## NEET AIPMT Physics Chapter Wise Solutions – Waves

NEET AIPMT Physics Chapter Wise SolutionsBiology Chemistry

**1. 4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 JK ^{-1} mol^{-1}. If the speed of sound in this gas at NTP is 952 ms^{-1}, then the heat capacity at constant pressure is (Take gas constant R = 8.3 JK^{-1} mol^{-1})**

**2. A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms ^{-1} at an angle of 60° with the source observer line as shown in the figure.**

The observer is at rest.The apparent frequency observed by the observer (velocity of sound in air 330 ms

^{-1}), is

(a) 106 Hz

(b) 97 Hz

(c) 100 Hz

(d) 103 Hz

**(AIPMT 2015)**

**3. The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is**

(a) 120 cm

(b) 140 cm

(c) 80 cm

(d) 100 cm** (AIPMT 2015, Cancelled)**

**4. if n _{1}, n_{2} and n_{3} are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by**

**5. The number of possible natural oscillations of air column in a pipe closed at one epd of length 85 cm whose frequencies lie below 11250 Hz are (Velocity of sound = 340 m s ^{-1})**

(a) 4

(b) 5

(c) 7

(d) 6

**(APMT 2014)**

**6. A speeding motorcyclist sees traffic jam ahead him. He slows down to 36 km hour ^{-1}. He finds that traffic has eased and a car moving ahead of him at 18 km hour^{-1} is honking at a frequency of 1392 Hz. If the speed of sound is 343 m s^{-1}, the frequency of the honk as heard by him will be**

(a) 1332 Hz

(b) 1372 Hz

(c) 1412 Hz

(d) 1454 Hz

**(AIPMT 2014)**

**7. If we study the vibration of a pipe open at both ends, then the following statement is not true.**

(a) All harmonics of the fundamental frequency will be generated.

(b) Pressure change will be maximum at both ends.

(c) Open end will be antinode.

(d) Odd harmonics of the fundamental frequency will be generated. **(MEET 2013)**

**8. A wave travelling in the +ve x-direction having displacement along indirection as 1 m, wavelength 2π m and frequency of 1/π Hz is represented by**

**9. A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is**

(a) 240 Hz

(b) 260 Hz

(c) 254 Hz

(d) 246 Hz** (NEET 2013)**

**10. The length of the wire between two ends of a sonometer is 100 cm. What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio 1 : 3 : 5.**

**11. Two sources P and Q produce notes of frequency 660 Hz each. A listener moves from P to Q with a speed of 1 ms ^{-1}. If the speed of sound is 330 m/s, then the number of beats heard by the listener per second will be**

(a) 4

(b) 8

(c) 2

(d) zero

**(Karnataka NEET 2013)**

**12. When a string is divided into three segments of length l _{1}, l_{2}, and l_{3} the fundamental frequencies of these three segments are υ_{1,} υ_{2} and υ_{3 }respectively. The original fundamental frequency (υ) of the string is**

**13. Two sources of sound placed close to each other, are emitting progressive waves given by y _{1} = 4sin600πt and y2 = 5sin608πt An observer located near these two sources of sound will hear**

(a) 4 beats per second with intensity ratio 25 : 16 between waxing and waning.

(b) 8 beats per second with intensity ratio 25 : 16 between waxing and waning.

(c) 8 beats per second with intensity ratio 81:1 between waxing and waning.

(d) 4 beats per second with intensity ratio 81:1 between waxing and waning.

**(Prelims 2012)**

**14. The equation of a simple harmonic wave is given by y = 3 sinπ/2(50t – x), ****where x and y are in metres and t in seconds. The ratio of maximum particle velocity to the wave velocity** **is**

**15. A train moving at a speed of 220 ms ^{-1} towards a stationary object, emits a sound of frequency 1000 Hz. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is**

**(Speed of sound in air is 330 ms**

^{-1})(a) 3500 Hz

(b) 4000 Hz

(c) 5000 Hz

(d) 3000 Hz

**(Mains 2012)**

**16. Two waves are represented by the equations ****y _{1} = asin(ωt +kx + 0.57) m and
y_{2} = acos(ωt + kx) m, where x is in meter and t in sec. The phase difference between them is**

(a) 1.0 radian

(b) 1.25 radian

(c) 1.57 radian

(d) 0.57 radian

**(Prelims 2011)**

**17. Sound waves travel at 350 m/s through a warm air and at 3500 m/s through brass. The wavelength of a 700 Hz acoustic wave as it enters brass from warm air**

