference between the two waves

=

xtay

2sin11

and

+=

xtay

2c!s22

is[MP PMT 1994]

(a)

2 (b)

+

22

(c)

2

2

(d)

2

15. ave equations of two particles are given b)sin(1 kxtay = , )sin(2 tkxay += , then [&U 1995]

(a) The are moving in opposite direction

(b) hase between them is &01

(c) hase between them is #'01

(d) hase between them is 01

16. quation of a progressive wave is given b

+

=

#5sin4

xty

Then which of the following is correct [CSE PMT

1993]

(a) sec/5mv= (b) m1"=

(c) ma 04.0= (d) Hzn 50=

17. There is a destructive interference between the

two waves of wavelength coming from two

different paths at a point. To get ma*imum sound

or constructive interference at that point, the path

of one wave is to be increased b[MP PET 1985]

(a) 4

(b) 2

(c) 43

(d)

18. hen two sound waves with a phase difference

of 2/ , and each having amplitude A andfrequenc , are superimposed on each other,

then the ma*imum amplitude and frequenc of

resultant wave is [MP PMT 1989]

(a) 2$

2

A

(b)$

2

A

(c) 2$2

A(d) $2A

19. "f the ratio of amplitude of wave is 2 #, then th

ratio of ma*imum and minimum intensit is [M& CE1999]

(a) & # (b) # &

(c) % # (d) # %

20. The distance between the nearest node and antinod

in a stationar wave is[MP PET 1984; CSE PMT 1993; A!MC 1996; RPET 200

(a) (b) 2

(c) 4

(d) 2

21. "n stationar wave [MP PET 1987; &U 1995]

(a) 3train is ma*imum at nodes

(b) 3train is ma*imum at antinodes

(c) 3train is minimum at nodes

(d) Amplitude is 4ero at all the points

22. The phase difference between the two particle

situated on both the sides of a node is[MP PET 2002]

(a) 01 (b) &01

(c) #'01 (d) +-01

23. hich of the propert maes difference betwee

progressive and stationar waves[MP PMT 1987]

(a) Amplitude (b) 6requenc

(c) ropagation of energ (d)hase of the wave

24. 6or the stationar wave)#c!s(

15sin4 t

xy

=, th

distance between a node and the ne*t antinode is[MP PMT 1987]

(a) $.5 (b) #5

(c) 22.5 (d) +0

25. The equation of stationar wave along a stretche

string is given bt

xy

40c!s

3sin5=

, wherex and

are in cm and tin second. The separation betweetwo ad7acent nodes is[CPMT 1990; MP PET 1999; AMU 1999;

(a) #.5 cm (b) + cm

(c) - cm (d) % cm

26. A wave represented b the given equatio

)c!s( tkxay = is superposed with another wave tform a stationar wave such that the pointx 8 0 is

node. The equation for the other wave is[IIT 1988; MP PMT 1994$ 97;

AIIMS 1998; SCRA 1998; MP PET 2001; #CET 2001

AIEEE 2002; UPSEAT 200

(a) )sin( tkxay += (b) )c!s( tkxay +=

(c) )c!s( tkxay = (d) )sin( tkxay =

27. "n stationar waves, antinodes are the points wher

there is[MP PMT 199

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(a) 9inimum displacement and minimum

pressure change

(b) 9inimum displacement and ma*imum

pressure change

(c) 9a*imum displacement and ma*imum

pressure change

(d) 9a*imum displacement and minimumpressure change

28. hich two of the given transverse waves will

give stationar waves when get superimposed[RPET 1997; MP PET 1993]

)c!s(1 tkxaz = .....(A))c!s(2 tkxaz += .....(:)

)c!s(3 tkyaz = .....(;)

(a) A and : (b) A and ;

(c) : and ; (d) An two

29. A # cm long string vibrates with fundamental

frequenc of 25-Hz. "f the length is reduced to

cm4

1

eeping the tension unaltered, the new

fundamental frequenc will be[&U 1997]

(a) -% (b) 25-

(c) 5#2 (d) #02%

30. 3tanding waves are produced in a #0 m long

stretched string. "f the string vibrates in 5

segments and the wave velocit is 20 m!s, the

frequenc is[CSE PMT 1997; AIIMS 1998; 'IPMER 2000]

(a) 2Hz (b) %Hz() 5 Hz () 10 Hz

31. The velocit of waves in a string fi*ed at both

ends is 2 m!s. The string forms standing waveswith nodes 5.0 cm apart. The frequenc of

vibration of the string inHzis[SCRA 1998]