(a) decrease by a factor 10

(b) increase by a factor 20

(c) increase by a factor 10

(d) decrease by a factor 20 **(Prelims 2011)**

**18. Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be**

(a) 0.01

(b) 0.02

(c) 0.03

(d) 0.04 **(Mains 2011)**

**19. A transverse wave is represented by y = Asin(ωt – kx). For what value of the wave length is the wave velocity equal to the maximum particle velocity?**

**20. A tuning fork of frequency 512 Hz makes 4 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was**

(a) 510 Hz

(b) 514 Hz

(c) 516 Hz

(d) 508 Hz **(Prelims 2010)**

**21. Each of the two strings of length 51.6 cm and 49.1 cm are tensioned separately by 20 N force. Mass per unit length of both the strings is same j and equal to 1 g/m. When both the strings vibrate simultaneously the number of beats is**

(a) 7

(b) 8

(c) 3

(d) 5** (Prelims 2009)**

**22. The driver of a car travelling with speed 30 m/sec towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is 330 m/s, the frequency of reflected sound as heard by driver is**

(a) 555.5 Hz

(b) 720 Hz

(c) 500 Hz

(d) 550 Hz **(Prelims 2009)**

**23. A wave in a string has an amplitude of 2 cm. The wave travels in the +ve direction of x axis with a speed of 128 m/sec. and it is noted that 5 complete waves fit in 4 m length of the string. The equation describing the wave is**

**24. A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin(ωt + π/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?**

(a) T/3

(b) T/12

(c) T/8

(d) T/6 **(Prelims 2008)**

**25. Two periodic waves of intensities l _{1} and l_{2} pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is**

**26. The wave described by y = 0.25 sin(10πx – 2πt), where x and y are in meters and t in seconds, is a wave travelling along the**

(a) +ve x direction with frequency 1 Hz and wavelength λ= 0.2 m.

(b) -ve x direction with amplitude 0.25 m and wavelengthλ = 0.2 m.

(c) -ve x direction with frequency 1 Hz.

(d) +ve x direction with frequency p Hz and wavelength λ= 0.2 m.** (Prelims 2008)**

**27. Two vibrating tuning forks produce waves given by y _{1} = 4 sin500πt/ and y_{2} = 2 sin506 πt. Number of beats produced per minute is**

(a) 360

(b) 180

(c) 60

(d) 3

**(2006)**

**28. Two sound waves with wavelengths 5.0 m and 5.5. m respectively, each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second.**

(a) 6

(b) 12

(c) 0

(d) 1.** (2006)**

**29. The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A?**

(a) 1

(b) 2

(c) 4

(d) 1/2.** (2006)**

**30. A transverse wave propagating along x-axis is represented by y(x, t) = 8.0sin(0.5πx -4 π – π/4) where x is in metres and t is in seconds. The speed of the wave is**

(a) 8 m/s

(b) 4π m/s

(c) 0.5πm/s

(d) π/4 m/s. **(2006)**

**31. Which one of the following statements is true?**

(a) both light and sound waves can travel in vacuum

(b) both light and sound waves in air are transverse

(c) the sound waves in air are longitudinal while the light waves are transverse

(d) both light and sound waves in air are longitudinal. **(2006)**

**32. A point source emits sound equally in all directions in a non-absorbing medium. Two points P and Q are at distances of 2 m and 3 m respectively from the source. The ratio of the intensities of the waves at P and Q is**

(a) 3 : 2

(b) 2 : 3

(c) 9:4

(d) 4:9.** (2005)**

**33. The phase difference between two waves, represented by y _{1}= 10^{-6}sin[100t + (x/50) + 0.5] m , y_{2}= 10^{-6} cos[100t + (x/50)] m, where x is expressed in metres and t is expressed in seconds, is approximately.**

(a) 1.07 radians

(b) 2.07 radians

(c) 0.5 radians

(d) 1.5 radians

**(2004)**

**34. A car is moving towards a high cliff. The driver sounds a hom of frequency fThe reflected sound heard by the driver has frequency 2f. If v is the velocity of sound, then the velocity of the car, in the same velocity units, will be**

**35. An observer moves towards a stationary source of sound with a speed 1/5 ^{th} of the speed of sound.The wavelength and frequency of the source emitted are λ and f respectively. The apparent frequency and wavelength recorded by the observer are respectively**

**36. A whistle revolves in a circle with angular speed ω = 20 rad/sec using a string of length 50 cm. If the frequency of sound from the whistle is 385 Hz, then what is the minimum frequency heard by an observer which is far away from the centre (velocity of sound = 340 m/s)**

(a) 385 Hz

(b) 374 Hz

(c) 394 Hz

(d) 333 Hz. **(2002)**

**37. A wave travelling in positive A-dircction with a = 0.2 mt., velocity = 360 mt/sec. and X = 60 mts, then correct expression for the wave is**

**38. The equation of a wave is represented by y = 10 ^{-4} sin (100t –) m, then the velocity of wave will be**

(a) 100 m/s

(b) 4 m/s

(c) 1000 m/s

(d) 10 m/s.

**(2001)**

**39. Two waves having equation , x _{1} = asin (ωt-Kx+ Φ_{1})+ x_{2} = asin (ωt – kx +Φ_{2}) If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is**

**40. If the tension and diameter of a sonometer wire of fundamental frequency n is doubled and density is halved then its fundamental frequency will become**

**41. The equations of two waves acting in perpendicular directions are given as x = acos(ωt + δ) and y = acos(ωt + α), where δ = α+π/2, the resultant wave represents**

(a) a parabola

(b) a circle

(c) an ellipse

(d) a straight line **(2000)**

**42. A string is cut into three parts, having fundamental frequencies n _{1,} n_{2}, n_{3} respectively. Then original fundamental frequency n related by the expression as**

**43. Two stationary sources each emitting waves of wavelength λ, an observer moves from one source to another with velocity u. Then number of beats heard by him**

**44. Two waves of lengths 50 cm and 51 cm produced 12 beats per sec. The velocity of sound is**

(a) 340 m/s

(b) 331 m/s

(c) 306 m/s

(d) 360 m/s** (1999)**

**45. A transverse wave is represented by the equation y=y _{0} sin 2π/λ (vt-x)For what value of X, is the maximum particle velocity equal to two times the wave velocity?**

**46. A vehicle, with a horn of frequency n is moving with a velocity of 30 m/s in a direction perpendicular to the straight line joining the observer and the vehicle. The observer perceives the sound to have a frequency n + n _{1 }Then (if the sound velocity in air is 300 m/s)**

(a) n

_{1}= 0.ln

(b) n

_{1}= 0

(c) n

_{1}= 10n

(d) n

_{1}= -0.1 n

**(1998)**

**47. A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is**

(a) 6.05 Å

(b) 2.42 Å

(c) 1.21 Å

(d) 3.63 Å** (1998)**

**48. In a sinusoidal wave, the time required for a particular point to move from maximum displacement to zero displacement is 0.170 sec. The frequency of wave is**

(a) 0.73 Hz

(b) 0.36 Hz

(c) 1.47 HZ

(d) 2.94 Hz** (1998)**

**49. Standing waves are produced in 10m long stretched string. If the string vibrates in 5 segments and wave velocity is 20 m/s, the frequency is**

(a) 5 Hz

(b) 10 Hz

(c) 2 Hz

(d) 4 Hz. **(1997)**

**50. A cylindrical tube, open at both ends has fundamental frequency f in air. The tube is dipped vertically in water, so that half of it is in water. The fundamental frequency of air column is now**

(a) f//2

(b) 3f//4

(c) 2f

(d) f** (1997)**

**51. The equation of a sound wave is y =0.0015 sin (62.4x + 316t). The wavelength of this wave is**

(a) 0.3 unit

(b) 0.2 unit

(c) 0.1 unit

(d) cannot be calculated. **(1996)**

**52. Two sound waves having a phase difference of 60° have path difference of**

**53. 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 of 1:2:3?**

(a) 60 cm and 90 cm

(b) 30 cm and 60 cm

(c) 30 cm and 90 cm

(d) 40 cm and 80 cm. **(1995)**

**54. A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is 4.2 MHz. The speed of sound in a tissue is 1.7 km/s. The wavelength of sound in the tissue is close to**

(a) 4 x 10^{-3} m

(b) 8 x 10^{-3}m

(c) 4 x 10^{-4} m

(d)8 x 10^{-4}m. **(1995)**

**55. A source of sound gives 5 beats per second, j when sounded with another source of frequency 100 second ^{-1}. The second harmonic of the source, together with a source of frequency 205 sec^{-1} gives 5 beats per second. What is the frequency of the source?**

(a) 105 second

^{-1}

(b) 205 second

^{-1}

(c) 95 second

^{-1}

(d) 100 second

^{-1}.