(a) %0 (b) +0

(c) 20 (d) #0

32. "f the tension of sonometerength of a string tied to two rigid supports is %

cm. 9a*imum length (wavelength in cm) o f stationar wave produced on it is

[AIEEE 2002]

(a) 20 (b) '0

(c) %0 (d) #20

38. Three similar wires of frequenc n#, n2 and n+ ar

7oined to mae one wire. "ts frequenc will be

[CSE PMT 2000]

(a) 321 nnnn ++= (b) 321

1111

nnnn++=

(c) 321

1111

nnnn++=

(d)23

22

21

1

1111

nnnn++=

39. A tube closed at one end and containing air i

e*cited. "t produces the fundamental note o

frequenc 5#2Hz. "f the same tube is open at bot

the ends the fundamental frequenc that can b

produced is [RPET 1999]

(a) #02%Hz (b) 5#2Hz

(c) 25-Hz (d) #2'Hz

40. A closed pipe and an open pipe have their firsovertones identical in frequenc. Their lengths are i

the ratio[R**+,-- 199

(a) # 2 (b) 2 +

(c) + % (d) % 5

41. "f the velocit of sound in air is +50 m!s. Then th

fundamental frequenc of an open organ pipe o

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:

A

;

length 50 cm, will be [CPMT 1997; M& CET 2001; P%.PMT 2001]

(a) +50Hz (b) #$5Hz

(c) &00Hz (d) $50Hz

42. The fundamental note produced b a closed

organ pipe is of frequenc .f The fundamental

note produced b an open organ pipe of samelength will be of frequenc

[&U 2001]

(a) 2f

(b) f

(c) f2 (d) f4

43. A clindrical tube, open at both ends, has a

fundamental frequenc 0f in air. The tube is

dipped verticall into water such that half of itslength is inside water. The fundamental

frequenc of the air column now is[RPET 1999; RPMT 1998$ 2000; ' # CET 2000;

#CET 2002; &U 2002; CECE 2003]

(a) 4/3 0f (b) 0f

(c) 2/0f (d) 02f

44. "f the length of a closed organ pipe is #.5 mandvelocit of sound is ++0 m/s, then the frequenc

for the second note is[CSE PMT 2002]

(a) 220Hz (b) #-5Hz

(c) ##0Hz (d) 55Hz

45. An organ pipe, open from both end produces 5

beats per second when vibrated with a source of

frequenc 200 Hz. The second harmonic of the

same pipes produces #0 beats per second with a

source of frequenc %20 Hz. The frequenc of

source is [DCE 2005]

(a) #&5Hz (b) 205Hz

(c) #&0Hz (d) 2#0Hz

46. The wavelength is #20 cmwhen the source is

stationar. "f the source is moving with relative

velocit of -0 m!sectowards the observer, then

the wavelength of the sound wave reaching to the

observer will be (velocit of sound 8 ++0 m!s)

(a) &' cm (b) #%0 cm

(c) #20 cm (d) #%% cm

47. An observer moves towards a stationar source o

sound of frequenc n. The apparent frequenc hear

b him is 2n. "f the velocit of sound in air is ++m!sec, then the velocit of the observer is

[MP PET 1990]

(a) #-- m!sec (b) --% m!sec

(c) ++2 m!sec (d) #+2' m!sec

48. A person feels 2.5= difference of frequenc of

motor?car horn. "f the motor?car is moving to th

person and the velocit of sound is +20 m!sec, thethe velocit of car will be[CPMT 1981; MP PET 1989]

(a) ' m!s(appro*.) (b) '00 m!s

(c) $ m!s (d) - m!s(appro*.)

49. Two passenger trains moving with a speed of #0

km!hour cross each other. @ne of them blows

whistle whose frequenc is $50Hz. "f sound spee

is ++0 m!s, then passengers sitting in the other train

after trains cross each other will hear sound whos

frequenc will be [MP PMT 1991]

(a) &00Hz (b) -25Hz

(c) $50Hz (d) '00Hz

50. ith what velocit an observer should mov

relative to a stationar source so that he hears

sound of double the frequenc of source[MP PMT 1991]

(a) elocit of sound towards the source

(b) elocit of sound awa from the source

(c) Balf the velocit of sound towards the source(d) Couble the velocit of sound towards the source

51. A small source of sound moves on a circle as show

in the figure and an observer is standing on O . >e

21,nn and 3n be the frequencies heard when th

source is at BA, and C respectivel. Then [UPSEAT2002]

(a) 321 nnn >>

(b) 132 nnn >>

(c) 321 nnn >=

(d) 312 nnn >>