**(1995)**

**56. A star, which is emitting radiation at a wavelength of5000 A, is approaching the earth with a velocity of 1.5 x 104 m/s. The change in wavelength of the radiation as received on the earth is**

**57. Which one of the following represents a wave?**

(a) y = A sin (ωt – kx)

(b) y = A cos (at – bx + c)

(c) y = A sin kx

(d) y = A sin ωr. **(1994)**

**58. A wave of frequency 100 Hz travels along a string j towards its fixed end. When this wave travels : back, after reflection, a node is formed at a j distance of 10 cm from the fixed end. The speed of the wave (incident and reflected) is**

(a) 20 m/s

(b) 40 m/s

(c) 5 m/s

(d) 10 m/s.** (1994)**

**59. A stationary wave is represented by y = A sin (100t) cos (0.01x), where y and A are in millimetres, t is in seconds and x is in metres. The velocity of the wave is**

(a) 10^{4} m/s

(b) not derivable

(c) 1 m/s

(d) 10^{2} m/s.** (1994)**

**60. A source of frequency υ gives 5 beats/second when sounded with a source of frequency 200 Hz. The second harmonic of frequency 2υ of source gives 10 beats/second when sounded with a source of frequency 420 Hz. The value of is**

(a) 205 Hz

(b) 195 Hz

(c) 200 Hz

(d) 210 Hz. **(1994)**

**61. Wave has simple harmonic motion whose period is 4 seconds while another wave which also possesses simple harmonic motion has its period 3 sec. If both are combined, then the resultant wave will have the period equal to**

(a) 4 sec

(b) 5 sec

(c) 12 sec

(d) 3 sec **(1993)**

**62. A stretched string resonates with tuning fork frequency 512 Hz when length of the string is 0.5 m. The length of the string required to vibrate resonantly with a tuning fork of frequency 256 Hz would be**

(a) 025 m

(b) 0.5 m

(c) lm

(d) 2m** (1993)**

**63. The temperature at which the speed of sound becomes double as was at 27°C is**

(a) 273°C

(b 0°C

(c) 927°C

(d) 1027°C **(1993)**

**64. For production of beats the two sources must have**

(a) different frequencies and same amplitude

(b) different frequencies

(c) different frequencies, same amplitude and same phase

(d) different frequencies and same phase** (1992)**

**65. The frequency of sinusodial wave y = 0.40cos [2000 t + 0.80] would be**

**66. With the propogation of a longitudinal wave through a material medium, the quantities transmitted in the propogation direction are**

(a) energy, momentum and mass

(b) energy .

(c) energy and mass

(d) energy and linear momentum **(1992)**

**67. Two trains move towards each other with the same speed. The speed of sound is 340 m/s. If the height of the tone of the whistle of one of them heard on the other changes to 9/8 times, then the speed of each train should be**

(a) 20 m/s

(b) 2 m/s

(c) 200 m/s

(d) 2000 m/s** (1991)**

**68. A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has**

(a) three nodes and three antinodes

(b) three nodes and four antinodes

(c) four nodes and three antinodes

(d) four nodes and four antinodes** (1991)**

**69. Velocity of sound waves in air is 330 m/s. For a particular sound wave in air, a path difference of 40 cm is equivalent to phase difference of 1.6 n. The frequency of this wave is**

(a) 165 Hz

(b) 150 Hz

(c) 660 Hz

(d) 330 Hz **(1990)**

**70. A 5.5 metre length of string has a mass of0.035 kg. If the tension in the string in 77 N, the speed of a wave on the string is**

(a) 110 ms^{-1}

(b) 165 ms^{-1}

(c) 77 ms^{-1}

(d) 102 ms^{-1}** (1989)**

**71. If the amplitude of sound is doubled and the frequency reduced to one fourth, the intensity of sound at the same point will be**

(a) increasing by a factor of 2

(b) decreasing by a factor of 2

(c) decreasing by a factor of 4

(d) unchanged** (1989)**

**72. The velocity of sound in any gas depends upon**

(a) wavelength of sound only

(b) density and elasticity of gas

(c) intensity of sound waves only

(d) amplitude and frequency of sound** (1988)**

**73. Equation of progressive wave is given by y = 4sin [( – )+π/6]
where y, x are in cm and t is in seconds. Then which of the following is correct ? **

(a) v = 5 cm

(b) λ = 18 cm

(c) a = 0.04 c = m

(d) f=50 Hz (1988)

### Explanations